California Mathematics Grade 7 Resource Masters - Chapter 1

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Chapter 1
Resource Masters
Consumable Workbooks Many of the worksheets contained in the Chapter Resource
Masters are available as consumable workbooks in both English and Spanish.
Study Guide and Intervention Workbook
Skills Practice Workbook
Practice Workbook
Word Problem Practice Workbook
MHID
0-07-878882-X
0-07-878884-6
0-07-878886-2
0-07-878888-9
ISBN
978-0-07-878882-6
978-0-07-878884-0
978-0-07-878886-4
978-0-07-878888-8
0-07-878883-8
0-07-878885-4
0-07-878887-0
0-07-878889-7
978-0-07-878883-3
978-0-07-878885-7
978-0-07-878887-1
978-0-07-878889-7
Spanish Versions
Study Guide and Intervention Workbook
Skills Practice Workbook
Practice Workbook
Word Problem Practice Workbook
Answers for Workbooks The answers for Chapter 1 of these workbooks can be
found in the back of this Chapter Resource Masters booklet.
StudentWorks PlusTM This CD-ROM includes the entire Student Edition test along
with the English workbooks listed above.
TeacherWorks PlusTM All of the materials found in this booklet are included for
viewing, printing, and editing in this CD-ROM.
Spanish Assessment Masters MHID: 0-07-878890-0 ISBN: 978-0-07-878890-1
These masters contain a Spanish version of Chapter 1 Test Form 2A and Form 2C.
Copyright © by the McGraw-Hill Companies, Inc. All rights reserved. Permission is
granted to reproduce the material contained herein on the condition that such
material be reproduced only for classroom use; be provided to students, teachers,
and families without charge; and be used solely in conjunction with Glencoe
California Mathematics, Grade 7. Any other reproduction, for use or sale, is
prohibited without prior written permission of the publisher.
Send all inquiries to:
Glencoe/McGraw-Hill
8787 Orion Place
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ISBN: 978-0-07-878308-1
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Printed in the United States of America
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CAGR7 CRM1
CONTENTS
Teacher’s Guide to Using the Chapter 1
Resource Masters .........................................iv
Chapter Resources
Chapter
Chapter
Chapter
Chapter
Chapter
Chapter
Chapter
1
1
1
1
1
1
1
Student-Made Glossary ...................1
Family Letter (English) .....................3
Family Activity (English) ...................4
Family Letter (Spanish) ....................5
Family Activity (Spanish)..................6
Anticipation Guide (English).............7
Anticipation Guide (Spanish) ...........8
Lesson 1-1
A Plan for Problem Solving
Lesson Reading Guide ......................................9
Study Guide and Intervention ..........................10
Skills Practice...................................................11
Practice ............................................................12
Word Problem Practice ....................................13
Enrichment .......................................................14
Lesson 1-2 Variables, Expressions,
and Properties
Lesson Reading Guide ....................................15
Study Guide and Intervention ..........................16
Skills Practice...................................................17
Practice ............................................................18
Word Problem Practice ....................................19
Enrichment .......................................................20
TI-73 Activity ....................................................21
Lesson 1-3
Integers and Absolute Value
Lesson Reading Guide ....................................22
Study Guide and Intervention ..........................23
Skills Practice...................................................24
Practice ............................................................25
Word Problem Practice ....................................26
Enrichment .......................................................27
TI-83/84 Plus Activity .......................................28
Study Guide and Intervention ..........................42
Skills Practice...................................................43
Practice ............................................................44
Word Problem Practice ....................................45
Enrichment .......................................................46
TI-83/84 Plus Activity .......................................47
Lesson 1-7 Writing Equations
Lesson Reading Guide ....................................48
Study Guide and Intervention ..........................49
Skills Practice...................................................50
Practice ............................................................51
Word Problem Practice ....................................52
Enrichment .......................................................53
Lesson 1-8 Problem-Solving
Investigation: Work Backward
Study Guide and Intervention ..........................54
Skills Practice...................................................55
Practice ............................................................56
Word Problem Practice ....................................57
Lesson 1-9 Solving Addition and
Subtraction Equations
Lesson Reading Guide ....................................58
Study Guide and Intervention ..........................59
Skills Practice...................................................60
Practice ............................................................61
Word Problem Practice ....................................62
Enrichment .......................................................63
Lesson 1-10 Solving Multiplication
and Division Equations
Lesson Reading Guide ....................................64
Study Guide and Intervention ..........................65
Skills Practice...................................................66
Practice ............................................................67
Word Problem Practice ....................................68
Enrichment .......................................................69
Lesson 1-4 Adding Integers
Assessment
Lesson Reading Guide ....................................29
Study Guide and Intervention ..........................30
Skills Practice...................................................31
Practice ............................................................32
Word Problem Practice ....................................33
Enrichment .......................................................34
Student Recording Sheet ................................71
Rubric for Scoring Pre-AP................................72
Chapter 1 Quizzes 1 and 2 .............................73
Chapter 1 Quizzes 3 and 4 .............................74
Chapter 1 Mid-Chapter Test............................75
Chapter 1 Vocabulary Test ..............................76
Chapter 1 Test, Form 1 ...................................77
Chapter 1 Test, Form 2A.................................79
Chapter 1 Test, Form 2B.................................81
Chapter 1 Test, Form 2C.................................83
Chapter 1 Test, Form 2D.................................85
Chapter 1 Test, Form 3 ...................................87
Chapter 1 Extended-Response Test ...............89
Chapter 1 Standardized Test Practice ............90
ANSWERS ...............................................A1-A41
Lesson 1-5 Subtracting Integers
Lesson Reading Guide ....................................35
Study Guide and Intervention ..........................36
Skills Practice...................................................37
Practice ............................................................38
Word Problem Practice ....................................39
Enrichment .......................................................40
Lesson 1-6 Multiplying and
Dividing Integers
Lesson Reading Guide ....................................41
iii
Teacher’s Guide to Using the
Chapter 1 Resource Masters
The Chapter 1 Resource Masters includes the core materials needed for Chapter 1. These
materials include worksheets, extensions, and assessment options. The answers for these
pages appear at the back of this booklet.
All of the materials found in this booklet are included for viewing and printing on the
TeacherWorks PlusTM CD-ROM.
Chapter Resources
Lesson Resources
Student-Built Glossary (pages 1-2) These
masters are a student study tool that
presents up to twenty of the key vocabulary
terms from the chapter. Students are to
record definitions and/or examples for each
term. You may suggest that students
highlight or star the terms with which they
are not familiar. Give this to students
before beginning Lesson 1-1. Encourage
them to add these pages to their
mathematics study notebooks. Remind them
to complete the appropriate words as they
study each lesson.
Lesson Reading Guide Get Ready for the
Lesson reiterates the questions from the
beginning of the Student Edition lesson.
Read the Lesson asks students to interpret
the context of and relationships among
terms in the lesson. Finally, Remember
What You Learned asks students to
summarize what they have learned using
various representation techniques. Use as a
study tool for note taking or as an informal
reading assignment. It is also a helpful tool
for ELL (English Language Learners).
Study Guide and Intervention This
master provides vocabulary, key concepts,
additional worked-out examples and Check
Your Progress exercises to use as a
reteaching activity. It can also be used in
conjunction with the Student Edition as an
instructional tool for students who have
been absent.
Family Letter and Family Activity
(pages 3-6) The letter informs your students’
families of the mathematics they will be
learning in this chapter. The family activity
helps them to practice problems that are
similar to those on the state test. A full
solution for each problem is included.
Spanish versions of these pages are also
included. Give these to students to take
home before beginning the chapter.
Skills Practice This master focuses more
on the computational nature of the lesson.
Use as an additional practice option or as
homework for second-day teaching of the
lesson.
Anticipation Guide (pages 7-8) This
master, presented in both English and
Spanish, is a survey used before beginning
the chapter to pinpoint what students may
or may not know about the concepts in the
chapter. Students will revisit this survey
after they complete the chapter to see if
their perceptions have changed.
Practice This master closely follows the
types of problems found in the Exercises
section of the Student Edition and includes
word problems. Use as an additional
practice option or as homework for secondday teaching of the lesson.
iv
Vocabulary Test This test is suitable for
all students. It includes a list of vocabulary
words and 10 questions to assess students’
knowledge of those words. This can also be
used in conjunction with one of the leveled
chapter tests.
Word Problem Practice This master
includes additional practice in solving word
problems that apply the concepts of the
lesson. Use as an additional practice or as
homework for second-day teaching of the
lesson.
Enrichment These activities may extend
the concepts of the lesson, offer an historical
or multicultural look at the concepts, or
widen students’ perspectives on the
mathematics they are learning. They are
written for use with all levels of students.
Leveled Chapter Tests
• Form 1 contains multiple-choice questions
and is intended for use with below grade
level students.
• Forms 2A and 2B contain multiple-choice
questions aimed at on grade level
students. These tests are similar in format
to offer comparable testing situations.
Graphing Calculator, Scientific
Calculator, or Spreadsheet Activities
These activities present ways in which
technology can be used with the concepts in
some lessons of this chapter. Use as an
alternative approach to some concepts or as
an integral part of your lesson presentation.
• Forms 2C and 2D contain free-response
questions aimed at on grade level
students. These tests are similar in format
to offer comparable testing situations.
• Form 3 is a free-response test for use with
above grade level students.
Assessment Options
All of the above mentioned tests include a
free-response Bonus question.
The assessment masters in the Chapter 1
Resources Masters offer a wide range of
assessment tools for formative (monitoring)
assessment and summative (final)
assessment.
Extended-Response Test Performance
assessment tasks are suitable for all
students. Sample answers and a scoring
rubric are included for evaluation.
Student Recording Sheet This master
corresponds with the standardized test
practice at the end of the chapter.
Standardized Test Practice These three
pages are cumulative in nature. It includes
three parts: multiple-choice questions with
bubble-in answer format, griddable
questions with answer grids, and shortanswer free-response questions.
Pre-AP Rubric This master provides
information for teachers and students on
how to assess performance on open-ended
questions.
Answers
• The answers for the Anticipation Guide
and Lesson Resources are provided as
reduced pages with answers appearing in
red.
Quizzes Four free-response quizzes offer
assessment at appropriate intervals in the
chapter.
• Full-size answer keys are provided for the
assessment masters.
Mid-Chapter Test This 1-page test
provides an option to assess the first half of
the chapter. It parallels the timing of the
Mid-Chapter Quiz in the Student Edition
and includes both multiple-choice and freeresponse questions.
v
NAME ________________________________________ DATE ______________ PERIOD _____
Student-Built Glossary
This is an alphabetical list of new vocabulary terms you will learn in
Chapter 1. As you study the chapter, complete each term’s definition
or description. Remember to add the page number where you found
the term. Add this page to your math study notebook to review
vocabulary at the end of the chapter.
Vocabulary Term
Found
on Page
Definition/Description/Example
absolute value
additive inverse
algebra [AL-juh-brah]
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
algebraic [AL-juh-BRAY-ihk]
expression
conjecture
coordinate
counterexample
equation [ih-KWAY-zhuhn]
evaluate
inequality
integer [IHN-tih-juhr]
Chapter 1
1
Glencoe California Mathematics, Grade 7
Chapter Resources
1
NAME ________________________________________ DATE ______________ PERIOD _____
1
Student-Built Glossary
Vocabulary Term
Found
on Page
(continued)
Definition/Description/Example
inverse operations
negative number
numerical expression
opposites
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
order of operations
positive number
powers
property
solution
solve
variable
Chapter 1
2
Glencoe California Mathematics, Grade 7
NAME ________________________________________ DATE ______________ PERIOD _____
Family Letter
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Dear Parent or Guardian:
relate concepts learned in
One of the goals of this class is to
example, integers are a
the classroom to the real world. For
used to describe things
part of our daily lives. They are often
e, and money. Knowing
such as sports scores, temperature, tim
make important decisions
how to work with integers helps us
at work and at home.
r child will learn about
In Chapter 1, Algebra: Integers, you
g, about variables,
developing a plan for problem solvin
phing data, and about
expressions, and properties, about gra
dividing integers. Your
adding, subtracting, multiplying, and
absolute value of
child will also learn how to find the
ns. In the study of this
integers, and write and solve equatio
iety of daily classroom
chapter, your child will complete a var
ly produce a chapter
assignments and activities and possib
project .
it with your child, you
By signing this letter and returning
ting involved. Enclosed is
agree to encourage your child by get
ld that practices how the
an activity you can do with your chi
1 might be tested. You
math we will be learning in Chapter
th.com for self-check
may also wish to log on to ca.gr7ma
have any questions or
quizzes and other study help. If you
school.
comments, feel free to contact me at
Sincerely,
Signature of Parent or Guardian ______________________________________ Date ________
Chapter 1
3
Glencoe California Mathematics, Grade 7
Chapter Resources
1
NAME ________________________________________ DATE ______________ PERIOD _____
1
Family Activity
Standards Practice
Fold the page along the dashed line. Work each problem on another piece of
paper. Then unfold the page to check your work.
2. Jarred has five fewer model cars than
Cammie. Half of the sum of their
combined model cars is equal to 10.
How many model cars does Cammie
have?
1. Evan stepped into an elevator in a very
tall building in downtown New York City.
The buttons he could choose from ranged
from Basement Level D (4) to 64.
64
Which equation can be used to find the
number of model cars Cammie has?
c5
A 10
0 street level
1
2
3
D 4
B
2
c c 5
2
10
C c c 5 10 2
D c 5 10
How many stories high is this building
(including its basements)?
A 60 stories high
B 68 stories high
C 67 stories high
D 61 stories high
Fold here
Solution
Solution
2. Hint: A letter (or variable) is used to
represent a number that we do not know,
in this case the number of cars Cammie
has. In order to solve the problem, you
also will need to write an expression for
the number of cars that Jared has based
on the number Cammie has.
1. There are 64 stories above ground and
4 stories below ground, which means
there are 64 4, or 68 stories.
The number of cars that Cammie has
can be represented by the letter c. We
know that Jared has 5 less cars than
Cammie, or c 5. If we add their cars
together (c c 5) and divide by 2, the
number should equal 10.
The answer is B.
Chapter 1
The answer is B.
4
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2
NOMBRE ______________________________________ FECHA ____________ PERÍODO
Carta a la familia
Chapter Resources
1
___
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Estimado padre o apoderado:
relacionar los conceptos
Uno de los objetivos de esta clase es
real. Por ejemplo, los
aprendidos en el salón con el mundo
Se usan para describir
enteros son parte de la vida cotidiana.
tro deportivo, la tempecosas como el marcador de un encuen
saber usar los enteros
ratura, la hora, el dinero, etcétera. Al
en el trabajo y en el
podemos tomar importantes decisiones
hogar.
su hijo(a) aprenderá a
En el Capítulo 1, Álgebra: Enteros,
blemas, aprenderá sobre
desarrollar un plan para resolver pro
así como a graficar datos y
variables, expresiones y propiedades,
nes y divisiones de enteros.
a realizar sumas, restas, multiplicacio
ar el valor absoluto de
Su hijo(a) aprenderá también a calcul
ones. En este capítulo, él o
enteros y escribirá y resolverá ecuaci
eas y actividades diarias y es
ella completará una variedad de tar
del capítulo.
posible que trabaje en un proyecto
su hijo(a), usted se comAl firmar esta carta y devolverla con
en su aprendizaje. Junto con
promete a ayudarlo(a) a participar
que puede realizar con
esta carta, va incluida una actividad
rían encontrar en las prueél(ella) y la cual practica lo que pod
aprenderán en el
bas de los conceptos matemáticos que
th.com para ver autoCapítulo 1. Además, visiten ca.gr7ma
o. Si tiene cualquier precontroles y otras ayudas para el estudi
teme en la escuela.
gunta o comentario, por favor contác
Cordialmente,
Firma del padre o apoderado
Capítulo 1
________________________________________ Fecha
5
______
Glencoe California Mathematics, Grade 7
NOMBRE ______________________________________ FECHA ____________ PERÍODO
1
___
Actividad en familia
Práctica de estándares
Doblen la página a lo largo de las líneas punteadas. Resuelvan cada problema
en otra hoja de papel. Luego, desdoblen la página y revisen las respuestas.
2. Jarred tiene cinco autos a escala más
que Cammie. La mitad de la suma de
los autos a escala que tienen entre los
dos es igual a 10. ¿Cuántos autos a
escala tiene Cammie?
1. Evan se subió al elevador de un edificio
muy alto en el centro de la ciudad de
Nueva York. Los botones que podía elegir
variaban de sótano nivel D (4) a 64.
64
¿Qué ecuación sirve para calcular el
número de autos a escala que tiene
Cammie?
0 nivel de la calle
c5
A 10
¿Cuántos pisos tiene este edificio,
incluyendo los sótanos?
A 60 pisos
B 68 pisos
C 67 pisos
D 61 pisos
B
2
c c 5
2
10
C c c 5 10 2
D c 5 10
Doblen aquí
Solución
Solución
1. Hay 64 pisos sobre el suelo y 4 niveles
en el sótano. Esto significa que hay
64 4 ó 68 pisos.
2. Ayuda: Para representar un número
cuyo valor se desconoce se usa una letra
(o variable). En este caso, el número de
autos de Cammie. Para resolver este
problema, también tienen que escribir
una expresión que represente el número
de autos de Jared, en base al número de
autos de Cammie.
Los autos de Cammie se pueden
representar con la letra c. Sabemos que
Jared tiene 5 autos menos que Cammie
o c 5. Si sumamos ambas cantidades
(c c 5) y dividimos entre 2, el
resultado deberá ser 10.
La respuesta es B.
La respuesta es B.
Capítulo 1
6
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2
NAME ________________________________________ DATE ______________ PERIOD _____
1
Anticipation Guide
Step 1
Before you begin Chapter 1
• Read each statement.
• Decide whether you Agree (A) or Disagree (D) with the statement.
• Write A or D in the first column OR if you are not sure whether you agree or disagree,
write NS (Not Sure).
STEP 1
A, D, or NS
STEP 2
A or D
Statement
1. A conjecture is a statement proven to be true.
2. Algebraic expressions are any mathematical expressions that
contain at least one operation symbol.
3. According to the Order of Operations, all operations within
grouping symbols must be completed first.
4. According to the Order of Operations, all addition and
subtraction should be done before multiplication and division.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. The Commutative Property is true only for addition and
multiplication.
6. Negative integers can be used to express values less than zero.
7. When comparing two negative integers, the greater integer is
the one with the greater absolute value.
8. The sum of a positive integer and a negative integer is always
negative.
9. When subtracting a negative integer, add its opposite.
10. The product of two negative integers is always positive.
11. The quotient of two negative integers is always negative.
12. Any letter can be used to represent an unknown in an
expression or equation.
Step 2
After you complete Chapter 1
• Reread each statement and complete the last column by entering an A or a D.
• Did any of your opinions about the statements change from the first column?
• For those statements that you mark with a D, use a piece of paper to write an
example of why you disagree.
Chapter 1
7
Glencoe California Mathematics, Grade 7
Chapter Resources
Algebra: Integers
NOMBRE ______________________________________ FECHA ____________ PERÍODO
1
___
Ejercicios preparatorios
Álgebra: Enteros
Paso 1
Antes de comenzar el Capítulo 1
• Lee cada enunciado.
• Decide si estás de acuerdo (A) o en desacuerdo (D) con el enunciado.
• Escribe A o D en la primera columna O si no estás seguro(a) de la respuesta,
escribe NS (No estoy seguro(a)).
PASO 1
A, D o NS
PASO 2
AoD
Enunciado
1. Una conjetura es un enunciado que se ha probado como
verdadero.
2. Las expresiones matemáticas son cualesquiera expresiones matemáticas que contengan por lo menos un símbolo de operación.
3. Según el orden de las operaciones, todas las operaciones dentro
de signos de agrupación deben completarse primero.
5. La propiedad conmutativa es verdadera solo para la adición y
la multiplicación.
6. Se pueden usar los números enteros negativos para expresar
valores menores que cero.
7. Cuando se comparan dos enteros negativos, el entero mayor es
aquél con el mayor valor absoluto.
8. La suma de un entero positivo y un entero negativo es siempre
negativa.
9. Cuando se sustrae un entero negativo, se suma su opuesto.
10. El producto de dos enteros negativos es siempre positivo.
11. El cociente de dos enteros negativos es siempre negativo.
12. Cualquier letra puede usarse para representar una incógnita
en una expresión o ecuación.
Paso 2
Después de completar el Capítulo 1
• Vuelve a leer cada enunciado y completa la última columna con una A o una D.
• ¿Cambió cualquiera de tus opiniones sobre los enunciados de la primera columna?
• En una hoja de papel aparte, escribe un ejemplo de por qué estás en desacuerdo con los
enunciados que marcaste con una D.
Capítulo 1
8
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. De acuerdo con el orden de las operaciones, toda adición y sustracción debe efectuarse antes que la multiplicación y división.
NAME ________________________________________ DATE ______________ PERIOD _____
1-1
Lesson Reading Guide
7MR1.1, 6AF2.3
A Plan for Problem Solving
Get Ready for the Lesson
Complete the Mini Lab at the top of page 24 in your textbook.
Write your answers below.
1. How many white tiles does it take to border each of these three gardens?
2. Predict how many white tiles it will take to border the next-largest
garden. Check your answer by modeling the garden.
Lesson 1–1
3. How many tiles will it take to border a garden that is 6 tiles long?
Explain your reasoning.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Read the Lesson
4. Read the Check section in Example 1 at the bottom of page 25. In the
equation 8 18 26, what does the 8 stand for? What does the 18 stand
for?
5. Look at the Explore section in Example 2 on page 26. What does the word
“difference” mean? Now read the Plan section. Explain how to find the
distance traveled in 1 minute when you know the distance per second.
6. Look at the graph in Example 2 on page 26. Explain how the animals in
the chart are listed. Why is the cheetah first?
Remember What You Learned
7. Early problem solvers care is a mnemonic aid to remember the first
letters of the steps in the problem-solving plan. Write a mnemonic aid of
your own using the first letters of the steps.
Chapter 1
9
Glencoe California Mathematics, Grade 7
NAME ________________________________________ DATE ______________ PERIOD _____
1-1
Study Guide and Intervention
7MR1.1, 6AF2.3
A Plan for Problem Solving
You can always use the four-step plan to solve a problem.
Explore
Determine what information is given in the problem and what you need to find.
Plan
Select a strategy including a possible estimate.
Solve
Solve the problem by carrying out your plan.
Check
Examine your answer to see if it seems reasonable.
Example 1
Plant A and Plant B are two new experimental apple trees being
grown in a laboratory. The table displays their heights, in
millimeters, when they are 5 to 10 days old.
Day
5
6
7
8
9
10
Plant A
36
39
42
45
48
51
Plant B
32
36
40
44
48
52
Explore
You know their heights for days 5 to 10. You need to determine
their heights in two more days.
Plan
Determine whether there is a pattern and extend that pattern to
day 12.
Solve
Comparing each plant’s heights on consecutive days, we see that
Plant A’s height increases by 3 millimeters each day, while
Plant B’s height increases by 4 millimeters each day. To estimate
Plant A’s height on day 12, assume that it will grow 3 millimeters
each day past day 10, so it will be 51 3 3 or 57 millimeters. To
estimate Plant B’s height on day 12, assume that it will grow
4 millimeters each day past day 10, so it will be 52 4 4 or
60 millimeters.
Check
Given what we know about each plant’s height and how plants
grow in general, both estimates seem reasonable.
Exercises
Use the four-step plan to solve each problem.
1. MOVIES A movie ticket costs $3.50. A large popcorn costs $3.75 and a
large soda costs $3.00. How much will it cost two friends to go to a movie
if they share a popcorn and each has a large soda?
2. FLOUR BEETLES The population of a flour beetle doubles in about a week.
How long would it take for the population to grow to eight times its
original size?
Chapter 1
10
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Estimate the height of each plant on day 12.
NAME ________________________________________ DATE ______________ PERIOD _____
1-1
Skills Practice
7MR1.1, 6AF2.3
A Plan for Problem Solving
Use the four-step plan to solve each problem.
1. GAS MILEAGE Each day Ernesto drives 52 miles. If he can drive 26 miles
on one gallon of gasoline, how many days can he drive on 14 gallons of
gasoline?
2. FIELD TRIP A school policy requires that there be at least one chaperone
for every 8 students on a field trip. How many chaperones are required
for a field trip with 67 students?
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. PRODUCE At the local grocery store, lemons are 52 cents each and limes
are 21 cents each. How many lemons and limes can you buy for exactly
$3.75?
5. PIZZA The Chess Club sold 2,116 pizzas during a fundraiser that lasted
for all of March, April, and May. How many pizzas did they sell per day?
6. GUPPIES In January, Tate’s fish tank had 12 guppies. In February, it had
18, and in March it had 24. How many guppies do you expect to be in
Tate’s fish tank in May?
Find a pattern in the list of numbers. Then find the next number in
the list.
7. 1860, 1890, 1920, 1950, 1980
8. 1024, 256, 64, 16, 4
Draw the next two figures in each of the patterns below.
9.
10.
Chapter 1
11
Glencoe California Mathematics, Grade 7
Lesson 1–1
3. EXERCISE Trevor jogs every 3 days and swims every 4 days. How often
does he jog and swim on the same day?
NAME ________________________________________ DATE ______________ PERIOD _____
1-1
Practice
7MR1.1, 6AF2.3
A Plan for Problem Solving
Use the four-step plan to solve each problem.
1. FOOD The table shows a portion of the price list for
a local pizzeria. Tony has $17 that he can spend to
buy one large pizza. If the pattern in the prices
continues, what is the greatest number of toppings
that Tony can order on his pizza? What is the cost
of that pizza?
Toppings
Price
1
$12.99
2
$13.79
3
$14.59
4
$15.39
2. MOVIES Mr. Sedgwick paid $13 for one adult ticket and one child ticket
for a movie. Mrs. Wong paid $18 for one adult ticket two child tickets to
see the same movie, and Mr. Gomez paid $23 for one adult ticket and
three child tickets. If the pattern continues, how much should Mrs.
Beauregard expect to pay for one adult ticket and four child tickets?
4. GEOGRAPHY The land area of Washington, D.C., is 61 square miles. In
2003, the population of Washington, D.C., was 563,384. If one square mile
is equal to 640 acres, about how many people per acre were there in
Washington, D.C., in 2003?
5. ART SUPPLIES At the craft store, a paint brush costs $0.79, and a small
bottle of paint costs $0.89. What combination of paint brushes and bottles
of paint could you buy for exactly $4.15?
6. GEOMETRY Draw the next two figures in the pattern.
Chapter 1
12
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3. SPORTS The track coach must buy at least two bottles of water for each
participant in a track meet. One team has 35 members, and the other
team has 28 members. If each case of water contains 24 bottles, what is
the fewest number of full cases that the coach can buy?
NAME ________________________________________ DATE ______________ PERIOD _____
1-1
Word Problem Practice
7MR1.1, 6AF2.3
A Plan for Problem Solving
Use the four-step plan to solve each problem.
SKATEBOARDING For Exercises 1 and 2, use the table
at the right. It shows the results of a recent survey
in which teenagers were asked who the best
professional skateboarder is.
Skater
Votes
Bob Burnquist
18
Danny Way
15
Bam Margera
11
Arto Saari
9
2. How many more teenagers preferred
Burnquist to Saari?
3. HISTORY The area of Manhattan
Island is 641,000,000 square feet.
According to legend, the Native
Americans sold it to the Dutch for $24.
Estimate the area that was purchased
for one cent.
4. TRAVEL Britney’s flight to Rome
leaves New York City at 5:15 P.M. on
Wednesday. The flight time is
7.5 hours. If Rome is 6 hours ahead of
New York City, use Rome time to
determine when she is scheduled to
arrive.
5. OFFICE SUPPLIES At an office supply
store, pens are $1.69 per dozen and
note pads are $4.59 per dozen. Can
Shirley buy 108 pens and 108 note
pads for $50? Explain your reasoning.
6. SHOPPING Yoshi bought two pairs of
shoes. The regular price of each pair
was $108. With the purchase of one
pair of shoes at regular price, the
second pair was half price. How much
did Yoshi pay altogether for the two
pairs of shoes?
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Lesson 1–1
1. Estimate the total number of teenagers
who voted.
Chapter 1
13
Glencoe California Mathematics, Grade 7
NAME ________________________________________ DATE ______________ PERIOD _____
1-1
Enrichment
7MR2.3
Logical Reasoning
When planning how to solve problems, it is helpful to be familiar with a
number of problem-solving strategies. When a problem presents a large
amount of information, one strategy that can be effective is logical reasoning
combined with the use of a table to organize the information.
Holly, Keisha, Sandra, and Jamal are Bexley
Middle School’s student council officers. The
offices they hold are president, vice-president,
secretary, and treasurer. Sandra is the
president, Holly is not the treasurer, and Keisha
is the vice-president. What office does Jamal
hold?
Holly
President
Vice President
Secretary
Treasurer
Keisha Sandra Jamal
N
N
N
Y
N
N
Y
N
N
N
N
N
Using the table, mark Y for relationships that are true, and N for relationships that are not
true. For example, since you know that Sandra is the president, put a Y in that cell and put
an N in each of the other cells of that column and in the president row. Fill in the
remaining cells to show that Jamal must be the treasurer.
Five male athletes won events in the district track and field meet. Each boy won exactly
one event. From the clues below, find each boy’s name, school name, and the event he won.
•
•
•
•
•
•
•
•
Two boys competed in the field events and three boys competed in the three track
events.
No boy participated in both track events and field events.
The athlete from North Middle School, who is not Mitch, placed last in the 100-meter.
The 100-meter winner lost to the South Middle School student in another event.
The boy from Wilson Academy, who placed second in the discus throw, was not in any
event with Mitch or Rob.
The South Middle School boy and Kyle, who is not from Wilson, were not in any of the
same events.
The student from Taft Junior High did not participate in any field events.
In one event Nick beat the student from North Middle School and the 400-meter
winner.
Vine
Field
Track
Chapter 1
North
South
Taft
Shot Put
Discus
400-m
100-m
Hurdles
Mitch
Kyle
Rob
Nick
Cory
Shot Put
Discus
400-m
100-m
Hurdles
14
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Use the process of logical reasoning and the table below to answer the following
question.
NAME ________________________________________ DATE ______________ PERIOD _____
1-2
Lesson Reading Guide
7AF1.2, 7AF1.3, 7AF1.4
Variables, Expressions, and Properties
Get Ready for the Lesson
Complete the Mini Lab at the top of page 29 in your textbook.
Write your answers below.
1. Complete the table below.
Figure Number
1
2
Perimeter
4
8
3
4
5
6
What is the relationship between the figure number and the perimeter
of the figure?
2. What would be the perimeter of Figure 10?
Read the Lesson
____ Addition
____ Multiplication
____ Subtraction
____ Division
For Exercises 4–8, describe how each pair of numerical expressions is
different. Then determine whether the two expressions are equal to
each other. If the expressions are equal, name the property that says
they are equal.
4. 2 5, 5 2
5. (6 4) 1, 6 (4 1)
6. 2(5 3), 2 5 2 3
7. 5 (4 7), (5 4) 7
8. 10 2, 2 10
Remember What You Learned
9. The word counter has several meanings in the English language. Use a
dictionary to find the meaning of counter when it is used as a prefix in
the word counterexample. Then write your own definition of
counterexample.
Chapter 1
15
Glencoe California Mathematics, Grade 7
Lesson 1–2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3. Number the operations in the correct order for simplifying
2 4(9 6 3). Then simplify the expression.
NAME ________________________________________ DATE ______________ PERIOD _____
1-2
Study Guide and Intervention
7AF1.2, 7AF1.3, 7AF1.4
Variables, Expressions, and Properties
When finding the value of an expression with more than one operation, perform the operations in the
order specified by the order of operations.
Order of Operations
1. Perform all operations within grouping symbols first; start with the innermost grouping symbols.
2. Evaluate all powers before other operations.
3. Multiply and divide in order from left to right.
4. Add and subtract in order from left to right.
Evaluate the expression (5 7) 2 3 (8 1).
(5 7) 2 3 (8 1) 12 2 3 (8 1)
12 2 3 9
639
18 9
9
Example 2
Add inside the left parentheses.
Add inside the remaining parentheses.
Divide.
Multiply.
Subtract.
Evaluate the expression 3x2 4y if x 3 and y 2.
3x2 4y 3(3)2 4(2)
3(9) 4(2)
27 8
19
Replace x with 3 and y with 2.
Evaluate the power first.
Do all multiplications.
Subtract.
Exercises
Evaluate each expression.
1. 4 5 8
2. 16 12 4
3. 14 2 3(5)
4. 5 6 2 3
5. 2 32 10 14
6. 22 32 8 5
7. (10 5) 3
8. 52 (8 6)
9. (17 5)(6 5)
10. 3 7(14 8 2)
14
3 2
11. 5[24 (6 8)]
12. 2 Evaluate each expression if a 3, b 5, and c 6.
13. a 3b
14. 4b 3c
15. 2a b 5c
16. (ab)2
17. a(b c)
18. 3(bc 8) a
Chapter 1
16
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Example 1
NAME ________________________________________ DATE ______________ PERIOD _____
1-2
Skills Practice
7AF1.2, 7AF1.3, 7AF1.4
Variables, Expressions, and Properties
Evaluate each expression.
1. 10 2 8
2. 4(9) 36 3
3. 24 12 4
4. 25 2 8 4
5. 49 (32 8 3)
6. 2(20 5) 7. (27 24)(27 24)
8. 23 4 3 6
9. (4 4) 4 4 4
28 7
11. 42 13
34 14
4
10. 3[(8 2) 5] 7
12. (15 9)2 (5 4)
13. 3n p
14. t 2p
15. 3p n 4
16. (np)2
17. np2
18. 5(2t n)
19. p(n t)
20. 6t2 t
npt
21. 22. 4(pt 3) n
p2 4
23. pn
24. 25. n2 3n 8
26. 2t2 t 9
3
3t 5
2
t 10
Name the property shown by each statement.
27. (4 5)3 4(3) 5(3)
28. 1 x2 x2
29. 2(bc) (2b)c
30. (6 2) 5 6 (2 5)
31. 2(bc) 2(cb)
32. (4 5) 0 4 5
33. 13 (5 10) (5 10) 13
34. 3(7 2) 3(7) 3(2)
Chapter 1
17
Glencoe California Mathematics, Grade 7
Lesson 1–2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Evaluate each expression if n 4, p 3, and t 6.
NAME ________________________________________ DATE ______________ PERIOD _____
1-2
Practice
7AF1.2, 7AF1.3, 7AF1.4
Variables, Expressions, and Properties
Evaluate each expression if r = 3, s = 5, and t = 2.
1. 3r s
2. 4s 5t
3. 8 6t r
4. rs2
5. (st)2
r2 1
6. t 3
7. s(7 t) r
8. 2s2 8s 3
Name the property shown by each statement.
9. 6(5 1) 6(5) 6(1)
11. (10 7) 4 10 (7 4)
10. 1(2 3) 2 3
12. 5 (1 9) 5 (9 1)
State whether each conjecture is true or false. If false, provide a
counter example.
13. The sum of an even number and an odd number is always even.
Rewrite each expression using the indicated property.
15. (x 7) 3, Associative Property
16. 5(3) 5(4), Distributive Property
17. INTERNET A bookstore offers wireless Internet access to its customers for a charge. The
m
cost of using this service is given by the expression $1.50 , where m is the number
20
of minutes online. How much would it cost to be online 40 minutes?
18. TEMPERATURE When a temperature in degrees Celsius C is known, the expression
9C 160
can be used to find the temperature in degrees Fahrenheit. If a thermometer
5
shows that a temperature is 20C, what is the temperature in degrees Fahrenheit?
Chapter 1
18
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
14. Multiplication of whole numbers is associative.
NAME ________________________________________ DATE ______________ PERIOD _____
1-2
Word Problem Practice
7AF1.2, 7AF1.3, 7AF1.4
Variables, Expressions, and Properties
FOOTBALL For Exercises 1 and 2, use the table that shows statistics
from the 2006 Super Bowl.
Touchdowns Extra Points Field Goals
Pittsburgh
3
3
0
Seattle
1
1
1
1. Each team’s final score for a football
game can be found using the expression
6t e 3f, where t is the number of
touchdowns, e is the number of extra
points, and f is the number of field
goals. Find Pittsburgh’s final score in
the 2006 Super Bowl.
2. Use the expression 6t e 3f to find
Seattle’s final score in the 2006 Super
Bowl.
3. GEOMETRY The expression 6s2 can be
used to find the surface area of a cube,
where s is the length of an edge of the
cube. Find the surface area of a cube
with an edge of length 10 centimeters.
4. VERTICAL MOTION The height of an
object dropped from the top of a 300foot tall building can be described by
the expression 300 16t2, where t is
the time, in seconds, after the ball is
dropped. Find the height of the object
3 seconds after it is dropped.
10 cm
5. MOVIE RENTALS Mario intends to rent
10 movies for his birthday party. He
can rent new releases for $4 each,
while older ones are $2 each. If he
rents n new releases, the total cost, in
dollars, of the 10 movies is represented
by the expression 4n 2(10 n).
Evaluate the expression to find the
total cost if he rents 7 new releases.
6. CIRCULAR MOTION Pelipa is able to spin
her yo-yo along a circular path. The
yo-yo is kept in this path by a force
which can be described by the
mv2
r
expression . Evaluate the
expression to find the force when
m 12, v 4, and r 8.
r
Chapter 1
19
Glencoe California Mathematics, Grade 7
Lesson 1–2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Team
NAME ________________________________________ DATE ______________ PERIOD _____
1-2
Enrichment
7AF1.3
Division by Zero?
Some interesting things happen when you try to divide by zero. For example,
look at these two equations.
5
x
0
0
y
0
Because multiplication “undoes” division, you can write two equivalent
equations for the ones above.
0x5
0y0
There is no number that will make the left equation true. This equation has
no solution. For the right equation, every number will make it true. The
solution set for this equation is “all numbers.”
Because division by zero leads to impossible situations, it is not a “legal” step
in solving a problem. People say that division by zero is undefined, or not
possible, or simply not allowed.
Explain what is wrong with each of these “proofs.”
0 1 0 and 0 2 0
Step 2
Therefore, 0 1 and 0 2.
Step 3
Therefore, 1 2.
0
0
But, 1 2 is a contradiction.
2. Step 1
Assume a b.
Step 2
0 a 0 and 0 b 0
Step 3
Therefore, 0 a and 0 b.
Step 4
Therefore, a b.
0
0
But, a b contradicts a b.
Describe the solution set for each equation.
3. 4x 0
4. x 0 0
5. x 0 x
6. 0 0
7. 0 x
8. 0 0
x
Chapter 1
x
x
20
y
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1. Step 1
NAME ________________________________________ DATE ______________ PERIOD _____
1-2
TI-73 Activity
Evaluating Expressions
Graphing calculators follow the order of operations. So there is no need to
perform each operation separately. To evaluate an expression, enter it just as it is
written. If an expression contains parentheses, enter them in the calculator just
as they are written.
Example
Evaluate 3(x 6) 2 (x2 15) for x 8 and for x 12.
You could enter the expression, replacing the x with 8 and then enter it again, replacing x
with 12. But it is easier to enter the expression just once and store the values for x.
Step 1
Evaluate the expression for x 8.
8 STO
3
ENTER
6
(
2
(
15
Step 2
)
)
ENTER
Evaluate the same expression for x 12.
You do not need to reenter the expression.
2nd
[ENTRY] to redisplay the previous
entries you made.
Press
2nd
[ENTRY] to redisplay the line
that stores the value for x.
Use the cursor keys to move to the 8. Insert 12 in place of the 8.
DEL
2nd
Press
2nd
Press
ENTER
[INS] 12
[ENTRY]
ENTER
2nd
[ENTRY] to redisplay the expression.
to reevaluate the expression.
Exercises
Use a graphing calculator to evaluate each expression for x 3, x 6, and x 15.
1. x2 9
2. 2x2 10
16x2
3. 4. x(20 x)
3
5. How would you evaluate xy2 for x 4 and y 7 on a TI-73 graphing calculator?
(Hint: Enter Y by pressing
2nd
[TEXT] and using the cursor keys to select Y and
then Done.)
Chapter 1
21
Glencoe California Mathematics, Grade 7
Lesson 1–2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Use
NAME ________________________________________ DATE ______________ PERIOD _____
1-3
Lesson Reading Guide
7NS2.5
Integers and Absolute Value
Get Ready for the Lesson
Read the introduction at the top of page 35 in your textbook.
Write your answers below.
1. What does an elevation of 86 meters represent?
2. What does a temperature of 35º represent?
Read the Lesson
The symbol ... is called an ellipsis.
3. Look on page 35 in your textbook to find the meaning of the ellipsis as it
is used in the list 1, 4, 7, 10,... .
4. Use a dictionary to find the meaning of the ellipsis as it is used in the
sentence The marathon began...downtown.
6. Look at the number line on page 35 of your textbook. How are the ellipses
(plural of ellipsis) in the set of integers {...,4, 3, 2, 1, 0, 1, 2, 3, 4,...}
represented on the number line?
Complete each sentence with either left or right to make a true
sentence. Then write a statement comparing the two numbers with
either or .
7. 45 lies to the ________ of 0 on a number line.
8. 72 lies to the ________ of 0 on a number line.
9. 3 lies to the ________ of 95 on a number line.
10. 6 lies to the ________ of 7 on a number line.
11. Describe the symbol for the absolute value of 3. Then write the symbol.
Remember What You Learned
12. Write a mathematical expression that represents the following sentence.
(Hint: Let f represent the 49ers’ score and s represent the Seahawks’
score.)
The Seahawks and the 49ers scored within 3 points of each other.
Chapter 1
22
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. How can you explain the usage of the ellipsis in the list in Exercise 3 in
terms of the meaning for the ellipsis in the sentence in Exercise 4?
NAME ________________________________________ DATE ______________ PERIOD _____
1-3
Study Guide and Intervention
7NS2.5
Integers and Absolute Value
A number line can help you order a set of integers. When graphed on a number line, the smaller of two
integers is always to the left of the greater integer.
Example 1
Order the set of integers {10, 3, 9, 4, 0} from least to greatest.
Graph each integer on a number line.
10 8 6 4 2
0
2
4
6
8 10
The numbers from left to right are {9, 3, 0, 4, 10}.
The absolute value of a number is the distance of that number from 0 on a number line.
Example 2
Evaluate the expression |20| |10|.
|20| |10| 20 |10|
20 10
30
The absolute value of 220 is 20.
The absolute value of 10 is 10.
Simplify.
Order each set of integers in each set from least to greatest.
1. {3, 0,5, 1, 4}
2. {6,8, 3,1,4}
3. {2, 13,11,21, 5}
4. {31, 0,34,9, 7}
Evaluate each expression.
7. |3| |5|
5. |13|
6. |21|
8. |9| |8|
9. |13| |15|
11. |11| |5|
12. |4| |4|
10. |21 18|
13. |23 15|
Evaluate each expression if a 6, b 4, and c 5.
14. |a| 14
15. |c b|
16. b |c|
17. |3b|
18. 2|a| c
19. |2b c|
Chapter 1
23
Glencoe California Mathematics, Grade 7
Lesson 1–3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Exercises
NAME ________________________________________ DATE ______________ PERIOD _____
1-3
Skills Practice
7NS2.5
Integers and Absolute Value
Write an integer for each situation.
1. 3 strokes below par
2. 10 strokes above par
3. a 6-yard loss
4. an 8-yard gain
5. 12 centimeters longer
6. 7 inches below normal
7. $5 off the original price
8. a gain of 6 hours
9. 2° above zero
10. a loss of 15 pounds
11. a $35 withdrawal
12. a $75 deposit
13. 1 mile above sea level
14. 20 fathoms below the surface
15. 12 4
16. 4 5
17. 10 8
18. 3 13
19. |6| |6|
20. |4| |5|
Order each set of integers in each set from least to greatest.
21. {0, 6, 7, 2, 4}
22. {1, 2, 3, 3, 2, 1}
Evaluate each expression.
23. |8|
24. |31|
25. |1|
26. |256|
27. |3| |19|
28. |12| |13|
29. |28| |26|
30. |28| |26|
31. |24| |15|
Evaluate each expression if a 3, b 8, and c 5.
32. |a| 5
33. |b| 2
34. 2|c| b
35. a |a|
36. |3b|
37. |a 16|
Chapter 1
24
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Replace each with , , or to make a true sentence.
NAME ________________________________________ DATE ______________ PERIOD _____
1-3
Practice
7NS2.5
Integers and Absolute Value
Replace each with , , or to make a true sentence.
1. 0 8
2. 5 3
3. 1 7
4. 4 4
5. 12 10
6. 5 6
7. 6 7
8. 0 8
9. 10 10
Order each set of integers from least to greatest.
10. {5, 7, 0, 5, 7}
11. {1, 2, 3, 4}
12. {2, 4, 6, 8, 10, 12}
13. {0, 9, 3, 7, 1, 1}
Evaluate each expression.
14. |19|
15. |15|
16. |0|
17. |1||3|
18. |19||8|
19. |12||4|
20. |m| 6
21. n |p|
22. k |p|
23. 5|n| k
24. |n| 4
25. 9|m| 14
TEMPERATURE For Exercises 26 and 28, use the following information.
During a five-day cold spell, Jose recorded the temperature each day at noon.
The temperature was 3F on Monday, 5F on Tuesday, 4F on Wednesday,
1F on Thursday, and 0F on Friday.
26. On which day was it the coldest at noon?
27. On which day was it the warmest at noon?
28. The temperature at noon on Saturday was 25 warmer than the temperature on
Tuesday. What was the temperature on Saturday? Justify your answer using a number
line.
Chapter 1
25
Glencoe California Mathematics, Grade 7
Lesson 1–3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Evaluate each expression if k 4, m 2, n 7, and p 5.
NAME ________________________________________ DATE ______________ PERIOD _____
1-3
Word Problem Practice
7NS2.5
Integers and Absolute Value
GOLF For Exercises 1 and 2, use the table that lists ten players and
their scores in Round 3 of the 2005 60th U.S. Women’s Open.
Gulbis, Natalie
Score
0
Player
Kim, Birdie
Score
2
Icher, Karine
1
Kung, Candie
Jo, Young
1
Lang, Brittany
1
Kane, Lorie
5
Pressel, Morgan
1
Kerr, Cristie
1
Ochoa, Lorena
6
0
1. Order the scores in the table from least
to greatest.
2. Who had the lowest score?
3. LONGITUDE London, England, is located
at 0° longitude. Write integers for the
locations of New York City whose
longitude is 74° west and Tokyo whose
longitude is 140° east. Assume that
east is the positive direction.
4. STOCK MARKET Your stock loses 53
points on Monday and 23 points on
Tuesday, but gains 67 points on
Wednesday. Write an integer for each
day's change.
5. SOLAR SYSTEM The average
temperature of Saturn is 218°F, while
the average temperature of Jupiter is
162°F. Which planet has the lower
average temperature?
6. OCEAN TRENCHES The elevation of the
Puerto Rican Trench in the Atlantic
Ocean is 8,605 meters, the elevation
of the Mariana Trench in the Pacific
Ocean is 10,924 meters, and the
elevation of the Java Trench in the
Indian Ocean is 7,125 meters. Which
trench has the the lowest elevation?
Chapter 1
26
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Player
NAME ________________________________________ DATE ______________ PERIOD _____
1-3
Enrichment
7AF1.3
When You Want to Be Negative
Many symbols and signs use a slash mark such as /, \, or | to mean is not or
no. For example, the symbol means is not equal to.
Which of the symbols, , , and will make the statement true?
Some problems have more than one correct answer.
1. 2 ____ 0
2. |4| ____ |4|
3. For any number x, |x| ____ x.
4. For any nonzero integer n, n ____ n.
5. A number x is either greater than 0 or less than 0. So, x ____ 0.
6. ____ means the same as .
7.
8.
9.
10.
11.
12.
Lesson 1–3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
What does each of these signs mean?
13. Create three different “no” signs of your own.
Chapter 1
27
Glencoe California Mathematics, Grade 7
NAME ________________________________________ DATE ______________ PERIOD _____
1-3
TI-83/84 Plus Activity
Absolute Value
A graphing calculator can be used to evaluate problems containing
absolute value. The absolute value function on the TI-83/84 Plus is
found in the MATH (NUM) menu.
Example 1
Simplify |17|.
Enter:
MATH
1
(–)
)
ENTER
3 + 8
)
17
17
So, |17| 17.
Example 2
Simplify |3 8|.
Enter:
MATH
1
(–)
ENTER
5
So, |3 8| 5.
Example 3
Simplify |5| |14|.
Enter:
MATH
1
(–)
5
)
—
MATH
1 14
)
ENTER
9
Exercises
Simplify.
1. ⏐4⏐
2. ⏐8⏐
3. ⏐12⏐
4. ⏐10⏐
5. ⏐7⏐
6. ⏐25⏐
7. ⏐6 4⏐
8. ⏐15 8⏐
9. ⏐3 14⏐
10. ⏐1 4⏐
11. ⏐7 9⏐
12. ⏐2 (5)⏐
13. ⏐7⏐ ⏐15⏐
14. ⏐14⏐ ⏐5⏐
15. ⏐8⏐ ⏐12⏐
16. ⏐3⏐ ⏐9⏐
17. ⏐11⏐ ⏐8⏐
18. ⏐6⏐ ⏐7⏐
Chapter 1
28
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
So, |5| |14| 9.
NAME ________________________________________ DATE ______________ PERIOD _____
1-4
Lesson Reading Guide
7NS1.2, 7AF1.3
Adding Integers
Get Ready for the Lesson
Read the introduction at the top of page 41 in your textbook.
Write your answers below.
1. Write an integer that describes the game show host’s statement.
2. Write an addition sentence that describes this situation.
Read the Lesson
3. Look at your answer for Exercise 2. Identify each number in the addition
sentence as either an addend or a sum.
4. 4, 8
5. 3, 5
6. 9, 12
7. 23, 16
Determine whether you add or subtract the absolute values of the
numbers to find the sum. Give a reason for your answer.
8. 4 8
9. 3 5
10. 9 (12)
11. 23 (16)
Determine whether the sum is positive or negative. Then find the sum.
12. 4 8
13. 3 5
14. 9 (12)
15. 23 (16)
Add.
16. 3 (4)
17. 3 4
18. 6 (4)
19. 7 8
20. 25 (17)
21. 34 (17)
22. 43 4
23. 11 (30)
24. 81 (63)
25. 39 124
26. 97 (165)
27. 49 (75)
Remember What You Learned
28. You have seen what a negative number means in terms of weather or
money. Describe what a negative number means on a video cassette
recorder.
Chapter 1
29
Glencoe California Mathematics, Grade 7
Lesson 1–4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Identify the number with the greater absolute value.
NAME ________________________________________ DATE ______________ PERIOD _____
1-4
Study Guide and Intervention
7NS1.2, 7AF1.3
Adding Integers
To add integers with the same sign, add their absolute values. The sum has the same sign as the
integers.
Example 1
Find 3 (4).
3 (4) 7
Add |3| |4|. Both numbers are negative, so the sum is negative.
To add integers with different signs, subtract their absolute values. The sum has the same sign as the
integer with the greater absolute value.
Example 2
Find 16 12.
16 12 4
Subtract |12| from |16|. The sum is negative because |16| |12|.
Exercises
1. 9 16
2. 10 (10)
3. 18 (26)
4. 23 (15)
5. 45 35
6. 39 (38)
7. 55 81
8. 61 (39)
9. 74 36
10. 5 (4) 8
11. 3 10 (6)
13. 3 (10) (16) 11
12. 13 (8) (12)
14. 17 31 (14) 26
Evaluate each expression if x 4 and y 3.
15. 11 y
16. x (6)
17. y 2
18. |x y|
19. |x| y
20. x |y|
Chapter 1
30
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Add.
NAME ________________________________________ DATE ______________ PERIOD _____
1-4
Skills Practice
7NS1.2, 7AF1.3
Adding Integers
Add.
1. 2 (3)
2. 4 7
3. 8 9
4. 12 (3)
5. 27 18
6. 11 (13)
7. 44 26
8. 44 (26)
9. 15 (51)
11. 53 (28)
12. 86 77
13. 10 (4) 6
14. 16 (5) 12
15. 2 17 (12)
16. 35 (31) (39)
17. 8 (12) 15 (13)
18. 23 (18) 41 (17)
Evaluate each expression if a 9, b 12, and c 8.
19. 3 a
20. b 8
21. 6 c
22. |a| b
23. |a| |c|
24. |b c|
Chapter 1
31
Glencoe California Mathematics, Grade 7
Lesson 1–4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10. (17) (13)
NAME ________________________________________ DATE ______________ PERIOD _____
1-4
Practice
7NS1.2, 7AF1.3
Adding Integers
Find each sum.
1. 1 (8)
2. 13 15
3. 19 (7)
4. 14 (14)
5. 12 10
6. 5 (26)
7. 46 27
8. 33 55
9. 29 (25)
10. 6 14 (12)
11. 15 (17) 10
12. 13 (13) (18)
13. 5 8 (1) (6)
14. 8 (7) (8) (9) 15. 15 10 (16) 12
POPULATION For Exercises 16 and 17, use the table below that shows the
change in population for four cities between 2000 and 2005.
2000 Population
(thousands)
589
Change as of 2005
(thousands)
Las Vegas, Nevada
478
67
Pittsburgh, Pennsylvania
335
18
Rochester, New York
220
8
Boston, Massachusetts
30
Source: U.S. Census Bureau
16. What is the population of each of these cities as of 2005?
17. What was the total population change for these four cities?
Write an addition expression to describe each situation. Then find
each sum and explain its meaning.
18. GAMES On one turn, you move 10 spaces forward around the game board.
On the next turn, you move 4 spaces backward.
19. CAMPING While hiking down into a canyon, Manuel passed a sign stating
that the elevation was 100 feet below sea level. He descended another 56
feet before reaching his campsite.
20. WEATHER Before you went to sleep last night, the temperature was 3F.
During the night the temperature dropped by 5.
21. ELEVATOR Mrs. Brown parked in the parking garage 30 feet below street level.
She then got in an elevator and went up 80 feet to her office.
Chapter 1
32
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
City
NAME ________________________________________ DATE ______________ PERIOD _____
1-4
Word Problem Practice
7NS1.2, 7AF1.3
1. FOOTBALL A football team loses 5 yards
on one play and then loses 8 yards on
the next play. Write an addition
expression that represents the change
in position of the team for the two
plays. Then find the sum.
2. ELEVATOR You park in a garage 3 floors
below ground level. Then you get in the
elevator and go up 12 floors. Write an
addition expression to represent this
situation. Then find the sum.
3. GOLF In 2005, Tiger Woods won the
Masters Tournament. His scores were
2, 6, 7, and 1 for four rounds.
Write an addition expression that
represents his final score. Then find the
sum.
4. INVENTORY A local bookstore has
30 copies of a bestseller when it opens
Monday morning. On Monday, it sells
6 copies of the book. On Tuesday, it
sells 3 copies. On Wednesday, it receives
a shipment containing 24 copies of the
book and also sells 8 copies. Write an
addition expression that represents the
number of copies of the book that store
has at the end of the day on
Wednesday. Then find the sum.
5. OCEANOGRAPHY A research team
aboard an underwater research vessel
descends 1,500 feet beneath the surface
of the water. They then rise 525 feet
and descend again 350 feet. Write an
addition expression to represent this
situation. Then find the sum.
6. SPORTS Peter weighs 156 pounds, but
he would like to wrestle in a lower
weight class. He loses 4 pounds one
week, gains back 2 pounds the next
week, loses 5 pounds the third week,
and loses 3 pounds the fourth week.
Write an addition expression to
represent this situation. Then find the
sum.
Lesson 1–4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Adding Integers
Chapter 1
33
Glencoe California Mathematics, Grade 7
NAME ________________________________________ DATE ______________ PERIOD _____
1-4
Enrichment
7NS1.2
Adding Integers
Listed below are the scores for a game of cards in which the highest score
wins. The three players recorded their scores for each hand, but did not total
the scores until they were done playing.
Hand
Micah Juanita Taylor
1
125
30
68
2
72
54
0
3
15
105
95
4
0
5
20
5
146
37
110
6
82
15
62
7
25
130
47
8
40
0
12
1. Who had the highest total score after round 3? How many points did this
player have?
2. Who had the lowest score after round 5? What was his or her score at this
point in the game?
3. What was each player’s score after round 6?
4. Who was in second place after round 7? How many points did this player
have?
5. Who won the game?
6. What was each player’s final score at the end of the game?
Chapter 1
34
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Refer to the table above to answer the following questions.
NAME ________________________________________ DATE ______________ PERIOD _____
1-5
Lesson Reading Guide
7NS1.2
Get Ready for the Lesson
Complete the Mini Lab at the top of page 46 in your textbook.
Write your answers below.
1. How does this result compare with the result of 3 (5)?
2. Use algebra tiles to find 4 2.
3. How does this result compare to 4 (2)?
4. Use algebra tiles to find each difference and sum. Compare the results in
each group.
a. 1 5; 1 (5)
b. 6 4; 6 (4)
Read the Lesson
5. Find the opposite of 7.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
6. Find the additive inverse of 7.
7. How is the opposite of a number different from the additive inverse of the
number?
Rewrite each difference as a sum. Then find the sum.
9. 3 8
8. 2 9
10. 10 (12)
11. 5 (16)
Subtract.
12. 3 (5)
13. 3 5
14. 7 (3)
15. 6 8
16. 23 (17)
17. 24 (12)
18. 41 4
19. 31 (26)
20. 81 (33)
21. 139 134
22. 97 (265)
23. 59 (77)
24. Describe the method for subtracting integers.
Remember What You Learned
25. Subtraction and addition are often referred to as opposite operations.
Explain in your own words the relationship between addition and
subtraction.
Chapter 1
35
Glencoe California Mathematics, Grade 7
Lesson 1–5
Subtracting Integers
NAME ________________________________________ DATE ______________ PERIOD _____
1-5
Study Guide and Intervention
7NS1.2
Subtracting Integers
To subtract an integer, add its opposite or additive inverse.
Example 1
Find 8 15.
8 15 8 (15)
7
Example 2
To subtract 15, add 15.
Add.
Find 13 (22).
13 (22) 13 22
35
To subtract 22, add 22.
Add.
Exercises
1. 3 4
2. 5 (2)
3. 10 8
4. 15 (12)
5. 23 (28)
6. 16 9
7. 9 16
8. 21 16
9. 28 37
11. 65 (6)
12. 19 |29|
10. 34 (46)
Evaluate each expression if a 7, b 3, and c 5.
13. a 8
14. 20 b
15. a c
16. c b
17. b a c
18. c b a
Chapter 1
36
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Subtract.
NAME ________________________________________ DATE ______________ PERIOD _____
1-5
Skills Practice
7NS1.2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Subtract.
1. 6 7
2. 12 8
3. 9 9
4. 17 18
5. 13 (25)
6. 14 (19)
7. 25 15
8. 21 (23)
9. 34 (11)
10. 56 94
11. 38 (39)
12. 72 27
13. 36 47
14. 33 (68)
15. 76 18
16. 4 |6|
17. |10| |7|
18. |52| 49
Evaluate each expression if k 8, m 7, and p 10.
19. k 19
20. 19 m
21. p 11
22. k m
23. p m
24. m 3
25. m k
26. k m 16
27. k m p
Chapter 1
37
Glencoe California Mathematics, Grade 7
Lesson 1–5
Subtracting Integers
NAME ________________________________________ DATE ______________ PERIOD _____
1-5
Practice
7NS1.2
Subtracting Integers
Subtract.
1. 15 7
2. 3 12
3. 8 9
4. 4 (12)
5. 18 (7)
6. 8 (9)
7. 14 (18)
8. 19 (13)
9. 8 (22)
10. 1 15
11. 12 19
12. 10 (5)
13. d 10
14. g 15
15. d g
16. d f
17. d f g
18. g d f
GEOGRAPHY For Exercises 1921, use
the table that shows the elevations
above sea level of the lowest and
highest points on six continents.
19. How far below the highest point in
Australia is the lowest point in
Australia?
20. How far below the highest point in
North America is the lowest point
in Asia?
21. Find the difference between the
lowest point in South America and
the lowest point in Africa.
Lowest
Point (m)
Africa
156
Highest
Point (m)
5,895
Asia
400
8,850
Australia
12
2,228
Europe
28
5,642
North America
86
6,194
South America
42
6,960
Continent
Source: www.worldoffacts.com
Simplify.
22. 29 (4) (15)
23. 10 [8 (16)]
24. 25 [16 (9)]
25. [22 (18)] (5 11)
26. (5 9) (20 12)
27. [15 (7)] (8 11)
Chapter 1
38
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Evaluate each expression if d 4, f 7, and g 11.
NAME ________________________________________ DATE ______________ PERIOD _____
1-5
Word Problem Practice
7NS1.2
GEOGRAPHY For Exercises 1 and 2, use the table. The table shows the
elevations of several places on Earth.
Place
Elevation (feet)
Mt. McKinley
20,320
Puerto Rican Trench
28,232
Mt. Everest
29,035
1,348
Dead Sea
282
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Death Valley
1. Find the difference in elevation
between the top of Mt. McKinley and
and the top of Mt. Everest.
2. Find the difference in elevation
between Death Valley and the
Dead Sea.
3. TEMPERATURE The highest recorded
temperature on Earth was recorded in
Africa at 136°F, while the lowest was
129°F in Antarctica. What is the
range of temperatures recorded
on Earth?
4. WEATHER If the overnight temperature
at the Arctic Circle was 14°F, but the
temperature rose to 8°F during the day,
what was the difference between these
high and low temperatures?
5. WATER The boiling point of water is
212°F, while 460°F is its absolute
lowest temperature. Find the
difference between these two
temperatures.
6. STOCK MARKET During the course of
one day, the price of a stock fluctuated
between a high of $3 above the
previous day’s closing price and a low of
$2 below the previous day’s closing
price. What was the difference between
the high and low prices for that day?
Chapter 1
39
Glencoe California Mathematics, Grade 7
Lesson 1–5
Subtracting Integers
NAME ________________________________________ DATE ______________ PERIOD _____
1-5
Enrichment
7NS2.5
Distance on the Number Line
The absolute value of the difference between two integers can be interpreted
as the distance between two points on a number line. That is, if point A has a
as a coordinate and point B has b as a coordinate, then |a b| is the distance
between points A and B.
Graph each pair of points on the number line. Then write an
expression using absolute value to find the distance between the
points.
1. H at 4 and G at 2
8
7
6
5
4
3
2
1
0
1
2
3
4
5
6
7
8
3
2
1
0
1
2
3
4
5
6
7
8
3
2
1
0
1
2
3
4
5
6
7
8
6
7
8
6
7
8
8
7
6
5
4
3. A at 5 and B at 5
8
7
6
5
4
Use the number lines to solve the problems.
4. Graph two points, M and N, that are each 5 units from 2. Make M N.
8
7
6
5
4
3
2
1
0
1
2
3
4
5
5. Graph the two solutions to the equation |y 2| 3. Call the points y1
and y2.
8
7
Chapter 1
6
5
4
3
2
1
0
40
1
2
3
4
5
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2. X at 7 and Y at 1
NAME ________________________________________ DATE ______________ PERIOD _____
1-6
Lesson Reading Guide
7NS1.2, 7AF1.3
Multiplying and Dividing Integers
Get Ready for the Lesson
Read the introduction at the top of page 51 in your textbook.
Write your answers below.
2. Write a multiplication sentence that could be used to find this same
depth. Explain your reasoning.
3. Write a multiplication sentence that could be used to find the
submersible’s depth after 10 minutes. Then find the product.
Read the Lesson
4. Identify each number in the multiplication sentence 3(120) 360 as
either a factor or a product.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Complete each sentence with either positive or negative.
5. The product of two integers with different signs is __________ .
6. The product of two integers with the same signs is __________ .
7. The quotient of two integers with different signs is __________ .
8. The quotient of two integers with the same signs is __________ .
Determine whether each product or quotient is positive or negative.
Then evaluate the expression.
9. 4 8
10. 3 5
11. 9(2)
12. 6(7)
13. 12 (4)
14. 35 (7)
21
15. 64
16. 3
8
Remember What You Learned
17. Explain how to find the mean of a set of numbers. What is another name
for the mean?
Chapter 1
41
Glencoe California Mathematics, Grade 7
Lesson 1–6
1. Write two different addition sentences that could be used to find the
submersible’s depth after 3 minutes. Then find their sums.
NAME ________________________________________ DATE ______________ PERIOD _____
1-6
Study Guide and Intervention
7NS1.2, 7AF1.3
Multiplying and Dividing Integers
Use the following rules to determine whether the product or quotient of two integers is positive or
negative.
• The product of two integers with different signs is negative.
• The product of two integers with the same sign is positive.
• The quotient of two integers with different signs is negative.
• The quotient of two integers with the same sign is positive.
7(4) 28
Example 2
5(6) 30
Example 3
15 (3) 5
Example 4
54 (6) 9
Find 7(4).
The factors have different signs. The product is negative.
Find 5(6).
The factors have the same sign. The product is positive.
Find 15 (3).
The dividend and divisor have different signs. The quotient is negative.
Find 54 (6).
The dividend and divisor have the same sign. The quotient is positive.
Exercises
Multiply or divide.
1. 8(8)
2. 3(7)
3. 9(4)
4. 12(8)
5. 33 (3)
6. 25 5
7. 48 4
8. 63 (7)
9. (4)2
75
10. 15
11. 6(3)(5)
143
12. 13
Evaluate each expression if a 1, b 4, and c 7.
13. 3c b
Chapter 1
14. a(b c)
15. c2 5b
42
a6
16. c
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Example 1
NAME ________________________________________ DATE ______________ PERIOD _____
1-6
Skills Practice
7NS1.2, 7AF1.3
Multiplying and Dividing Integers
1. 2 3
2. 3(3)
3. 4(2)
4. 5 7
5. 9(8)
6. 11 12
7. 15(3)
8. 7(13)
10. (10)2
11. 6(8)(3)
12. (4)3
14. 1(3)(4)
15. (10)3
16. 3(4)(7)
17. 15 3
18. 40 (5)
19. 63 (7)
20. 76 4
56
21. 48
22. 57
23. 75
24. 9. 5(2)(7)
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
13. (9)2
Divide.
4
16
19
5
Evaluate each expression if a 2, b 5, and c 6.
25. abc
26. 2b c
2b c
27. 28. ab c
29. c
2a c
30. 31. b2 5a
32. (c)2
ab
Chapter 1
b
a
43
Glencoe California Mathematics, Grade 7
Lesson 1–6
Multiply.
NAME ________________________________________ DATE ______________ PERIOD _____
1-6
Practice
7NS1.2, 7AF1.3
Multiplying and Dividing Integers
Multiply.
1. 5(7)
2. 3 12
3. 8(9)
4. 4(12)
5. (7)2
6. 2(5)(3)
8. 35 (7)
9. 48 (6)
Divide.
7. 14 2
66
10. 6
80
12. 5
56
11. 7
13. s + 5t
14. 10 rt
5s
15. t4
42
16. rt
17. r2 16
18. (2t 4)2 4
Find the mean of each set of integers.
19. 8, 5, 3, 9, 5, 2
20. 11, 15, 16, 17, 20, 18, 22
21. 5, 4, 8, 12, 10
22. 22, 19, 14, 17, 18
Find each product or quotient.
23. (3)2 (4)2
24. 3(5)2
10(15)
26. 6
27. 25. 5(2)(4)(3)
4 12
28. 8
122
12
29. MONEY If you have $216 and you spend $12 each day, how long would it be until you
had no money left?
30. WEATHER During a six hour period, the temperature dropped 18F. Find the average
hourly change in the temperature.
Chapter 1
44
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Evaluate each expression if r 4, s 11, and t 7.
NAME ________________________________________ DATE ______________ PERIOD _____
1-6
Word Problem Practice
7NS1.2, 7AF1.3
1. STOCK MARKET The price of a stock
decreased $2 per day for four
consecutive days. What was the total
change in value of the stock over the
four-day period?
2. EVAPORATION The height of the water
in a tank decreases 3 inches each week
due to evaporation. What is the change
in the height of the water over a fiveweek period due to evaporation?
3. FOOTBALL A football team lost 9 yards
on each of three consecutive plays.
What was the team’s total change in
position for the three plays?
4. HIKING A group of hikers is descending
a mountain at a rate of 400 feet per
hour. What is the change in the
elevation of the hikers after 6 hours?
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
G 10 20 30 40 50 40 30 20 10 G
5. WEATHER On a certain day, the
temperature changed at a rate
of 2ºF per hour. How long did
it take for the change in
temperature to be 14ºF?
6. GEOLOGY The length of an island is
changing at the rate of 17 inches per
year. How long will it take for the
change in the length of the island to be
255 inches?
14 F
7. DEPRECIATION The value of a piece of
office equipment is changing at a rate
of $175 per year. How long will it take
for the change in value to be $1,050?
Chapter 1
45
8. POPULATION The population of a small
town is changing at a rate of 255
people per year. How long will it take
for the change in population to be
2,040 people?
Glencoe California Mathematics, Grade 7
Lesson 1–6
Multiplying and Dividing Integers
NAME ________________________________________ DATE ______________ PERIOD _____
1-6
Enrichment
7NS1.2, 7AF1.3
Doubles and Halves
Most numbers are easy to double or halve mentally. And, many types of
multiplication problems can be done mentally by using doubling and halving.
In working problems of this type, it is helpful to remember that 5 equals 10
divided by 2. And, dividing by 2 is the same as multiplying by one-half. So,
multiplying by 5 is the same as first multiplying by 10 and then halving.
10
1
5
; 5 10 ; 87 5 87 10 2 870 2 435
2
2
Double each number. Use mental math.
1. 13
2. 214
3. 48
4. 2,512
5. 57
6. 609
7. 383
8. 6,523
10. 468
11. 690
12. 1,484
13. 72
14. 56
15. 38
16. 54
17. 116
18. 364
19. 5,296
20. 7,436
9. 64
Compute mentally.
21. 5 126
22. 5 234
23. 5 (872)
24. 20 93
25. 20 361
26. 20 317
Transform each product into an expression that uses doubling or
halving. Change only the second factor.
27. 256 20
28. 613 5
29. 472 50
30. 57 40
31. 138 25
32. 93 125
Chapter 1
46
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Halve each number. Use mental math.
NAME ________________________________________ DATE ______________ PERIOD _____
1-6
TI-83/84 Plus Activity
Calculating with Integers
You can solve problems involving integers on a graphing calculator.
When a number is positive, you do not need to enter a sign. But when
a number is negative, use the (–) key before you enter the number.
Example 1
Find 6 (10).
Enter: 6 +
(–)
10
ENTER
4
Example 2
1–6
Lesson X–6
So, 6 (10) 5 (4).
Find 24 (3).
Enter:
(–)
24 3
(–)
8
ENTER
So, 24 (3) 8.
Example 3
Evaluate g t if g 4 and t 1.
Enter:
(–)
4
—
(–)
1
ENTER
3
So, g t 3 when g 4 and t 1.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Exercises
Perform the indicated operation.
1. 8 16
2. 4 (11)
3. 5 17
4. 6 12
5. 48 (3)
6. 3 (9)
7. 12 (11)
8. 36 (11)
9. 84 (3)
Evaluate each expression if x 4, y 5, and z 1.
10. 15 x
11. y (4)
12. 10 z
13. 0 y
14. z (6)
15. 14 (z)
16. x y
17. y z
18. x y z
19. x (z)
20. x y (2)
21. x y z
Chapter 1
47
Glencoe California Mathematics, Grade 7
NAME ________________________________________ DATE ______________ PERIOD _____
1-7
Lesson Reading Guide
7AF1.1, 7AF1.4
Writing Equations
Get Ready for the Lesson
Read the introduction at the top of page 57 in your textbook.
Write your answers below.
1. What is the relationship between the number of guests and the cost of
the party?
2. Write an expression representing the cost of a party with g guests.
3. What does the equation g 8 120 represent in this situation?
Read the Lesson
Look at the steps for writing an algebraic equation on page 57. Then
determine whether each situation requires addition, subtraction,
multiplication, or division.
5. Find the cost per person when the price of a pizza is split among several
people.
6. Find the price of an airline ticket after the price has been decreased by
$50.
7. Find how much an executive spent on breakfast, lunch, and dinner.
8. Find the flight time after the time has been increased by 15 minutes.
9. Find the product of the price of a calculator and the number of students
in the class.
10. Find the high temperature on Wednesday if this temperature is 3º less
than the high temperature on Tuesday.
11. Find the ratio of the amount of gasoline used and the distance traveled.
Remember What You Learned
12. Devise your own way to determine how a verbal description should be
translated as an algebraic equation.
Chapter 1
48
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. Find the difference between the cost of a gallon of premium gasoline and
the cost of a gallon of regular gasoline.
NAME ________________________________________ DATE ______________ PERIOD _____
1-7
Study Guide and Intervention
7AF1.1, 7AF1.4
Writing Equations
The table shows several verbal phrases for each algebraic expression.
Phrases
Expression
Phrases
Expression
8 more than a number
the sum of 8 and a number
x plus 8
x increased by 8
x8
the difference of r and 6
6 subtracted from a number
6 less than a number
r minus 6
r6
Phrases
Expression
Phrases
Expression
4 multiplied by n
4 times a number
the product of 4 and n
a number divided by 3
the quotient of z and 3
the ratio of z and 3
4n
z
3
Sentences
Equation
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9 less than a number is equal to 45.
The difference of a number and 9 is 45.
A number decreased by 9 is 45.
45 is equal to a number minus 9.
n 9 45
Exercises
Write each verbal phrase as an algebraic expression.
1. the sum of 8 and t
2. the quotient of g and 15
3. the product of 5 and b
4. p increased by 10
5. 14 less than f
6. the difference of 32 and x
Write each verbal sentence as an algebraic equation.
7. 5 more than a number is 6.
8. The product of 7 and b is equal to 63.
9. The sum of r and 45 is 79.
10. The quotient of x and 7 is equal to 13.
11. The original price decreased by $5 is $34.
12. 5 shirts at $d each is $105.65.
Chapter 1
49
Glencoe California Mathematics, Grade 7
Lesson 1-7
The table shows several verbal sentences that represent the same equation.
NAME ________________________________________ DATE ______________ PERIOD _____
1-7
Skills Practice
7AF1.1, 7AF1.4
Writing Equations
Write each verbal phrase as an algebraic expression.
1. a number divided by 5
2. the sum of d and 7
3. the product of 10 and c
4. the difference of t and 1
5. the score increased by 8 points
6. the cost split among 4 people
7. the cost of 7 CDs at $d each
8. the height decreased by 2 inches
9. $500 less than the sticker price
11. 2 hours more than the estimate
10. the total of Ben’s score and 75
12. 25 times the number of students
Write each verbal sentence as an algebraic equation.
13. The sum of a number and 16 is equal to 45.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
14. The product of 6 and m is 216.
15. The difference of 100 and x is 57.
16. The quotient of z and 10 is equal to 32.
17. $12 less than the original price is $48.
18. 17 more than some number is equal to 85.
19. The number of members divided by 6 is 15.
20. The total of Joshua’s savings and $350 is $925.
21. 65 is 5 times a number.
22. The total area decreased by 75 square feet is 250 square feet.
23. The cost of 10 books at $d each is $159.50.
24. Carla’s height plus 4 inches is 68 inches.
Chapter 1
50
Glencoe California Mathematics, Grade 7
NAME ________________________________________ DATE ______________ PERIOD _____
1-7
Practice
7AF1.1, 7AF1.4
Writing Equations
Define a variable. Then write an equation to model each situation.
1. After receiving $25 for her birthday, Latisha had $115.
2. At 14 years old, Adam is 3 years younger than his brother Michael.
3. A class of 30 students separated into equal sized teams results in 5
students per team.
4. When the bananas were divided evenly among the 6 monkeys, each
monkey received 4 bananas.
5. GRADES Kelly’s test score was 6 points higher than Michelle’s. If Kelly’s
test score was 88, what was Michelle’s test score?
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
6. GEOMETRY A rectangle's width is one-third its length. If the width is 8
inches, what is the length of the rectangle?
7. FOOTBALL A team had a total gain of 15 yards over several plays with
an average gain of 5 yards per play. How many plays are represented?
Write an equation to model the relationship between the quantities
in each table.
8.
9.
Feet, f
Yards, y
1,000
3
1
2
2,000
6
2
3
3,000
9
3
4
4,000
12
4
k
g
f
y
Kilograms, k
Grams, g
1
10. MONEY Carlotta earns $3 for every hour
that she baby sits. Complete the table of
values showing the amount she earns for
baby sitting 1, 2, 3, 4, and h hours. Given
h, a number of hours, write an equation to
find a, the amount that Carlotta earns.
Chapter 1
51
Hours, h
Amount, a
Glencoe California Mathematics, Grade 7
Lesson 1-7
Define a variable. Then write an equation that could be used to solve
each problem.
NAME ________________________________________ DATE ______________ PERIOD _____
1-7
Word Problem Practice
7AF1.1, 7AF1.4
1. AGE Julia is 3 years younger than
Kevin. Kevin is 13. Define a variable
and write an equation to find Julia’s
age.
2. CIVICS In the 2004 presidential election,
Texas had 23 more electoral votes than
Tennessee. Define a variable and write
an equation to find the number of
Tennessee’s electoral votes if Texas had
34 votes.
3. ENERGY One year, China consumed
4 times as much energy as Brazil.
Define a variable and write an equation
to find the amount of energy Brazil
used that year if China used 12,000
kilowatt-hours.
4. CHEMISTRY The atomic number of
cadmium is half the atomic number of
curium. The atomic number for
cadmium is 48. Define a variable and
write an equation to find the atomic
number of curium.
5. LIBRARIES The San Diego Public Library
has 44 fewer branches than the Chicago
Public Library. Define a variable and
write an equation for the number of
branches in the San Diego Public
Library if Chicago has 79 branches.
6. ASTRONOMY Saturn is 6 times farther
from the Sun than Mars. Define a
variable and write an equation to find
the distance of Mars from the Sun if
Saturn is about 1,429,400,000 km from
the sun.
7. POPULATION The population of
Oakland, California, is 9,477 more than
the population of Omaha, Nebraska.
Omaha has a population of 390,007.
Define a variable and write an equation
to find the population of Oakland.
8. GEOGRAPHY Kings Peak in Utah is
8,667 feet taller than Spruce Knob in
West Virginia. Spruce Knob is 4,861
feet tall. Define a variable and write an
equation to find the height of Kings
Peak.
Chapter 1
52
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Writing Equations
NAME ________________________________________ DATE ______________ PERIOD _____
1-7
Enrichment
7AF1.1
Writing Equations to Describe Sequences
A sequence can be extended by finding the pattern, describing it, and then applying the
description to produce successive terms. To describe the pattern in words, we could write,
“Add four to the previous term to find the next term.” Determine the pattern rule for the
sequence below. What are the next three terms?
Position
Term
1
4
2
8
3
12
4
16
5
20
6
7
8
A. 2, 4, 6, 8, 10, 12, ___, ___, ___
B. 3, 6, 9,12, 15, 18, ___, ___, ___
C. 3, 5, 7, 9, 11, 13, ___, ___, ___
D. 3, 9, 27, 81, 243, ___, ___, ___
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
E. 6,230, 623, 62.3, 6.23, 0.623, ___, ___, ___ F. 1, 4, 9, 16, 25, 36, ___, ___, ___
The rule of a sequence can be generalized into an equation so that it is possible to find the
10th term, 100th term, or nth term without writing out of the terms in between. The rule of
the sequence shows the relationship between a term and its position number.
Look again at the beginning example. The rule is multiply the position number by four.
If we call the position numbers n, the algebraic expression for the rule is 4n. For each
term t 4n.
Write an equation rule for each of the sequences in exercises 1–6. Be
careful that your rule gives the correct first term.
1. Sequence A
2. Sequence B
3. Sequence C
4. Sequence D
5. Sequence E
6. Sequence F
Write an equation rule for each of the sequences below. Then use the
equation to find the 100th term.
7. 4, 7, 10, 13, 16, …
9. 0, 2, 4, 6, 8, …
8. 2, 5, 10, 17, 26, …
10. 0.75, 1.5, 2.25, 3, 3.75, …
11. 11, 12, 13, 14, 15, …
12. Write your own sequence rule and
find the first 5 terms.
Chapter 1
53
Glencoe California Mathematics, Grade 7
Lesson 1-7
Pattern
4
4
4
4
Describe the pattern in words and write the next three terms in each of the
following sequences.
NAME ________________________________________ DATE ______________ PERIOD _____
1-8
Study Guide and Intervention
7MR1.1, 7NS1.2
Problem-Solving Investigation: Work Backward
You may need to work backward to solve a problems.
Explore
• Determine what information is given in the problem and what you need to find.
Plan
• Select a strategy including a possible estimate.
Solve
• Solve the problem by carrying out your plan.
Check
• Examine your answer to see if it seems reasonable.
Example 1
Explore
You know that Mari put $200 in the bank on the fourth week. You need to know
how much money she put in the bank on the first week.
Plan
Start with the amount she put in the bank on the last week and work
backward.
Solve
Start with the $200 Mari put in the bank on the fourth week.
Fourth Week
$200
This is $20
more than the
third week.
Check
Third Week
Second Week
$180
$40
$220
Work
This is $40 less
Work
This is twice as
backward. than the second backward.
much as the
Subtract
week.
Add $40.
first week.
$20.
$20
2
First Week
$110
Work
backward.
Divide by
2.
Start with $110 for the first week and work forward. On the second week she
deposited twice as much money in the bank than on the first week, which is
$220. On the third week, she deposited $40 less than the second week, which is
$180. On the fourth week she deposited $20 more than on the third week, or
$200. This is what you know she deposited on the fourth week.
Exercises
Use the work backward strategy to solve each problem.
1. SHOPPING Jack spent a total of $87.58 when he went shopping for camping supplies. He
spent $36.89 on food, $23.24 on a sleeping bag, and bought lunch. When he got home,
he had $15.70. How much did he spend on lunch?
2. AGE Sam is 4 years older than Eliot. Eliot is 9 years younger than Xing. Xing is 3 years
older than Damien. If Damien is 15 years old, how old are each of the other boys?
Chapter 1
54
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Mari put money in her savings account each week. She put a certain amount of money in
the bank on the first week. On the second week she put twice as much money in the bank
as the first week. On the third week, she put $40 less in the bank than on the second week.
On the fourth week, she put $20 more in the bank than on the third week. Mari put $200 in
the bank on the fourth week. How much money did Mari put in the bank on the first week?
NAME ________________________________________ DATE ______________ PERIOD _____
1-8
Skills Practice
7MR1.1, 7NS1.2
Problem-Solving Investigation: Work Backward
Use the work backward strategy to solve each problem.
1. SKATEBOARDS On Monday, David’s skateboard shop received its first shipment of
skateboards. David sold 12 skateboards that day. On Thursday, he sold 9 skateboards.
On Friday, he received a shipment of 30 more skateboards and sold 10 skateboards. He
then had a total of 32 skateboards in his shop. How many skateboards were delivered
on Monday?
2. SHIPPING An overseas cargo ship was being loaded. At the end of each day, a scale
showed the total weight of the ship’s cargo. On Monday, 48 tons of cargo were loaded
onto the ship. On Tuesday, three times as much cargo was loaded on to the ship as on
Monday. On Wednesday, 68 tons of cargo were loaded onto the ship. On Thursday, 0.75
as much cargo was loaded onto the ship as on Wednesday. On Friday, 120 tons of cargo
were loaded onto the ship. At the end of the day on Friday, the scale showed that the
ship was carrying 690 tons of cargo. How much cargo was the ship carrying when it
first came into port on Monday?
4. JOGGING Edmund is training for a marathon. He ran a certain number of miles on
Monday. On Wednesday, he ran 2 more miles than on Monday. On Saturday, he ran
twice as far as on Wednesday. On Sunday, he ran 6 miles less than on Saturday. He ran
8 miles on Sunday. How many miles did Edmund run on Monday?
Use the table to solve each problem.
Flight Number
253
142
295
Airline Schedule
Minneapolis, MN to Dallas, TX
Departure Time
8:20 A.M.
11:52 A.M.
12:00 P.M.
Arrival Time
10:37 A.M.
1:45 P.M.
3:30 P.M.
5. Charles needs to take Flight 295. He needs 45 minutes to eat breakfast and pack. It
takes 25 minutes to get to the airport. To be at the airport 90 minutes early, what is
the latest time he can start eating breakfast?
6. Mrs. Gonzales left her office at 7:25 a.m. She planned that it would take her 30
minutes to get to the airport, but the traffic was so heavy it took an additional 20
minutes. It takes 30 minutes to check her baggage and walk to the boarding gate. What
is the first flight she can take to Dallas?
Chapter 1
55
Glencoe California Mathematics, Grade 7
Lesson 1-8
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3. NUMBERS Jana is thinking of a number. If she divides her number by 12 and then
multiplies the quotient by 8, the result is 520. What number is Jana thinking of?
NAME ________________________________________ DATE ______________ PERIOD _____
1-8
Practice
7MR1.1, 7NS1.2
Problem-Solving Investigation: Work Backward
4. ANALYZE TABLES The table below gives
the results from a poll taken at school
about the times in minutes that boys
and girls spend using the Internet for
school work and the total time spent
using the Internet each week.
Mixed Problem Solving
Use the work backward strategy to
solve Exercises 1 and 2.
1. TRAVEL Rajiv and his family left home
on a trip and drove for 2 hours before
they stopped to eat. After 1.5 hours,
they were back on the road. They
arrived at their destination 3 hours
later at 5:00 P.M. What time did they
leave home?
Gender Time Used for Total Time
School Work per Week
Boys
Girls
33 min
72 min
255 min
213 min
How many more minutes per week do
boys spend using the Internet for
purposes other than school work than
girls?
2. GRADES Kumiko had an average of 92
on her first three math tests. Her scores
on the second and third tests were 97
and 89. What was her score on the first
test?
Use any strategy to solve Exercises 3
and 4. Some strategies are shown below.
For Exercises 5 and 6, select an
appropriate operation to solve the
problem. Justify your solution and
solve the problem.
5. MOVIES The two animated films with
the highest box office receipts brought
in a total of $775 million. If one film
brought in $97 million more than the
other, how much did the film with the
highest receipts bring in?
Problem-Solving Strategies
• Use the four-step plan.
• Work backward.
3. BAKING Isabel doubled her recipe for
chocolate chip cookies. After her
brothers ate 8 cookies, she set aside half
of the remaining cookies for a school
party. Isabel then gave 2 dozen cookies
to her neighbor. She had 12 cookies left
over. How many cookies does one recipe
make?
Chapter 1
6. U.S. PRESIDENTS Harry S Truman was
elected president in 1944. He died in
1972 at the age of 88. How old was he at
the time he was elected?
56
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Select the Operation
NAME ________________________________________ DATE ______________ PERIOD _____
1-8
Word Problem Practice
7MR1.1, 7NS1.2
Problem-Solving Investigation: Work Backward
Use the work backward strategy to solve each problem.
CLARINET PRACTICE For Exercises 1 and 2, use the table at the right. It is a
record of the amount of time Elena practiced her clarinet in a week.
Tuesday
20 minutes
more than
Monday
Thursday
10 minutes
less than
Tuesday
Saturday
Twice as
long as
Thursday
Sunday
15 minutes
less than
Saturday–
45 minutes
1. How many minutes did Elena practice
the clarinet on Thursday?
2. How many minutes did Elena practice
on Monday?
3. HOCKEY During a hockey game,
Brandon played 7 less minutes than
Nick. Zach played 12 minutes more
than Brandon. Hunter played twice as
long as Zach. Hunter played for 44
minutes. How many minutes did Nick
play in the hockey game?
4. PACKAGES In the morning, a delivery
truck delivers 24 of it packages to a
factory. It then goes to a distribution
lot, where the remaining packages are
separated into 4 equal groups and put
on other trucks. There were 18
packages in each of the groups. How
many packages were on the delivery
truck to begin with?
5. WEATHER On Monday, Eliza read her
book. On Tuesday, she read three times
as long as she read on Monday. On
Wednesday she read 20 minutes less
than Tuesday. On Thursday she read
for 20 minutes, which was half as long
as she read on Wednesday How many
minutes did Eliza read over the 4-day
period?
6. STAMPS Zoe added 23 stamps to her
collection. Three months later her
collection had tripled in number to a
total of 159 stamps. How many stamp
did Zoe have to start her collection?
Chapter 1
57
Glencoe California Mathematics, Grade 7
Lesson 1-8
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Monday
?
NAME ________________________________________ DATE ______________ PERIOD _____
1-9
Lesson Reading Guide
6AF1.1
Solving Addition and Subtraction Equations
Get Ready for the Lesson
Complete the Mini Lab at the top of page 65 in your textbook.
Write your answers below.
Solve each equation using algebra tiles.
1. x 1 4
2. x 3 7
3. x (4) 5
4. Explain how you would find a value of x that makes x (3) 8 true
without using models.
Read the Lesson
x69
_____
a. Subtract 11 from each side.
s 5 14
_____
b. Subtract 6 from each side.
4 3 p
_____
c. Add 3 to each side.
11 m 33 _____
d. Add 5 to each side.
For Exercises 6–8, explain how to solve each equation.
6. w 7 2 _________________________
7. c 3 9
_________________________
8. 17 11 k _________________________
Solve each equation.
9. z 8 2
10. 3 7 r
11. 9 g 14
Remember What You Learned
12. Write two addition and two subtraction equations of your own. Trade
your equations with a partner and solve. Explain to each other the
method you used to solve the equations.
Chapter 1
58
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. Match the method of solving with the appropriate equation.
NAME ________________________________________ DATE ______________ PERIOD _____
1-9
Study Guide and Intervention
6AF1.1
Solving Addition and Subtraction Equations
You can use the following properties to solve addition and subtraction equations.
• Addition Property of Equality — If you add the same number to each side of an equation, the two
sides remain equal.
• Subtraction Property of Equality — If you subtract the same number from each side of an equation,
the two sides remain equal.
Example 1
Solve w 19 45. Check your solution.
w 19 45
w 19 19 45 19
w 26
w 19¬ 45
26 19¬ 45
45¬ 45 ✓
Check
19 19 0 and 45 19 26. w is by itself.
Write the original equation.
Replace w with 26. Is this sentence true?
26 19 45
Solve h 25 76. Check your solution.
h 25¬ 76
h 25 25¬ 76 25
h¬ 51
Check
Subtract 19 from each side.
h 25¬ 76
51 25¬ 76
76¬ 76 ✓
Write the equation.
Add 25 to each side.
25 25 0 and 76 25 51. h is by itself.
Write the original equation.
Replace h with 51. Is this sentence true?
51 25 51 (25) or 76
Exercises
Solve each equation. Check your solution.
1. s 4 12
2. d 2 21
3. h 6 15
4. x 5 8
5. b 10 34
6. f 22 6
7. 17 c 41
8. v 36 25
9. y 29 51
10. 19 z 32
11. 13 t 29
12. 55 39 k
13. 62 b 45
14. x 39 65
15. 56 47 n
Chapter 1
59
Glencoe California Mathematics, Grade 7
Lesson 1-9
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Example 2
Write the equation.
NAME ________________________________________ DATE ______________ PERIOD _____
1-9
Skills Practice
6AF1.1
Solving Addition and Subtraction Equations
1. x 3 4
2. y 6 5
3. t 2 2
4. z 5 1
5. a 4 3
6. h 3 6
7. u 4 1
8. 8 d 14
9. 19 x 7
10. 17 b 8
11. 19 z 21
12. 22 y 29
13. 16 24 p
14. 17 19 x
15. f 25 35
16. y 37 59
17. s 46 72
18. m 65 11
19. r 53 19
20. n 75 42
21. g 35 62
22. 111 x 68
23. 54 32 w
24. 27 z 47
Chapter 1
60
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Solve each equation. Check your solution.
NAME ________________________________________ DATE ______________ PERIOD _____
1-9
Practice
6AF1.1
Solving Addition and Subtraction Equations
Solve each equation. Check your solution.
1. t 7 12
2. h 3 8
3. 8 b 9
4. k 4 14
5. m 9 7
6. y 10 3
7. 14 2 d
8. 15 n 10
9. 8 r 6
10. 11 w 5
11. 9 g 9
12. 12 c 16
13. GEOMETRY Two angles are supplementary if
the sum of their measures is 180. The two
angles shown are supplementary. Write and
solve an equation to find the measure of
angle R.
140
R S
15. FUND RAISING During a five-day fund raiser, Shantell sold 8 boxes of
greeting cards the first day, 6 boxes the second day, 10 boxes the third
day, and 7 boxes the fourth day. If she sold a total of 45 boxes of greeting
cards during the five days, write an equation that can be used to find the
number of boxes Shantell sold the fifth day. Explain two methods of
solving this equation. Then solve the equation.
16. ANALYZE TABLES The total points scored by both
teams in the 2006 Super Bowl was 14 less than
the total points for 2005. Write and solve an
equation to find the total points for 2005.
Total Points Scored by Both
Teams in Super Bowl
Year
Points
2005
p
2006
31
Source: www.superbowl.com
Chapter 1
61
Glencoe California Mathematics, Grade 7
Lesson 1-9
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
14. ARCHITECTURE The Sears Tower in Chicago was the tallest building in the
world when it was completed. Twenty-three years later, a taller building
was completed in 1996 on Taiwan. Write and solve an equation to find the
year that the Sears Tower was completed.
NAME ________________________________________ DATE ______________ PERIOD _____
1-9
Word Problem Practice
6AF1.1
1. AGE Walter lived 2 years longer than
his brother Martin. Walter was 79 at
the time of his death. Write and solve
an addition equation to find Martin’s
age at the time of his death.
2. CIVICS New York has 24 fewer members
in the House of Representatives than
California. New York has 29
representatives. Write and solve a
subtraction equation to find the
number of California representatives.
3. GEOMETRY Two angles are
supplementary if the sum of their
measures is 180°. Angles A and B are
supplementary. If the measure of
angle A is 78°, write and solve an
addition equation to find the measure
of angle B.
4. BANKING After you withdraw $40 from
your checking account, the balance is
$287. Write and solve a subtraction
equation to find your balance before
this withdrawal.
mA ⫽ 78˚
180˚
B A
5. WEATHER After the temperature
had risen 12°F, the temperature
was 7°F. Write and solve an
addition equation to find the
7 F
starting temperature.
6. CHEMISTRY The atomic number of
mercury is the sum of the atomic
number of aluminum and 67. The
atomic number of mercury is 80. Write
and solve an addition equation to find
the atomic number of aluminum.
7. ELEVATION The lowest point in
Louisiana is 543 feet lower than the
highest point in Louisiana. The
elevation of the lowest point is 8 feet.
Write and solve a subtraction equation
to find the elevation of the highest
point in Louisiana.
8. POPULATION In 2005, the population of
Honduras is the population of Haiti
decreased by 832,598. The population of
Honduras is 6,823,568. Write and solve
a subtraction equation to find the
population of Haiti.
Chapter 1
62
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Solving Addition and Subtraction Equations
NAME ________________________________________ DATE ______________ PERIOD _____
1-9
Enrichment
7AF1.1
Geometric Equations
Equations are often used to solve geometric problems. To work the problems
on this page, you will need to use the following facts.
Angles are complementary if their measures add to 90°. If their measures
add to 180°, they are supplementary. The total number of degrees in the
measures of the central angles of a circle is 360°. The sum of the measures of
the angles in a triangle is 180°. A straight angle measures 180°.
Match each equation in the chart at the bottom of the page with a
figure that could be used to solve for the missing angle measurement.
Then solve for that measurement.
A.
B.
C.
20˚
x˚ 90˚
x˚
x˚
150˚
72˚
D.
E.
x˚
45˚
F.
x˚
45˚
x˚
Equation
15˚
30˚
15˚
Letter of Figure
Angle Measurement (x)
35° 20° x° 180°
90° x° 15°
x° 72° 180°
360° x° 150° 90°
2(45°) x° 180°
30° x° 15° 90°
Chapter 1
63
Glencoe California Mathematics, Grade 7
Lesson 1-9
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
35˚
NAME ________________________________________ DATE ______________ PERIOD _____
1-10
Lesson Reading Guide
6AF1.1
Solving Multiplication and Division Equations
Get Ready for the Lesson
Read the introduction at the top of page 70 in your textbook.
Write your answers below.
1. If d represents the number of days the bamboo has been growing, write a
multiplication equation you could use to find how long it would take for
the bamboo to reach a height of 210 inches.
Read the Lesson
Complete each sentence.
2. To solve 3x 51, __________ each side by 3.
3. To solve b 4, __________ each side by 2.
2
5. To solve 7 d, __________ each side by 6.
6
Explain how to solve each equation.
6. u 13
_________________________
7. 2c 14
_________________________
8. 64 16k
_________________________
6
Solve each equation.
9. 8r 32
10. 3 x
11. 9 9g
7
Remember What You Learned
12. Write two multiplication and two division equations of your own. Trade
your equations with a partner and solve. Explain to each other the
method you used to solve the equations.
Chapter 1
64
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. To solve 65 5t, __________ each side by 5.
NAME ________________________________________ DATE ______________ PERIOD _____
1-10
Study Guide and Intervention
6AF1.1
Solving Multiplication and Division Equations
You can use the following properties to solve multiplication and division equations.
• Multiplication Property of Equality — If you multiply each side of an equation by the same number, the
two sides remain equal.
• Division Property of Equality — If you divide each side of an equation by the same nonzero number,
the two sides remain equal.
Example 1
Solve 19w 104. Check your solution.
19w 114
Write the equation.
19w
114
19
19
Divide each side of the equation by 19.
1w 6
19 19 1 and 114 19 6.
w6
19w¬ 114
Check
Write the original equation.
19(6)¬ 114
Replace w with 6.
This sentence is true.
Solve d 9. Check your solution.
15
d
9
15
d
(15) 9(15)
15
Multiply each side of the equation by 15.
d 135
Check
d
¬ 9
15
135
¬ 9
15
9¬ 9 ✓
Write the original equation.
Replace d with 135.
135 15 9
Exercises
Solve each equation. Check your solution.
1. r 6
2. 2d 12
3. 7h 21
4. 8x 40
5. f 6
6. x 7
7. 17c 68
8. h 12
9. 29t 145
11. 13t 182
12. 117 39k
5
10. 125 5z
Chapter 1
10
8
11
65
Glencoe California Mathematics, Grade 7
Lesson 1-10
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
114¬ 114 ✓
Example 2
Identity Property; 1w w
NAME ________________________________________ DATE ______________ PERIOD _____
1-10
Skills Practice
6AF1.1
Solving Multiplication and Division Equations
Solve each equation. Check your solution.
1. u 3
2. 3c 12
3. 5x 15
4. 7z 49
5. n 7
6. a 11
7. 14g 56
8. t 11
9. 18y 144
10. 135 9z
11. 11d 143
12. 116 29k
13. w 17
14. 14 15. 112 8v
16. 17c 136
17. 21a 126
18. s 9
19. m 7
20. 16q 272
21. 15 z
9
31
g
22
22. 23
Chapter 1
9
3
12
y
7
y
25
23. 16
19
14
24. 47k 517
66
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
7
NAME ________________________________________ DATE ______________ PERIOD _____
1-10
Practice
6AF1.1
Solving Multiplication and Division Equations
Solve each equation. Check your solution.
1. 5s 45
2. 8h 64
3. 36 9b
4. 3p 24
5. 12m 72
6. 56 7d
x
7. 11
5
v
8. 20
4
c
9. 43
2
y
10. 16 3
n
11. 9 8
a
12. 3
25
14. POPULATION The population of South Africa is four times the population of Greece. If
the population of South Africa is 44 million, write and solve a multiplication equation to
find the population of Greece.
MEASUREMENT For Exercises 15 and 16, refer to the table. Write and
solve an equation to find each quantity.
Customary System
15. the number of quarts in 24 pints
Conversions (capacity)
1 pint 2 cups
1 quart 2 pints
1 quart 4 cups
16. the number of gallons in 104 pints
1 gallon 4 quarts
1 gallon 8 pints
Solve each equation.
84
17. 3 g
Chapter 1
4
18. 8
x
144
19. 16
r
67
Glencoe California Mathematics, Grade 7
Lesson
Lesson 1-10
X–4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
13. CARS Mrs. Alvarez bought a new car. Her monthly payments are $525. If she will pay a
total of $25,200 in payments, write and solve a multiplication equation to find the
number of payments.
NAME ________________________________________ DATE ______________ PERIOD _____
1-10
Word Problem Practice
6AF1.1
1. WAGES Felipe earns $9 per hour for
helping his grandmother with her yard
work. Write and solve a multiplication
equation to find how many hours he
must help his grandmother in order to
earn $54.
2. SHOPPING Granola bars are on sale
for $0.50 each. If Brad paid $5 for
granola bars, write and solve a
multiplication equation to find how
many bars he bought.
3. EXERCISE Jasmine jogs 3 miles each day.
Write and solve a multiplication
equation to find how many days it will
take her to jog 57 miles.
4. TRAVEL On a trip, the Rollins family
drove at an average rate of 62 miles per
hour. Write and solve a multiplication
equation to find how long it took them
to drive 558 miles.
5. ROBOTS The smallest robot can travel
20 inches per minute through a pipe.
Write and solve a multiplication
equation to find how long it will take
this robot to travel through 10 feet of
pipe.
6. BANKING Nate withdraws $40 from his
checking account each day. Write and
solve a multiplication equation to find
how long it will take him to withdraw
$680.
7. AGE The product of Bart’s age and 26 is
338. Write and solve a multiplication
equation to find Bart’s age.
8. POPULATION The population of a small
town is increasing at a rate of 325
people per year. Write and solve a
multiplication equation to find how
long it will take the population to
increase by 6,825.
Chapter 1
68
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Solving Multiplication and Division Equations
NAME ________________________________________ DATE ______________ PERIOD _____
1-10
Enrichment
7AF1.1
Consecutive Integers
Equations can be used to solve problems that involve consecutive integers. In
solving these problems, you will need to translate certain phrases into
algebraic expressions. Here are some examples.
Phrase A
“five consecutive integers”
Expression A n, n 1, n 2, n 3, n 4
Phrase B
“five consecutive even integers”
Expression B n, n 2, n 4, n 6, n 8
Phrase C
“five consecutive odd integers”
Expression C n, n 2, n 4, n 6, n 8
Use Expressions A, B, and C for these problems.
1. What five consecutive integers does Expression A produce when n 8?
3. What five consecutive odd integers does Expression C produce when
n 9?
Write an equation to solve each problem.
4. Find the three consecutive integers that have a sum of 12.
5. Find the four consecutive odd integers with a sum of 80.
6. The larger of two consecutive even integers is 6 less than 3 times the
smaller. Find the integers.
7. Find four consecutive even integers such that the largest is twice the
smallest.
Chapter 1
69
Glencoe California Mathematics, Grade 7
Lesson
Lesson 1-10
X–4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2. What five consecutive even integers does Expression B produce when
n 0?
NAME ________________________________________ DATE ______________ PERIOD _____
1
Student Recording Sheet
Use this recording sheet with pages 80-81 of the Student Edition.
Read each question. Then fill in the
correct answer.
1.
A
B
C
D
2.
F
G
H
J
3.
A
B
C
D
4.
F
G
H
J
5.
A
B
C
D
6.
F
G
H
J
7.
A
B
C
D
8.
F
G
H
J
9.
A
B
C
D
10.
F
G
H
J
11.
A
B
C
D
Pre-AP
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Assessment
Record your answers for Question 12 on
the back of this paper.
Chapter 1
71
Glencoe California Mathematics, Grade 7
NAME ________________________________________ DATE ______________ PERIOD _____
1
Rubric for Scoring Pre-AP
(Use to score the Pre-AP question on page 81 of the Student Edition.)
General Scoring Guidelines
• If a student gives only a correct numerical answer to a problem but does not show how he or she
arrived at the answer, the student will be awarded only 1 credit. All extended response questions
require the student to show work.
• A fully correct answer for a multiple-part question requires correct responses for all parts of the
question. For example, if a question has three parts, the correct response to one or two parts of the
question that required work to be shown is not considered a fully correct response.
• Students who use trial and error to solve a problem must show their method. Merely showing that
the answer checks or is correct is not considered a complete response for full credit.
Exercise 12 Rubric
Specific Criteria
4
The values n 1, r 0, and t 4 are correctly determined. Explanations are correct
with properties correctly listed.
3
The values are correctly determined, but the explanations are not complete.
2
Two of the values and explanations are correct and the other value is not correct.
OR
The values and explanations are correct, but the properties are not named correctly.
1
Only one of the values and explanations is correct. OR
The values are correct, but there are no explanations.
0
Response is completely incorrect. OR
One or more of the values are correct, but the procedures are completely incorrect.
Chapter 1
72
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Score
NAME ________________________________________ DATE ______________ PERIOD _____
1
Chapter 1 Quiz 1
SCORE _____
(Lessons 1-1, 1-2, and 1-3)
Use the four-step plan to solve the problem.
1. SCHOOL SUPPLIES At the school store, a pencil costs $0.24,
and an eraser costs $0.18. What combination of pencils and
erasers could you buy for exactly $0.66?
1.
Evaluate each expression if x 4, y 2, and z 5.
2. 3x z
2.
3. 2(4 y) xz
3.
4. |6| |2|
4.
5. |15 6|
5.
NAME ________________________________________ DATE ______________ PERIOD _____
1
SCORE _____
Chapter 1 Quiz 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
(Lessons 1-4 and 1-5)
Add.
1. 10 6
1.
2. 32 (5)
2.
3. 17 (16)
3.
4. 9 (11) 2
4.
Subtract.
5. 9 12
5.
6. 11 2
6.
7. 15 (7)
7.
8. 8 (4)
8.
Evaluate each expression if a 6, b 15, and c 2.
9. |b| a
9.
10. a b c
10.
Chapter 1
73
Glencoe California Mathematics, Grade 7
Assessment
Evaluate each expression.
NAME ________________________________________ DATE ______________ PERIOD _____
1
Chapter 1 Quiz 3
SCORE _____
(Lessons 1-6 and 1-7)
Multiply or divide.
1. 6(4)
1.
2. 5(7)
2.
3. 50 2
3.
4. 27 (3)
4.
Evaluate each expression if x 7, y 1, and z 3.
xz
5. 5.
6. 10 xy
6.
2
Write each verbal phrase as an algebraic expression.
7. the sum of a number and 5
7.
8. $3 more than the other CD cost
8.
Write each verbal sentence as an algebraic equation.
9.
10. $15 less than the amount he spent is $12.50.
10.
NAME ________________________________________ DATE ______________ PERIOD _____
1
Chapter 1 Quiz 4
SCORE _____
(Lessons 1-8, 1-9, and 1-10)
Solve each equation. Check your solution.
1. x 9 11
1.
2. m 6 15
2.
3. k 2
3.
4. 72 6w
4.
14
5. MONEY During the school week, Joshua spent $3 each day
on lunch. On Tuesday, he bought a $5 ticket to the school play
and on Friday he loaned $2 to his friend. When he checked
his wallet at the end of the day Friday, he had $3 left. How
much money did he start the week with?
5.
Chapter 1
74
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9. 9 more than a number is equal to 24.
NAME ________________________________________ DATE ______________ PERIOD _____
1
Chapter 1 Mid-Chapter Test
SCORE _____
(Lessons 1-1 through 1-5)
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1. Evaluate 32 5 6 3.
A. 22
B. 28
C. 16
D. 19
1.
2. Evaluate |x| y if x 3 and y 4.
F. 7
G. 1
H. 1
J. 7
2.
3. Find 15 (12).
A. 27
B. 27
C. 3
D. 3
3.
4. Find 9 (5).
F. 4
H. 14
J. 4
4.
5. Name the property shown by the statement (x 9) 0 x 9.
A. Commutative ()
C. Distributive
B. Associative ()
D. Identity ()
5.
G. 14
6. Graph the set of integers {2, 2, 4, 0, 1} on a number line.
6.
7. Evaluate a b c if a 7, b 2, and c 6.
7.
8. GAMES During a card game, you give someone 5 cards,
then someone else gives you 7 cards. Write an addition
statement to describe this situation. Then find the sum.
8.
9. Draw the next two figures in the pattern below.
9.
10. FIELD TRIP Two classes are going on a field trip. The first
class has 27 students and 9 adults. The second class has
33 students and 11 adults. If one bus holds 42 people, how
many buses are needed for this field trip?
Chapter 1
75
4 3 2 1 0 1 2
10.
Glencoe California Mathematics, Grade 7
Assessment
Write the letter for the correct answer in the blank at the right of each question.
NAME ________________________________________ DATE ______________ PERIOD _____
1
Chapter 1 Vocabulary Test
absolute value
additive inverse
algebra
algebraic expression
conjecture
coordinate
counterexample
defining a variable
SCORE _____
equation
evaluate
inequality
integer
inverse operations
negative number
numerical expression
opposites
order of operations
positive number
property
powers
solution
solve
variable
1. Operations that "undo" each other are called __________.
1.
2. On a number line, the number that corresponds to a point is
called the __________ of that point.
2.
3. The distance between a number and 0 on a number line is
called the __________ of that number.
3.
4. A number less than 0 is a(n) __________.
4.
5. A statement that shows that a conjecture is false is
a(n) __________.
5.
6. An integer and its opposite are __________.
6.
7. Expressions that represent repeated multiplication are
called _________.
7.
8. The values of the variable that make an equation true are
called the _________ of the equation.
8.
9. When you find the numerical value of an expression, you
__________ the expression.
9.
10. A sentence containing the symbol is called a(n) __________. 10.
Define each term in your own words.
11. conjecture
12. property
Chapter 1
76
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Choose from the terms above to complete each sentence.
NAME ________________________________________ DATE ______________ PERIOD _____
1
Chapter 1 Test, Form 1
SCORE _____
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1. EXERCISE Every 5 days Alma rides her skateboard in the park. Every 4
days she bikes to her best friend’s house. How often does Alma do both?
A. every 10 days B. every 20 days C. every 4 days
D. every 5 days
1.
2. Evaluate the expression 2(9) 6 3.
F. 14
G. 2
H. 4
J. 16
2.
3. Evaluate the expression 2y x if x 4 and y 2.
A. 10
B. 12
C. 8
D. 14
3.
4. Name the property shown by the statement (2 6) 19 2 (6 19).
F. Commutative ()
H. Distributive
G. Associative ()
J. Identity ()
4.
5. Which of the following statements is true?
A. 7 1
B. 5 2
C. 3 0
D. 6 4
5.
6. Evaluate the expression |10||3|.
F. 7
G. 7
H. 13
J. 13
6.
7. Find 6 (21).
A. 15
B. 27
C. 15
D. 27
7.
8. Find 9 (15).
F. 6
G. 24
H. 24
J. 6
8.
9. BOOKS Marcos had 8 library books. Today he returned 3 books and
checked out 5 more. How many library books does Marcos have now?
A. 11
B. 7
C. 6
D. 10
9.
10. Find 8 12.
F. 4
G. 20
H. 4
J. 20
10.
11. Find 4 (9).
A. 5
B. 13
C. 13
D. 5
11.
Chapter 1
77
Glencoe California Mathematics, Grade 7
Assessment
Write the letter for the correct answer in the blank at the right of each question.
NAME ________________________________________ DATE ______________ PERIOD _____
1
Chapter 1 Test, Form 1
(continued)
12. Evaluate b a if a 7 and b 15.
F. 22
G. 8
H. 8
J. 22
12.
13. Find 2(7).
A. 14
B. 14
C. 9
D. 9
13.
14. Find 24 4.
F. 6
G. 6
H. 20
J. 20
14.
15. a number decreased by 9
A. 9 n
B. 9 n
C. 9n
D. n 9
15.
16. the sum of a number and 6
F. 6n
G. n
H. n (6)
J. n (6)
16.
6
17. SCHOOL DAY Winter Middle School must end at 3:00 P.M. for the buses.
There needs to be 5 hours for classes, 45 minutes for lunch, 10 minutes
for daily announcements, 25 total minutes for changing classes, and 1
2
hour for assemblies. What time does Winter Middle School need
to start in the morning?
A. 8:10 A.M.
B. 8:00 A.M.
C. 9:50 A.M.
D. 8:50 A.M.
17.
Solve each equation. Check your solution.
18. m 9 21
F. 12
G. 12
H. 30
J. 30
18.
19. 34 d 6
A. 28
B. 40
C. 28
D. 40
19.
20. 2r 46
F. 23
G. 23
H. 48
J. 46
20.
Bonus Draw the next two figures in the pattern below.
Chapter 1
78
B:
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Write each verbal phrase as an algebraic expression.
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 1 Test, Form 2A
1
SCORE _____
1. ENROLLMENT Use the information
in the table about enrollment at
South Middle School.
How many more 7th graders attended
South Middle School during the
2001–2002 school year than during
the 2005–2006 school year?
A. 23
B. 48
2. Evaluate 32 16 4 2.
F. 1
G. 7
School Year
Number of 7th Graders
2001–2002
2002–2003
2003–2004
2004–2005
2005–2006
164
189
195
155
141
C. 9
D. 57
1.
H. 17
J. 4
2.
3. Name the property shown by the statement (7 9)3 7(3) 9(3).
A. Commutative (
)
C. Distributive
B. Associative (
)
D. Identity (
)
3.
4. Graph the set of integers {5, 7, 2, 3} on a number line.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
F.
G.
7 6 5 4 3 2 1 0 1 2
3
3 2 1 0 1 2 3 4 5 6 7
H.
J.
7 6 5 4 3 2 1 0 1 2
3
3 2 1 0 1 2 3 4 5 6 7
4.
5. Evaluate |15||11|.
A. 26
B. 26
C. 4
D. 4
5.
6. Find 9 (3) 7.
F. 19
G. 13
H. 5
I. 1
6.
7. Find 15 (4).
A. 19
C. 11
D. 11
7.
8. Evaluate a b if a 10 and b 6.
F. 4
G. 16
H. 16
J. 4
8.
9. Find 3(2)(5).
A. 25
B. 25
C. 30
D. 30
9.
G. 5
H. 48
J. 48
B. 19
60
10. Find .
12
F. 5
Chapter 1
79
10.
Glencoe California Mathematics, Grade 7
Assessment
Write the letter for the correct answer in the blank at the right of each question.
NAME ________________________________________ DATE ______________ PERIOD _____
1
Chapter 1 Test, Form 2A
(continued)
11. Evaluate x 2y if x 3 and y 5.
A. 1
B. 2
C. 13
D. 7
11.
J. c
12.
D. 16 n 2
13.
12. Write 15 more dogs than cats as an algebraic expression.
F. c 15
G. c 15
H. 15c
15
Write each verbal sentence as an algebraic equation.
13. 16 is twice a number.
A. 16 2 n
B. 16 n
2
C. 16 2n
14. $20 less than the amount Josh earned is $6.50.
F. a 20 6.50
H. 20a 6.50
G. 20 a 6.50
J. a 20 6.50
14.
15. p 13 8
A. 5
B. 21
C. 5
D. 21
15.
16. 42 m 10
F. 52
G. 32
H. 52
J. 32
16.
17. 39 3x
A. 42
B. 36
C. 117
D. 13
17.
G. 5
H. 50
J. 20
18.
D. 30
19.
20. SHOPPING Jordan has $50 to spend on a new pair of jeans. He saves
$10 with a coupon. After he pays $2 in sales tax, he receives $23 in
change. What was the original price of the jeans?
F. $27
G. $35
H. $38
J. $31
20.
18. c 10
5
F. 2
Write and solve an equation to find each number.
19. If you increase a number by 45, the result is 15.
A. 3
B. 3
C. 30
Bonus Evaluate |x2 y2|3 if x 4 and y 6.
Chapter 1
80
B:
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Solve each equation. Check your solution.
NAME ________________________________________ DATE ______________ PERIOD _____
1
Chapter 1 Test, Form 2B
SCORE _____
Write the letter for the correct answer in the blank at the right of each question.
1. READING Use the information
in the table about the number
of books Tyrone has read.
How many more books did Tyrone
read during the first year than
during the last year?
A. 10 books
C. 1 books
B. 36 books
D. 5 books
Number of Books
2002
2003
2004
2005
2006
15
21
18
25
10
1.
H. 5
J. 4
3. Name the property shown by the statement 2 7 7 2.
A. Commutative (
)
C. Distributive
B. Associative (
)
D. Identity (
)
2.
3.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. Graph the set of integers {0, 2, 4, 1} on a number line.
F.
H.
5 4 3 2 1 0 1 2 3 4 5
G.
5 4 3 2 1 0 1 2 3 4 5
5 4 3 2 1 0 1 2 3 4 5
J.
5 4 3 2 1 0 1 2 3 4 5
4.
5. Evaluate |16| |5|.
A. 21
B. 11
C. 21
D. 11
5.
6. Find 10 6 (3).
F. 1
G. 7
H. 7
J. 1
6.
7. Find 12 (8).
A. 20
C. 4
D. 20
7.
8. Evaluate c d if c 7 and d 3.
F. 4
G. 10
H. 4
J. 10
8.
9. Find 5(4)(8).
A. 8
9.
B. 4
B. 160
C. 160
D. 8
G. 13
H. 56
J. 48
52
10. Find .
4
F. 13
Chapter 1
81
10.
Glencoe California Mathematics, Grade 7
Assessment
2. Evaluate 42 (8 6) 9.
F. 13
G. 17
Year
NAME ________________________________________ DATE ______________ PERIOD _____
1
Chapter 1 Test, Form 2B
(continued)
11. Evaluate 3m n if m 2 and n 1.
A. 2
B. 5
C. 5
D. 7
11.
J. m
12.
12. Write half of Latisha’s markers as an algebraic expression.
F. m 2
G. m 2
H. 2m
2
Write each verbal sentence as an algebraic equation.
13. 12 birds is 3 more birds than Rhonda saw yesterday.
A. 12 3b
C. 12 b 3
D. 12 b
H. 92 4 n
J. 92 n
14.
B. 12 3 b
13.
3
14. 92 is the product of 4 and a number.
F. 92 4 n G. 92 4n
4
15. r 15 7
A. 8
B. 22
C. 22
D. 8
15.
16. 25 n 10
F. 35
G. 35
H. 15
J. 15
16.
17. 3c 45
A. 48
B. 42
C. 15
D. 15
17.
18. 54 2m
F. 27
G. 27
H. 56
J. 52
18.
D. 2
19.
Write and solve an equation to find each number.
19. The difference of a number and 9 is 18.
A. 9
B. 9
C. 2
20. MONEY Phillip received money from his grandmother for his birthday.
He put half in the bank for savings and bought two $15 CDs. Later that
day, Phillip’s sister gave him $5 that she owed him. At the end of the day
Phillip had $25 left. How much money did his grandmother give him
for his birthday?
F. $120
G. $90
H. $100
J. $50
Bonus Two more than the opposite of a number is 3.
Use an equation to find the number.
Chapter 1
82
20.
B:
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Solve each equation. Check your solution.
NAME ________________________________________ DATE ______________ PERIOD _____
1
Chapter 1 Test, Form 2C
SCORE _____
1. FISH When Maria filled her fish tank the water was
12 inches deep. One week later she noticed that the water
was 10.5 inches deep, and after another week it was
9 inches deep. How deep will the water be after one more
week?
1.
2. 42 5 4 2
2.
54
3. 3
3.
4. |18|
4.
5. |14 9|
5.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2 1
Evaluate each expression if a 5, b 2, c 4, and
d 2.
6. 3b a
6.
7. b c d
7.
8. d c
8.
9. ab cd
9.
100
10. 10.
11. bcd
11.
ac
Add or subtract.
12. 19 9
12.
13. 5 (16)
Chapter 1
13.
83
Glencoe California Mathematics, Grade 7
Assessment
Evaluate each expression.
NAME ________________________________________ DATE ______________ PERIOD _____
1
Chapter 1 Test, Form 2C
(continued)
14. 7 7
14.
15. 12 (5)
15.
For Questions 16-19, multiply or divide.
16. 4(7)
16.
17. 5(2)(4)
17.
18. 32 4
18.
54
19. 19.
20. Write the sum of a number and 16 as an algebraic
expression.
20.
21. AGE Susan was 11 when her family moved into the house she
still lives in. That was 82 years ago. If the year is now 2006,
what year was Susan born?
21.
Solve each equation. Check your solution.
22. g 7 9
22.
23. 12 z 16
23.
24. 8x 96
24.
p
5
25. 10
25.
Bonus Evaluate 5{32 4[8 (23 18 2 3)]}.
Chapter 1
84
B:
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9
NAME ________________________________________ DATE ______________ PERIOD _____
1
Chapter 1 Test, Form 2D
SCORE _____
1. SHOPPING At the grocery store, a cucumber costs $0.33, and
a green pepper costs $0.52. What combination of cucumbers
and green peppers could you buy for exactly $5.00?
1.
2. 23 4 5 10
2.
69
3. 2
3.
4. |12|
4.
5. |6| |2|
5.
3 6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Evaluate each expression if w 2, x 4, y 3, and z 5.
6. x 2y
6.
7. x y z
7.
8. z w
8.
9. 3w x
9.
xyw
10. 12
10.
11. 4wz
11.
Add or subtract.
12. 27 (9)
12.
13. 8 (10)
13.
Chapter 1
85
Glencoe California Mathematics, Grade 7
Assessment
Evaluate each expression.
NAME ________________________________________ DATE ______________ PERIOD _____
1
Chapter 1 Test, Form 2D
(continued)
14. 12 10
14.
15. 5 (11)
15.
16. 8(10)
16.
17. 4(7)(5)
17.
18. 48 (6)
18.
72
19. 19.
20. Write 14 less than a number as an algebraic expression.
20.
9
21. SUMMER JOB Jonah mows lawns in the summer. In the past
three years he has averaged, 13, 6, and 12 lawns a week. What
is the minimum number of lawns he must mow per week on
average this summer in order to maintain an average of
10 lawns a week each summer?
21.
Solve each equation. Check your solution.
22. m 12 10
22.
23. 2 x 9
23.
24. 7y 91
24.
25. a 36
25.
4
bh
Bonus If A , write an expression for the value of h.
2
Chapter 1
86
B:
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
For Questions 16-19, multiply or divide.
NAME ________________________________________ DATE ______________ PERIOD _____
1
Chapter 1 Test, Form 3
SCORE _____
Use the four-step plan to solve each problem.
1. MONEY Kenji earned $40 mowing lawns last week. He
wants to use his money to buy 4 videos that cost $9.99,
$12.95, $6.75, and $10.39. Does he have enough money to
purchase the videos?
1.
2. (30 18)(24 6)
2.
3. 5[24 (9 3) 4]
3.
For Questions 4-7, evaluate each expression if a 5, b 2,
c 3, and d 4.
a2 9
4. 2
4.
5. |c| d a
5.
6. 10 cd
6.
7. 5(7 2c)2
7.
8. Order the integers in the set {15, 2, 26, 25, 3} from least
to greatest.
8.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
b
Add or subtract.
9. 10 5 (12)
9.
10. 35 (57)
10.
11. 16 (13)
11.
12. 8 |19|
12.
Chapter 1
87
Glencoe California Mathematics, Grade 7
Assessment
Evaluate each expression.
NAME ________________________________________ DATE ______________ PERIOD _____
1
Chapter 1 Test, Form 3
(continued)
For Questions 13–16, multiply or divide.
13. (3)4
13.
14. 5(2)3
14.
156
15. 15.
16. 78 (6)
16.
17. Find the mean of the set of integers {21, 17, 15, 25, 19}.
17.
13
18. 29 fewer points scored today than were scored yesterday
18.
19. the sum of a number and 12
19.
Write each verbal sentence as an algebraic equation.
20. 4 less than the opposite of a number is 10.
20.
21. GRADES Elena has scored an 87, a 93, and an 86 on her last
three math tests. What is the minimum score she must
make on her fourth, and final test, in order to maintain a
90 average for her math tests?
21.
Solve each equation. Check your solution.
22. 45 19 d
22.
23. x (3) 9
23.
24. t 15
24.
25. 17m 272
25.
7
h(a b)
Bonus If A , write an expression for the value of a.
2
Chapter 1
88
B:
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Write each verbal phrase as an algebraic expression.
NAME ________________________________________ DATE ______________ PERIOD _____
1
Chapter 1 Extended-Response Test
SCORE _____
Demonstrate your knowledge by giving a clear, concise solution to each problem.
Be sure to include all relevant drawings and justify your answers. You may show
your solution in more than one way or investigate beyond the requirements of the
problem. If necessary, record your answer on another piece of paper.
1. Theo has scores of 76, 87, 82, 91, and 79 on his first five math tests.
a. Explain how to find the average of Theo’s test scores. Then find the
average.
b. Graph Theo’s five test scores and his average score on a number line.
c. Find the difference between Theo’s first test score and his average test
score. Find the difference between each of his other four scores and his
average in the order that the scores are listed.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
e. Find the sum of the differences that you found in part c.
2. Tiffany has forgotten her score on the first test but remembers that her
remaining scores are 85, 73, 87, and 84. Furthermore, Theo’s average
score is three more than Tiffany’s average score.
a. Write and solve an addition equation relating Theo’s average to
Tiffany’s average. Use your result from Exercise 1a for Theo’s average.
What does the solution represent?
b. Let s represent the sum of Tiffany’s five test scores. The sum of
Tiffany’s five scores divided by 5 is equal to her average score. Write
and solve a division equation to find the value of s.
c. Let m represent the missing score. Find the sum of Tiffany’s four
known test scores. The sum of m and the number that you just found
is equal to the value of s that you found in part b. Write and solve an
addition equation to find the missing score.
d. Subtract Tiffany’s average score from each of her five test scores. Start
with the score you found in part b. List the five differences. Then find
their sum.
e. Compare the sums you found in part c with the sum you found in
Exercise 1e. Then make a conjecture about the sum of the differences
between a student’s actual test scores and average score.
Chapter 1
89
Glencoe California Mathematics, Grade 7
Assessment
d. Describe in at least two different ways the test scores for which the
differences you found in part c are negative.
NAME ________________________________________ DATE ______________ PERIOD _____
1
Standardized Test Practice
SCORE _____
(Chapter 1)
Part 1: Multiple Choice
Instructions: Fill in the appropriate circle for the best answer.
1. Evaluate 42 5 2 6 3. (Lesson 1-2)
A 40
B 24
C 16
D 12
1.
A
B
C
D
2.
F
G
H
J
D 15
3.
A
B
C
D
4. Which is in order from least to greatest? (Lesson 1-3)
F 15, 11, 5, 1, 6
H 6, 1, 5, 11, 15
G 1, 6, 5, 11, 15
J 1, 5, 6, 11, 15
4.
F
G
H
J
5. Which is in order from least to greatest? (Lesson 1-3)
A 15, 9, 1
C 5, 2, 1, 10
B 6, 4, 1
D 1, 0, 4, 6
5.
A
B
C
D
6. Find 16 (13). (Lesson 1-4)
F 29
G 3
H 3
J 29
6.
F
G
H
J
7. Find 8 (19) (Lesson 1-4)
A 27
B 11
C 11
D 27
7.
A
B
C
D
8. Find 6 (15) (Lesson 1-5)
F 21
G 9
J 21
8.
F
G
H
J
9.
A
B
C
D
10.
F
G
H
J
11.
A
B
C
D
2. Which equation is an example of the Distributive Property?
F 5(4 2) 5(4) 5(2)
G 8 (9 7) (8 9) 7
H (21 9) 3 3 (21 9)
J 1 2x 2x
3. Evaluate 52 3 · 4 (6 4) (Lesson 1-2)
A 7
B 10
C 11
H 9
9. TEMPERATURE At 4:00 A.M. the temperature was 2°F. At
1:00 P.M. the temperature was 15°F. How much did the
temperature change? (Lesson 1-5)
A 17°
B 13°
C 13°
D 17°
10. Find the mean of the set of integers {10, 6, 11, 8, 12, 7}.
(Lesson 1-6)
F 9
G 6
H 1
J 9
11. Sophia is 4 inches shorter than Maya. If Maya is x inches tall,
which expression represents Sophia’s height? (Lesson 1-7)
A 4x
B 4x
C. x 4
D x4
Chapter 1
90
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
(Lesson 1-2)
NAME ________________________________________ DATE ______________ PERIOD _____
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
(continued)
12. Kevin has two dogs. Spot is 5 years older than Tucker.
If S Spot’s age, which expression can be used to find
Tucker’s age? (Lesson 1-7)
F S5
H S5
G 5 S
J 5
S
12.
F
G
H
J
13. The sum of a number and 17 is 32. Which equation can be used
to to find the number. (Lesson 1-8)
A n 17 32
C 17 32 n
B n 17 32
D 32 17 n
13.
A
B
C
D
14. 45 is 16 more than a number. Which equation can be used to
find the number? (Lesson 1-9)
F y (45) 16
H y 45 16
G y 16 45
J 45y 16
14.
F
G
H
J
15. Solve t (7) 7 (Lesson 1-9)
A 14
C 14
B 0
D 49
15.
A
B
C
D
16. Solve c 16. (Lesson 1-9)
4
F 64
G 20
H 12
J 4
16.
F
G
H
J
17. Solve 5n 85. (Lesson 1-9)
A 90
C 17
B 80
D 425
17.
A
B
C
D
H 3
J 11
18.
F
G
H
J
C 1.5
D 54
19.
A
B
C
D
18. Evaluate |r s| if r 7 and s 4.
F 11
G 3
19. Solve
x
6
A 54
B 1.5
Chapter 1
9.
91
Glencoe California Mathematics, Grade 7
Assessment
Standardized Test Practice
1
NAME ________________________________________ DATE ______________ PERIOD _____
1
Standardized Test Practice
(continued)
Part 2: Short Response
Instructions: Write your answers below or to the right of the questions.
20. Evaluate 52 3 2 (9 4) (Lesson 1-2)
20.
21. Order the integers in the set {14,3,10, 1,1}
from least to greatest. (Lesson 1-3)
21.
4a
22. Evaluate if a 6 and b 2. (Lesson 1-6)
b
23. AGE Maria is 4 years older than Samantha. Define a
variable and write an expression for Maria’s age. (Lesson 1-7)
23.
24. The sum of a number and 12 is 6. Write and solve an
equation to find the number. (Lesson 1-8)
24.
Solve the following equation.
r
25. 5 (Lesson 1-10)
3
25.
26. Consider the set of integers {3, 0, 1, 2}. (Lessons 1-3)
a. Graph the set on a number line.
26a.
b. Explain how you can use a number line to order the
numbers from least to greatest.
26b.
c. Order the numbers from least to greatest.
Chapter 1
92
26c.
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
22.
Chapter 1
Before you begin Chapter 1
Algebra: Integers
Anticipation Guide
A1
D
A
D
A
A
D
D
A
A
D
A
3. According to the Order of Operations, all operations within
grouping symbols must be completed first.
4. According to the Order of Operations, all addition and
subtraction should be done before multiplication and division.
5. The Commutative Property is true only for addition and
multiplication.
6. Negative integers can be used to express values less than zero.
7. When comparing two negative integers, the greater integer is
the one with the greater absolute value.
8. The sum of a positive integer and a negative integer is always
negative.
9. When subtracting a negative integer, add its opposite.
10. The product of two negative integers is always positive.
11. The quotient of two negative integers is always negative.
12. Any letter can be used to represent an unknown in an
expression or equation.
After you complete Chapter 1
D
2. Algebraic expressions are any mathematical expressions that
contain at least one operation symbol.
Chapter 1
STEP 2
A or D
1. A conjecture is a statement proven to be true.
Statement
7
Glencoe California Mathematics, Grade 7
Answers
Glencoe California Mathematics, Grade 7
• Reread each statement and complete the last column by entering an A or a D.
• Did any of your opinions about the statements change from the first column?
• For those statements that you mark with a D, use a piece of paper to write an
example of why you disagree.
Step 2
STEP 1
A, D, or NS
• Read each statement.
• Decide whether you Agree (A) or Disagree (D) with the statement.
• Write A or D in the first column OR if you are not sure whether you agree or disagree,
write NS (Not Sure).
Step 1
1
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter Resources
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A Plan for Problem Solving
Lesson Reading Guide
7MR1.1, 6AF2.3
Chapter 1
9
Glencoe California Mathematics, Grade 7
7. Early problem solvers care is a mnemonic aid to remember the first
letters of the steps in the problem-solving plan. Write a mnemonic aid of
your own using the first letters of the steps. See students’ work.
Remember What You Learned
has the fastest top speed.
6. Look at the graph in Example 2 on page 26. Explain how the animals in
the chart are listed. Why is the cheetah first? In order of speed; it
The amount when two quantities are subtracted; since 1
minute 60 seconds, multiply the 1 second distance by 60.
5. Look at the Explore section in Example 2 on page 26. What does the word
“difference” mean? Now read the Plan section. Explain how to find the
distance traveled in 1 minute when you know the distance per second.
first blue tile; 18 is the number of additional white tiles
needed for 9 additional blue tiles.
4. Read the Check section in Example 1 at the bottom of page 25. In the
equation 8 18 26, what does the 8 stand for? What does the 18 stand
for? 8 is the number of white tiles needed to surround the
Read the Lesson
white tiles is two more than the last number of white tiles, so
Garden 6 would need 8 5(2) or 18 tiles.
3. How many tiles will it take to border a garden that is 6 tiles long?
Explain your reasoning. 18; Sample answer: The number of
2. Predict how many white tiles it will take to border the next-largest
garden. Check your answer by modeling the garden. 14;
Garden 1: 8; Garden 2: 10; Garden 3: 12
1. How many white tiles does it take to border each of these three gardens?
Complete the Mini Lab at the top of page 24 in your textbook.
Write your answers below.
Get Ready for the Lesson
1-1
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Anticipation Guide and Lesson 1-1)
Lesson 1–1
Chapter 1
A Plan for Problem Solving
Study Guide and Intervention
Solve the problem by carrying out your plan.
Examine your answer to see if it seems reasonable.
Solve
Check
36
7
40
42
8
44
45
9
A2
Comparing each plant’s heights on consecutive days, we see that
Plant A’s height increases by 3 millimeters each day, while
Plant B’s height increases by 4 millimeters each day. To estimate
Plant A’s height on day 12, assume that it will grow 3 millimeters
each day past day 10, so it will be 51 3 3 or 57 millimeters. To
estimate Plant B’s height on day 12, assume that it will grow
4 millimeters each day past day 10, so it will be 52 4 4 or
60 millimeters.
Given what we know about each plant’s height and how plants
grow in general, both estimates seem reasonable.
Solve
Check
Chapter 1
Glencoe California Mathematics, Grade 7
Glencoe California Mathematics, Grade 7
52
51
10
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10
2. FLOUR BEETLES The population of a flour beetle doubles in about a week.
How long would it take for the population to grow to eight times its
original size? 3 wk
1. MOVIES A movie ticket costs $3.50. A large popcorn costs $3.75 and a
large soda costs $3.00. How much will it cost two friends to go to a movie
if they share a popcorn and each has a large soda? $16.75
Use the four-step plan to solve each problem.
Exercises
Determine whether there is a pattern and extend that pattern to
day 12.
You know their heights for days 5 to 10. You need to determine
their heights in two more days.
48
48
Plan
Explore
32
Plant B
6
39
Estimate the height of each plant on day 12.
5
36
Day
Plant A
Plant A and Plant B are two new experimental apple trees being
grown in a laboratory. The table displays their heights, in
millimeters, when they are 5 to 10 days old.
Select a strategy including a possible estimate.
Plan
Example 1
Determine what information is given in the problem and what you need to find.
7MR1.1, 6AF2.3
Explore
You can always use the four-step plan to solve a problem.
1-1
NAME ________________________________________ DATE ______________ PERIOD _____
A Plan for Problem Solving
Skills Practice
7MR1.1, 6AF2.3
Chapter 1
10.
9.
11
Glencoe California Mathematics, Grade 7
Draw the next two figures in each of the patterns below.
8. 1024, 256, 64, 16, 4 The numbers are divided by 4; 1.
7. 1860, 1890, 1920, 1950, 1980 The numbers increase by 30; 2010.
Find a pattern in the list of numbers. Then find the next number in
the list.
6. GUPPIES In January, Tate’s fish tank had 12 guppies. In February, it had
18, and in March it had 24. How many guppies do you expect to be in
Tate’s fish tank in May? 36 guppies
23 pizzas
5. PIZZA The Chess Club sold 2,116 pizzas during a fundraiser that lasted
for all of March, April, and May. How many pizzas did they sell per day?
4. PRODUCE At the local grocery store, lemons are 52 cents each and limes
are 21 cents each. How many lemons and limes can you buy for exactly
$3.75? 6 lemons and 3 limes
3. EXERCISE Trevor jogs every 3 days and swims every 4 days. How often
does he jog and swim on the same day? every 12 days
2. FIELD TRIP A school policy requires that there be at least one chaperone
for every 8 students on a field trip. How many chaperones are required
for a field trip with 67 students? 9 chaperones
1. GAS MILEAGE Each day Ernesto drives 52 miles. If he can drive 26 miles
on one gallon of gasoline, how many days can he drive on 14 gallons of
gasoline? 7 days
Use the four-step plan to solve each problem.
1-1
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-1)
Lesson 1–1
Chapter 1
A Plan for Problem Solving
Practice
$13.79
$14.59
$15.39
2
3
4
A3
Chapter 1
12
6. GEOMETRY Draw the next two figures in the pattern.
3 paint brushes and 2 bottles of paint
Glencoe California Mathematics, Grade 7
Answers
Glencoe California Mathematics, Grade 7
5. ART SUPPLIES At the craft store, a paint brush costs $0.79, and a small
bottle of paint costs $0.89. What combination of paint brushes and bottles
of paint could you buy for exactly $4.15?
4. GEOGRAPHY The land area of Washington, D.C., is 61 square miles. In
2003, the population of Washington, D.C., was 563,384. If one square mile
is equal to 640 acres, about how many people per acre were there in
Washington, D.C., in 2003? About 14 people per acre
3. SPORTS The track coach must buy at least two bottles of water for each
participant in a track meet. One team has 35 members, and the other
team has 28 members. If each case of water contains 24 bottles, what is
the fewest number of full cases that the coach can buy? 6 cases
$28
Price
$12.99
1
Toppings
7MR1.1, 6AF2.3
2. MOVIES Mr. Sedgwick paid $13 for one adult ticket and one child ticket
for a movie. Mrs. Wong paid $18 for one adult ticket two child tickets to
see the same movie, and Mr. Gomez paid $23 for one adult ticket and
three child tickets. If the pattern continues, how much should Mrs.
Beauregard expect to pay for one adult ticket and four child tickets?
1. FOOD The table shows a portion of the price list for
a local pizzeria. Tony has $17 that he can spend to
buy one large pizza. If the pattern in the prices
continues, what is the greatest number of toppings
that Tony can order on his pizza? What is the cost
of that pizza? 6 toppings; $16.99
Use the four-step plan to solve each problem.
1-1
NAME ________________________________________ DATE ______________ PERIOD _____
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A Plan for Problem Solving
Word Problem Practice
Chapter 1
No; 9($1.69) 9($4.59) $50
5. OFFICE SUPPLIES At an office supply
store, pens are $1.69 per dozen and
note pads are $4.59 per dozen. Can
Shirley buy 108 pens and 108 note
pads for $50? Explain your reasoning.
3. HISTORY The area of Manhattan
Island is 641,000,000 square feet.
According to legend, the Native
Americans sold it to the Dutch for $24.
Estimate the area that was purchased
for one cent. 267,000 ft 2
13
1. Estimate the total number of teenagers
who voted. Sample answer: 55
Arto Saari
Bam Margera
Danny Way
Bob Burnquist
Skater
9
11
15
18
Votes
7MR1.1, 6AF2.3
Glencoe California Mathematics, Grade 7
6. SHOPPING Yoshi bought two pairs of
shoes. The regular price of each pair
was $108. With the purchase of one
pair of shoes at regular price, the
second pair was half price. How much
did Yoshi pay altogether for the two
pairs of shoes? $162
4. TRAVEL Britney’s flight to Rome
leaves New York City at 5:15 P.M. on
Wednesday. The flight time is
7.5 hours. If Rome is 6 hours ahead of
New York City, use Rome time to
determine when she is scheduled to
arrive. 6:45 A.M. Thursday
2. How many more teenagers preferred
Burnquist to Saari? 9 teenagers
SKATEBOARDING For Exercises 1 and 2, use the table
at the right. It shows the results of a recent survey
in which teenagers were asked who the best
professional skateboarder is.
Use the four-step plan to solve each problem.
1-1
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-1)
Lesson 1–1
Chapter 1
Enrichment
7MR2.3
N
Y
N
N
N
N
Y
N
Secretary
Treasurer
N
N
Y
N
N
Y
N
N
Keisha Sandra Jamal
President
Vice President
Holly
A4
Chapter 1
Track
Discus
400-m
100-m
Hurdles
Kyle
Rob
Nick
Cory
Shot Put
Mitch
Glencoe California Mathematics, Grade 7
Y
Y
Y
North
Y
Y
Y
South
Y
Y
14
Taft
Y
Discus
Y
400-m
Y
100-m
Y
Hurdles
Glencoe California Mathematics, Grade 7
Cory, from Wilson, won the shot put.
Kyle, from Vine, won the discus.
Mitch, from South, won the 400-m.
Nick, from Taft, won the 100-m. Rob,
from North, won the hurdles.
Y
Shot Put
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Y
Y
Vine
Two boys competed in the field events and three boys competed in the three track
events.
No boy participated in both track events and field events.
The athlete from North Middle School, who is not Mitch, placed last in the 100-meter.
The 100-meter winner lost to the South Middle School student in another event.
The boy from Wilson Academy, who placed second in the discus throw, was not in any
event with Mitch or Rob.
The South Middle School boy and Kyle, who is not from Wilson, were not in any of the
same events.
The student from Taft Junior High did not participate in any field events.
In one event Nick beat the student from North Middle School and the 400-meter
winner.
Field
•
•
•
•
•
•
•
•
Five male athletes won events in the district track and field meet. Each boy won exactly
one event. From the clues below, find each boy’s name, school name, and the event he won.
Use the process of logical reasoning and the table below to answer the following
question.
Using the table, mark Y for relationships that are true, and N for relationships that are not
true. For example, since you know that Sandra is the president, put a Y in that cell and put
an N in each of the other cells of that column and in the president row. Fill in the
remaining cells to show that Jamal must be the treasurer.
Holly, Keisha, Sandra, and Jamal are Bexley
Middle School’s student council officers. The
offices they hold are president, vice-president,
secretary, and treasurer. Sandra is the
president, Holly is not the treasurer, and Keisha
is the vice-president. What office does Jamal
hold?
When planning how to solve problems, it is helpful to be familiar with a
number of problem-solving strategies. When a problem presents a large
amount of information, one strategy that can be effective is logical reasoning
combined with the use of a table to organize the information.
Logical Reasoning
1-1
NAME ________________________________________ DATE ______________ PERIOD _____
7AF1.2, 7AF1.3, 7AF1.4
Variables, Expressions, and Properties
Lesson Reading Guide
4
1
8
2
3
4
5
6
12 16 20 24
2
____ Division
1
____ Multiplication
3
Chapter 1
15
Glencoe California Mathematics, Grade 7
is an example opposing or against a conjecture.
9. The word counter has several meanings in the English language. Use a
dictionary to find the meaning of counter when it is used as a prefix in
the word counterexample. Then write your own definition of
counterexample. Sample answer: opposing; a counterexample
Remember What You Learned
orders; not equal
8. 10 2, 2 10 The numbers are being divided in opposite
differently; equal; Assoc. ()
7. 5 (4 7), (5 4) 7 The numbers being multiplied are grouped
subtraction are different; equal; Dist.
6. 2(5 3), 2 5 2 3 The order of the multiplication and
grouped differently; not equal
5. (6 4) 1, 6 (4 1) The numbers being subtracted are
orders; equal; Comm. ()
4. 2 5, 5 2 The numbers are being added in opposite
For Exercises 4–8, describe how each pair of numerical expressions is
different. Then determine whether the two expressions are equal to
each other. If the expressions are equal, name the property that says
they are equal.
____ Subtraction
____ Addition 4
3. Number the operations in the correct order for simplifying
2 4(9 6 3). Then simplify the expression. 30
Read the Lesson
2. What would be the perimeter of Figure 10? 40 units
What is the relationship between the figure number and the perimeter
of the figure? The perimeter is 4 times the figure number.
Perimeter
Figure Number
1. Complete the table below.
Complete the Mini Lab at the top of page 29 in your textbook.
Write your answers below.
Get Ready for the Lesson
1-2
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lessons 1-1 and 1-2)
Lesson 1–2
Chapter 1
7AF1.2, 7AF1.3, 7AF1.4
Variables, Expressions, and Properties
Study Guide and Intervention
A5
3x2 4y 3(3)2 4(2)
3(9) 4(2)
27 8
19
6. 2 32 8 5 3
8. 52 (8 6) 50
5. 2 3 10 14 14
7. (10 5) 3 5
12. 2 2
14
3 2
18
Chapter 1
16. (ab)2 225
13. a 3b
16
17. a(b c) 33
14. 4b 3c 2
Glencoe California Mathematics, Grade 7
Answers
Glencoe California Mathematics, Grade 7
18. 3(bc 8) a 22
15. 2a b 5c 31
10. 3 7(14 8 2) 73
Evaluate each expression if a 3, b 5, and c 6.
11. 5[24 (6 8)] 50
9. (17 5)(6 5) 132
2
4. 5 6 2 3 1
3. 14 2 3(5) 22
2
2. 16 12 4 13
1. 4 5 8 28
Replace x with 3 and y with 2.
Evaluate the power first.
Do all multiplications.
Subtract.
Evaluate the expression 3x2 4y if x 3 and y 2.
Evaluate each expression.
Exercises
Example 2
Add inside the left parentheses.
Add inside the remaining parentheses.
Divide.
Multiply.
Subtract.
Evaluate the expression (5 7) 2 3 (8 1).
(5 7) 2 3 (8 1) 12 2 3 (8 1)
12 2 3 9
639
18 9
9
Example 1
Order of Operations
1. Perform all operations within grouping symbols first; start with the innermost grouping symbols.
2. Evaluate all powers before other operations.
3. Multiply and divide in order from left to right.
4. Add and subtract in order from left to right.
When finding the value of an expression with more than one operation, perform the operations in the
order specified by the order of operations.
1-2
NAME ________________________________________ DATE ______________ PERIOD _____
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
7AF1.2, 7AF1.3, 7AF1.4
Variables, Expressions, and Properties
Skills Practice
Chapter 1
17
Dist.
Glencoe California Mathematics, Grade 7
34. 3(7 2) 3(7) 3(2)
33. 13 (5 10) (5 10) 13
Comm. ()
32. (4 5) 0 4 5 Iden. ()
30. (6 2) 5 6 (2 5) Assoc. ()
28. 1 x2 x2 Iden. ()
31. 2(bc) 2(cb) Comm. ()
29. 2(bc) (2b)c Assoc. ()
27. (4 5)3 4(3) 5(3) Dist.
3
26. 2t2 t 9 75
2
t 10
pn
24. Name the property shown by each statement.
25. n2 3n 8 12
1
22. 4(pt 3) n 15
p2 4
23. 3t 5
24
npt
21. 3
20. 6t2 t 210
19. p(n t) 30
18. 5(2t n) 40
17. np2 36
14. t 2p
16. (np)2 144
15
15. 3p n 4 9
13. 3n p
0
12. (15 9)2 (5 4) 4
10. 3[(8 2) 5] 7 10
8. 23 4 3 6 20
Evaluate each expression if n 4, p 3, and t 6.
28 7
11. 7
42 13
9. (4 4) 4 4 4 33
7. (27 24)(27 24) 153
6. 2(20 5) 35
34 14
4
4. 25 2 8 4 29
3. 24 12 4 21
5. 49 (32 8 3) 16
2. 4(9) 36 3 24
1. 10 2 8 13
Evaluate each expression.
1-2
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-2)
Lesson 1–2
Chapter 1
7AF1.2, 7AF1.3, 7AF1.4
7. s(7 t) r 42
r2 1
6. 2
t 3
5. (st)2 100
Commutative Property of Addition
12. 5 (1 9) 5 (9 1)
Identity Property of Multiplication
10. 1(2 3) 2 3
8. 2s2 8s 3 13
A6
5(3 + 4)
16. 5(3) 5(4), Distributive Property
Chapter 1
68°F
Glencoe California Mathematics, Grade 7
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
18
18. TEMPERATURE When a temperature in degrees Celsius C is known, the expression
9C 160
can be used to find the temperature in degrees Fahrenheit. If a thermometer
5
shows that a temperature is 20C, what is the temperature in degrees Fahrenheit?
17. INTERNET A bookstore offers wireless Internet access to its customers for a charge. The
m
cost of using this service is given by the expression $1.50 , where m is the number
20
of minutes online. How much would it cost to be online 40 minutes? $3.50
x + (7 + 3)
15. (x 7) 3, Associative Property
Rewrite each expression using the indicated property.
14. Multiplication of whole numbers is associative. true
13. The sum of an even number and an odd number is always even. false; 2 3 5
State whether each conjecture is true or false. If false, provide a
counter example.
Associative Property of Addition
11. (10 7) 4 10 (7 4)
Distributive Property
9. 6(5 1) 6(5) 6(1)
Name the property shown by each statement.
3. 8 6t r 17
2. 4s 5t 10
1. 3r s 14
4. rs2 75
Variables, Expressions, and Properties
Practice
Evaluate each expression if r = 3, s = 5, and t = 2.
1-2
NAME ________________________________________ DATE ______________ PERIOD _____
7AF1.2, 7AF1.3, 7AF1.4
Variables, Expressions, and Properties
Word Problem Practice
1
600 cm2
Chapter 1
$34
5. MOVIE RENTALS Mario intends to rent
10 movies for his birthday party. He
can rent new releases for $4 each,
while older ones are $2 each. If he
rents n new releases, the total cost, in
dollars, of the 10 movies is represented
by the expression 4n 2(10 n).
Evaluate the expression to find the
total cost if he rents 7 new releases.
10 cm
19
3. GEOMETRY The expression 6s2 can be
used to find the surface area of a cube,
where s is the length of an edge of the
cube. Find the surface area of a cube
with an edge of length 10 centimeters.
1. Each team’s final score for a football
game can be found using the expression
6t e 3f, where t is the number of
touchdowns, e is the number of extra
points, and f is the number of field
goals. Find Pittsburgh’s final score in
the 2006 Super Bowl. 21
3
Seattle
1
0
r
Glencoe California Mathematics, Grade 7
24
expression to find the force when
m 12, v 4, and r 8.
expression . Evaluate the
mv2
r
6. CIRCULAR MOTION Pelipa is able to spin
her yo-yo along a circular path. The
yo-yo is kept in this path by a force
which can be described by the
4. VERTICAL MOTION The height of an
object dropped from the top of a 300foot tall building can be described by
the expression 300 16t2, where t is
the time, in seconds, after the ball is
dropped. Find the height of the object
3 seconds after it is dropped. 156 ft
2. Use the expression 6t e 3f to find
Seattle’s final score in the 2006 Super
Bowl. 10
1
3
Touchdowns Extra Points Field Goals
Pittsburgh
Team
FOOTBALL For Exercises 1 and 2, use the table that shows statistics
from the 2006 Super Bowl.
1-2
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-2)
Lesson 1–2
Chapter 1
Enrichment
7AF1.3
0
y
0
0y0
A7
x0
6. 0 0
Chapter 1
x
x0
3. 4x 0
x
7. 0 x
4. x 0 0
20
no solutions
y
x 0, y 0
x0
Glencoe California Mathematics, Grade 7
Answers
Glencoe California Mathematics, Grade 7
x
8. 0 0
all numbers 5. x 0 x
Describe the solution set for each equation.
But, a b contradicts a b.
Therefore, a b.
0
division by zero.
Therefore, 0 a and 0 b.
Step 3
Step 4
Step 3 involves
Assume a b.
0 a 0 and 0 b 0
Step 2
2. Step 1
0
division by zero.
Therefore, 1 2.
Step 3
But, 1 2 is a contradiction.
Step 2 involves
0
Therefore, 0 1 and 0 2.
0
0 1 0 and 0 2 0
Step 2
1. Step 1
Explain what is wrong with each of these “proofs.”
Because division by zero leads to impossible situations, it is not a “legal” step
in solving a problem. People say that division by zero is undefined, or not
possible, or simply not allowed.
There is no number that will make the left equation true. This equation has
no solution. For the right equation, every number will make it true. The
solution set for this equation is “all numbers.”
0x5
Because multiplication “undoes” division, you can write two equivalent
equations for the ones above.
5
x
0
Some interesting things happen when you try to divide by zero. For example,
look at these two equations.
Division by Zero?
1-2
NAME ________________________________________ DATE ______________ PERIOD _____
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Evaluating Expressions
TI-73 Activity
Evaluate 3(x 6) 2 (x2 15) for x 8 and for x 12.
)
(
ENTER
6
)
2nd
[ENTRY] to redisplay the previous
2nd
[ENTRY] to redisplay the line
Press
Press
DEL
[INS] 12
[ENTRY] to redisplay the expression.
ENTER
2nd
to reevaluate the expression.
[ENTRY]
2. 2x2 10
28; 82; 460
Chapter 1
then Done.)
2nd
21
Glencoe California Mathematics, Grade 7
[TEXT] and using the cursor keys to select Y and
See student’s work.
(Hint: Enter Y by pressing
16x2
3. 48; 192; 1,200
4. x(20 x) 51; 84; 75
3
5. How would you evaluate xy2 for x 4 and y 7 on a TI-73 graphing calculator?
1. x2 9 0; 27; 216
Use a graphing calculator to evaluate each expression for x 3, x 6, and x 15.
ENTER
2nd
2nd
Use the cursor keys to move to the 8. Insert 12 in place of the 8.
that stores the value for x.
Press
entries you made.
Use
You do not need to reenter the expression.
Evaluate the same expression for x 12.
15
2
3
(
ENTER
Evaluate the expression for x 8.
8 STO
Exercises
Step 2
Step 1
You could enter the expression, replacing the x with 8 and then enter it again, replacing x
with 12. But it is easier to enter the expression just once and store the values for x.
Example
Graphing calculators follow the order of operations. So there is no need to
perform each operation separately. To evaluate an expression, enter it just as it is
written. If an expression contains parentheses, enter them in the calculator just
as they are written.
1-2
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-2)
Lesson 1–2
Chapter 1
Integers and Absolute Value
Lesson Reading Guide
7NS2.5
A8
right; 72 0
left; 45 0
Chapter 1
Glencoe California Mathematics, Grade 7
22
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
|f s| 3 or |s f | 3
The Seahawks and the 49ers scored within 3 points of each other.
12. Write a mathematical expression that represents the following sentence.
(Hint: Let f represent the 49ers’ score and s represent the Seahawks’
score.)
Remember What You Learned
3 between two vertical bars; | 3|
11. Describe the symbol for the absolute value of 3. Then write the symbol.
10. 6 lies to the ________ of 7 on a number line. right; 6 7
9. 3 lies to the ________ of 95 on a number line. right; 3 95
8. 72 lies to the ________ of 0 on a number line.
7. 45 lies to the ________ of 0 on a number line.
Complete each sentence with either left or right to make a true
sentence. Then write a statement comparing the two numbers with
either or .
number line continues indefinitely in both directions.
6. Look at the number line on page 35 of your textbook. How are the ellipses
(plural of ellipsis) in the set of integers {...,4, 3, 2, 1, 0, 1, 2, 3, 4,...}
represented on the number line? The arrows indicate that the
Sample answer: The rest of the list has been omitted.
5. How can you explain the usage of the ellipsis in the list in Exercise 3 in
terms of the meaning for the ellipsis in the sentence in Exercise 4?
or phrase has been omitted.
4. Use a dictionary to find the meaning of the ellipsis as it is used in the
sentence The marathon began...downtown. Sample answer: A word
3. Look on page 35 in your textbook to find the meaning of the ellipsis as it
is used in the list 1, 4, 7, 10,... . The list continues without end.
The symbol ... is called an ellipsis.
Read the Lesson
2. What does a temperature of 35º represent? 35 degrees below zero
86 meters below sea level
1. What does an elevation of 86 meters represent?
Read the introduction at the top of page 35 in your textbook.
Write your answers below.
Get Ready for the Lesson
1-3
NAME ________________________________________ DATE ______________ PERIOD _____
Integers and Absolute Value
Study Guide and Intervention
7NS2.5
Order the set of integers {10, 3, 9, 4, 0} from least to greatest.
0
2
4
6
8 10
12. |4| |4| 0
9. |13| |15| 28
6. |21| 21
23
Glencoe California Mathematics, Grade 7
19. |2b c| 13
18. 2|a| c 17
17. |3b| 12
Chapter 1
16. b |c| 9
15. |c b| 1
38
3
14. |a| 14 20
13. |23 15|
10. |21 18|
7. |3| |5| 8
{34, 9, 0, 7, 31}
4. {31, 0,34,9, 7}
{8, 6, 4, 1, 3}
2. {6,8, 3,1,4}
Evaluate each expression if a 6, b 4, and c 5.
11. |11| |5| 6
8. |9| |8| 17
5. |13| 13
Evaluate each expression.
{21, 11, 2, 5, 13}
3. {2, 13,11,21, 5}
{5, 0, 1, 3, 4}
1. {3, 0,5, 1, 4}
Order each set of integers in each set from least to greatest.
Exercises
The absolute value of 220 is 20.
The absolute value of 10 is 10.
Simplify.
Evaluate the expression |20| |10|.
|20| |10| 20 |10|
20 10
30
Example 2
The absolute value of a number is the distance of that number from 0 on a number line.
The numbers from left to right are {9, 3, 0, 4, 10}.
10 8 6 4 2
Graph each integer on a number line.
Example 1
A number line can help you order a set of integers. When graphed on a number line, the smaller of two
integers is always to the left of the greater integer.
1-3
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-3)
Lesson 1–3
Chapter 1
Integers and Absolute Value
Skills Practice
2
1
75
A9
19. |6| |6| 18. 3 13 20. |4| |5| 17. 10 8 30. |28| |26| 54
29. |28| |26| 2
24
36. |3b| 24
35. a |a| 6
Chapter 1
33. |b| 2 6
32. |a| 5 8
Evaluate each expression if a 3, b 8, and c 5.
27. |3| |19| 22
26. |256| 256
31
24. |31|
Glencoe California Mathematics, Grade 7
Answers
Glencoe California Mathematics, Grade 7
37. |a 16| 19
34. 2|c| b 18
31. |24| |15| 9
28. |12| |13| 25
25. |1| 1
{3, 2, 1, 1, 2, 3}
23. |8| 8
Evaluate each expression.
{6, 4, 0, 2, 7}
22. {1, 2, 3, 3, 2, 1}
Order each set of integers in each set from least to greatest.
16. 4 5 15. 12 4 21. {0, 6, 7, 2, 4}
15
14. 20 fathoms below the surface 20
12. a $75 deposit
10. a loss of 15 pounds
8. a gain of 6 hours 6
6. 7 inches below normal 7
Replace each with , , or to make a true sentence.
13. 1 mile above sea level
11. a $35 withdrawal 35
9. 2° above zero
7. $5 off the original price 5
12
4. an 8-yard gain 8
3. a 6-yard loss 6
5. 12 centimeters longer
2. 10 strokes above par 10
7NS2.5
1. 3 strokes below par 3
Write an integer for each situation.
1-3
NAME ________________________________________ DATE ______________ PERIOD _____
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Integers and Absolute Value
Practice
5. 12 10 8. 0 8 4. 4 4 7. 6 7 18. |19||8| 27
15. |15|
19. |12||4| 8
16. |0| 0
39
24. |n| 4 3
21. n |p| 2
25. 9|m| 14 4
22. k |p| 9
Chapter 1
⫺5
5
0
5
5
5
10
5
15
5
20
25
Glencoe California Mathematics, Grade 7
26. On which day was it the coldest at noon? Tuesday
27. On which day was it the warmest at noon? Friday
28. The temperature at noon on Saturday was 25 warmer than the temperature on
Tuesday. What was the temperature on Saturday? Justify your answer using a number
line. 20
During a five-day cold spell, Jose recorded the temperature each day at noon.
The temperature was 3F on Monday, 5F on Tuesday, 4F on Wednesday,
1F on Thursday, and 0F on Friday.
TEMPERATURE For Exercises 26 and 28, use the following information.
23. 5|n| k
20. |m| 6 8
Evaluate each expression if k 4, m 2, n 7, and p 5.
17. |1||3| 4
14. |19| 19
Evaluate each expression.
{9, 7, 3, 1, 0, 1}
13. {0, 9, 3, 7, 1, 1}
12. {2, 4, 6, 8, 10, 12}
{12, 10, 6, 4, 2}
11. {1, 2, 3, 4} {3, 1, 2, 4}
9. 10 10 6. 5 6 3. 1 7 7NS2.5
10. {5, 7, 0, 5, 7} {7, 5, 0, 5, 7}
15
Order each set of integers from least to greatest.
2. 5 3 1. 0 8 Replace each with , , or to make a true sentence.
1-3
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-3)
Lesson 1–3
Chapter 1
Integers and Absolute Value
Word Problem Practice
Pressel, Morgan
Ochoa, Lorena
5
1
Kane, Lorie
Kerr, Cristie
A10
Chapter 1
Glencoe California Mathematics, Grade 7
0
6
1
1
Glencoe California Mathematics, Grade 7
Mariana Trench
6. OCEAN TRENCHES The elevation of the
Puerto Rican Trench in the Atlantic
Ocean is 8,605 meters, the elevation
of the Mariana Trench in the Pacific
Ocean is 10,924 meters, and the
elevation of the Java Trench in the
Indian Ocean is 7,125 meters. Which
trench has the the lowest elevation?
Tuesday: 23; Wednesday: 67
4. STOCK MARKET Your stock loses 53
points on Monday and 23 points on
Tuesday, but gains 67 points on
Wednesday. Write an integer for each
day's change. Monday: 53;
Birdie Kim
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. SOLAR SYSTEM The average
temperature of Saturn is 218°F, while
the average temperature of Jupiter is
162°F. Which planet has the lower
average temperature? Saturn
New York: 74; Tokyo: 140
3. LONGITUDE London, England, is located
at 0° longitude. Write integers for the
locations of New York City whose
longitude is 74° west and Tokyo whose
longitude is 140° east. Assume that
east is the positive direction.
2, 1, 1, 0, 0, 1, 1, 1, 5, 6
26
Lang, Brittany
1
Jo, Young
2
Score
7NS2.5
2. Who had the lowest score?
Kung, Candie
1
Icher, Karine
1. Order the scores in the table from least
to greatest.
Kim, Birdie
Player
0
Score
Gulbis, Natalie
Player
their scores in Round 3 of the 2005 60th U.S. Women’s Open.
GOLF For Exercises 1 and 2, use the table that lists ten players and
1-3
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment
7AF1.3
or or no bicycles
no parking
11.
8.
no U turn
no smoking
12.
9.
no littering
no left turn
Chapter 1
27
Glencoe California Mathematics, Grade 7
13. Create three different “no” signs of your own. Signs will vary.
10.
7.
What does each of these signs mean?
6. ____ means the same as . 4. For any nonzero integer n, n ____ n. 2. |4| ____ |4|
5. A number x is either greater than 0 or less than 0. So, x ____ 0.
3. For any number x, |x| ____ x. 1. 2 ____ 0
Which of the symbols, , , and will make the statement true?
Some problems have more than one correct answer.
Many symbols and signs use a slash mark such as /, \, or | to mean is not or
no. For example, the symbol means is not equal to.
When You Want to Be Negative
1-3
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-3)
Lesson 1–3
Chapter 1
Absolute Value
TI-83/84 Plus Activity
A11
(–)
1
(–)
)
1
(–)
So, |5| |14| 9.
MATH
5. ⏐7⏐
4. ⏐10⏐
MATH
Chapter 1
3
28
17. ⏐11⏐ ⏐8⏐
12
9
16. ⏐3⏐ ⏐9⏐
8
14. ⏐14⏐ ⏐5⏐
2
11. ⏐7 9⏐
7
8. ⏐15 8⏐
17
ENTER
13. ⏐7⏐ ⏐15⏐
5
10. ⏐1 4⏐
10
7. ⏐6 4⏐
7
8
4
10
2. ⏐8⏐
)
1. ⏐4⏐
5
)
ENTER
—
3 + 8
17
Simplify |5| |14|.
Enter:
Exercises
Simplify.
MATH
So, |3 8| 5.
Example 3
1
Simplify |3 8|.
Enter:
Example 2
So, |17| 17.
MATH
Simplify |17|.
Enter:
Example 1
1 14
5
9
Glencoe California Mathematics, Grade 7
Answers
Glencoe California Mathematics, Grade 7
1
18. ⏐6⏐ ⏐7⏐
20
15. ⏐8⏐ ⏐12⏐
7
11
9. ⏐3 14⏐
25
6. ⏐25⏐
12
3. ⏐12⏐
ENTER
12. ⏐2 (5)⏐
)
A graphing calculator can be used to evaluate problems containing
absolute value. The absolute value function on the TI-83/84 Plus is
found in the MATH (NUM) menu.
1-3
NAME ________________________________________ DATE ______________ PERIOD _____
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Adding Integers
Lesson Reading Guide
7. 23, 16 23
5. 3, 5 5
add; same sign
11. 23 (16)
subtract; different signs
9. 3 5
85
68
26. 97 (165)
39
22. 43 4
10
18. 6 (4)
19
124
27. 49 (75)
23. 11 (30)
15
19. 7 8
15. 23 (16) negative; 39
13. 3 5 positive; 2
Chapter 1
long a tape has been rewound.
29
Glencoe California Mathematics, Grade 7
28. You have seen what a negative number means in terms of weather or
money. Describe what a negative number means on a video cassette
recorder. Sample answer: A negative number shows for how
Remember What You Learned
144
51
25. 39 124
24. 81 (63)
8
21. 34 (17)
1
17. 3 4
20. 25 (17)
1
16. 3 (4)
Add.
14. 9 (12) negative; 3
12. 4 8 positive; 12
Determine whether the sum is positive or negative. Then find the sum.
subtract; different signs
10. 9 (12)
add; same sign
8. 4 8
Determine whether you add or subtract the absolute values of the
numbers to find the sum. Give a reason for your answer.
6. 9, 12 12
4. 4, 8 8
Identify the number with the greater absolute value.
addend; 2,600: addend; 13,200: sum
7NS1.2, 7AF1.3
3. Look at your answer for Exercise 2. Identify each number in the addition
sentence as either an addend or a sum. 3,200: addend; 7,400:
Read the Lesson
3,200 (7,400) (2,600) 13,200
2. Write an addition sentence that describes this situation.
13,200
1. Write an integer that describes the game show host’s statement.
Read the introduction at the top of page 41 in your textbook.
Write your answers below.
Get Ready for the Lesson
1-4
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lessons 1-3 and 1-4)
Lesson 1–4
Chapter 1
Adding Integers
Study Guide and Intervention
7NS1.2, 7AF1.3
A12
1
Chapter 1
18. |x y| 1
8
Glencoe California Mathematics, Grade 7
Glencoe California Mathematics, Grade 7
20. x |y| 7
17. y 2 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
30
19. |x| y 1
16. x (6) 2
Evaluate each expression if x 4 and y 3.
15. 11 y
33
12. 13 (8) (12)
14. 17 31 (14) 26 26
11. 3 10 (6)
13. 3 (10) (16) 11 12
9
10. 5 (4) 8
9. 74 36 38
8. 61 (39) 100
7. 55 81 26
1
6. 39 (38)
5. 45 35 10
4. 23 (15) 38
8
2. 10 (10) 20
3. 18 (26)
Subtract |12| from |16|. The sum is negative because |16| |12|.
Find 16 12.
1. 9 16 25
Add.
Exercises
16 12 4
Example 2
To add integers with different signs, subtract their absolute values. The sum has the same sign as the
integer with the greater absolute value.
Add |3| |4|. Both numbers are negative, so the sum is negative.
Find 3 (4).
3 (4) 7
Example 1
To add integers with the same sign, add their absolute values. The sum has the same sign as the
integers.
1-4
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 1
22. |a| b 3
31
23. |a| |c| 17
20. b 8 4
Glencoe California Mathematics, Grade 7
24. |b c| 4
21. 6 c 2
18. 23 (18) 41 (17) 17
16. 35 (31) (39) 105
Evaluate each expression if a 9, b 12, and c 8.
19. 3 a 6
66
24
12. 86 77 9
9. 15 (51)
6. 11 (13)
3. 8 9 1
7NS1.2, 7AF1.3
14. 16 (5) 12 9
11. 53 (28) 25
8. 44 (26) 18
5. 27 18 9
17. 8 (12) 15 (13) 2
15. 2 17 (12) 3
13. 10 (4) 6 12
10. (17) (13) 30
7. 44 26 18
4. 12 (3) 9
2. 4 7 11
Adding Integers
Skills Practice
1. 2 (3) 5
Add.
1-4
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-4)
Lesson 1–4
Chapter 1
Adding Integers
Practice
16
9
44
335
220
Pittsburgh, Pennsylvania
Rochester, New York
A13
8
18
67
30
Change as of 2005
(thousands)
Overall, you moved 6 spaces forward.
Chapter 1
32
Glencoe California Mathematics, Grade 7
Answers
Glencoe California Mathematics, Grade 7
30 80; 50; Mrs. Brown's office is 50 feet above street level.
21. ELEVATOR Mrs. Brown parked in the parking garage 30 feet below street level.
She then got in an elevator and went up 80 feet to her office.
temperature is 8F below zero.
20. WEATHER Before you went to sleep last night, the temperature was 3F.
During the night the temperature dropped by 5. 3 (5); 8; The
campsite is 156 feet below sea level.
19. CAMPING While hiking down into a canyon, Manuel passed a sign stating
that the elevation was 100 feet below sea level. He descended another 56
feet before reaching his campsite. 100 (56); 156; The
18. GAMES On one turn, you move 10 spaces forward around the game board.
On the next turn, you move 4 spaces backward. 10 (4); 6;
Write an addition expression to describe each situation. Then find
each sum and explain its meaning.
17. What was the total population change for these four cities? 11
Las Vegas: 545; Pittsburgh: 317; Rochester: 212
16. What is the population of each of these cities as of 2005? Boston: 559;
Source: U.S. Census Bureau
478
2000 Population
(thousands)
589
Las Vegas, Nevada
Boston, Massachusetts
City
POPULATION For Exercises 16 and 17, use the table below that shows the
change in population for four cities between 2000 and 2005.
4
22
14. 8 (7) (8) (9) 15. 15 10 (16) 12
8
12. 13 (13) (18)
9. 29 (25) 54
13. 5 8 (1) (6)
8. 33 55 22
7. 46 27 19
6. 5 (26) 31
11. 15 (17) 10
5. 12 10 2
4. 14 (14) 28
3. 19 (7) 12
7NS1.2, 7AF1.3
10. 6 14 (12)
2. 13 15 28
1. 1 (8) 9
Find each sum.
1-4
NAME ________________________________________ DATE ______________ PERIOD _____
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Chapter 1
1,500 525 (350); 1,325
5. OCEANOGRAPHY A research team
aboard an underwater research vessel
descends 1,500 feet beneath the surface
of the water. They then rise 525 feet
and descend again 350 feet. Write an
addition expression to represent this
situation. Then find the sum.
12
3. GOLF In 2005, Tiger Woods won the
Masters Tournament. His scores were
2, 6, 7, and 1 for four rounds.
Write an addition expression that
represents his final score. Then find the
sum. 2 (6) (7) (1);
5 (8); 13
Adding Integers
33
Glencoe California Mathematics, Grade 7
156 (4) 2 (5) (3);
146
6. SPORTS Peter weighs 156 pounds, but
he would like to wrestle in a lower
weight class. He loses 4 pounds one
week, gains back 2 pounds the next
week, loses 5 pounds the third week,
and loses 3 pounds the fourth week.
Write an addition expression to
represent this situation. Then find the
sum.
30 (6) (3) 24 (8);
37
4. INVENTORY A local bookstore has
30 copies of a bestseller when it opens
Monday morning. On Monday, it sells
6 copies of the book. On Tuesday, it
sells 3 copies. On Wednesday, it receives
a shipment containing 24 copies of the
book and also sells 8 copies. Write an
addition expression that represents the
number of copies of the book that store
has at the end of the day on
Wednesday. Then find the sum.
3 12; 9
7NS1.2, 7AF1.3
2. ELEVATOR You park in a garage 3 floors
below ground level. Then you get in the
elevator and go up 12 floors. Write an
addition expression to represent this
situation. Then find the sum.
Word Problem Practice
1. FOOTBALL A football team loses 5 yards
on one play and then loses 8 yards on
the next play. Write an addition
expression that represents the change
in position of the team for the two
plays. Then find the sum.
1-4
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-4)
Lesson 1–4
Chapter 1
Enrichment
7NS1.2
30
125
1
62
130
82
25
40
5
6
7
8
A14
Chapter 1
Glencoe California Mathematics, Grade 7
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
34
Micah: 425; Juanita: 276; Taylor: 350
6. What was each player’s final score at the end of the game?
5. Who won the game? Micah; 425
4. Who was in second place after round 7? How many points did this player
have? Taylor; 362
Micah: 410; Juanita: 146; Taylor: 315
3. What was each player’s score after round 6?
2. Who had the lowest score after round 5? What was his or her score at this
point in the game? Juanita; 161
1. Who had the highest total score after round 3? How many points did this
player have? Micah; 182
Refer to the table above to answer the following questions.
12
47
110
37
15
146
4
0
20
5
0
3
0
95
54
105
72
15
2
68
Micah Juanita Taylor
Hand
Listed below are the scores for a game of cards in which the highest score
wins. The three players recorded their scores for each hand, but did not total
the scores until they were done playing.
Adding Integers
1-4
NAME ________________________________________ DATE ______________ PERIOD _____
Subtracting Integers
Lesson Reading Guide
7NS1.2
7
b. 6 4; 6 (4) 10; 10
273
21. 139 134
362
22. 97 (265)
45
18. 41 4
18
23. 59 (77)
57
19. 31 (26)
14. 7 (3) 4 15. 6 8 2
11. 5 (16) 5 16; 11
9. 3 8 3 (8); 11
Chapter 1
35
Glencoe California Mathematics, Grade 7
addend may be undone by subtracting the second addend from the sum.
25. Subtraction and addition are often referred to as opposite operations.
Explain in your own words the relationship between addition and
subtraction. Sample answer: The addition of a second addend to a first
Remember What You Learned
subtraction sign to an addition sign, change the number to the right of
the subtraction sign to its opposite, and then add.
24. Describe the method for subtracting integers. Sample answer: Change the
48
20. 81 (33)
12
17. 24 (12)
16. 23 (17)
40
13. 3 5 8
12. 3 (5) 8
Subtract.
10. 10 (12) 10 12; 22
8. 2 9 2 (9); 7
Rewrite each difference as a sum. Then find the sum.
7. How is the opposite of a number different from the additive inverse of the
number? There is no difference.
6. Find the additive inverse of 7. 7
5. Find the opposite of 7.
Read the Lesson
a. 1 5; 1 (5) 4; 4
4. Use algebra tiles to find each difference and sum. Compare the results in
each group. The results are the same in each group.
3. How does this result compare to 4 (2)? The results are both 6.
2. Use algebra tiles to find 4 2. 6
The results are both 2.
1. How does this result compare with the result of 3 (5)?
Complete the Mini Lab at the top of page 46 in your textbook.
Write your answers below.
Get Ready for the Lesson
1-5
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lessons 1-4 and 1-5)
Lesson 1–5
Chapter 1
Subtracting Integers
Study Guide and Intervention
A15
8. 21 16 37
7. 9 16 7
36
Glencoe California Mathematics, Grade 7
Answers
Glencoe California Mathematics, Grade 7
18. c b a 15
17. b a c 1
16. c b 8
Chapter 1
15. a c 12
10
14. 20 b 23
12. 19 |29|
9. 28 37 9
6. 16 9 7
3. 10 8 18
7NS1.2
13. a 8 15
Evaluate each expression if a 7, b 3, and c 5.
11. 65 (6) 71
5. 23 (28) 5
4. 15 (12) 3
10. 34 (46) 12
2. 5 (2) 7
1. 3 4 7
Subtract.
Exercises
To subtract 22, add 22.
Add.
Find 13 (22).
13 (22) 13 22
35
Example 2
To subtract 15, add 15.
Add.
Find 8 15.
8 15 8 (15)
7
Example 1
To subtract an integer, add its opposite or additive inverse.
1-5
NAME ________________________________________ DATE ______________ PERIOD _____
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
17. |10| |7| 3
14. 33 (68) 35
11. 38 (39) 77
8. 21 (23) 44
5. 13 (25) 12
11
Chapter 1
25. m k 15
22. k m 15
19. k 19
37
26. k m 16 31
23. p m 3
20. 19 m 26
9. 34 (11)
18. |52| 49 3
15. 76 18 58
23
6. 14 (19) 33
3. 9 9 18
7NS1.2
12. 72 27 45
25
Glencoe California Mathematics, Grade 7
27. k m p
24. m 3 10
21. p 11 21
Evaluate each expression if k 8, m 7, and p 10.
16. 4 |6| 2
13. 36 47 83
10. 56 94 38
7. 25 15 40
4. 17 18 35
2. 12 8 4
Subtracting Integers
Skills Practice
1. 6 7 1
Subtract.
1-5
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-5)
Lesson 1–5
Chapter 1
A16
12. 10 (5) 5
6,960
Chapter 1
Glencoe California Mathematics, Grade 7
Glencoe California Mathematics, Grade 7
3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
38
27. [15 (7)] (8 11)
25. [22 (18)] (5 11) 34
24. 25 [16 (9)] 18
26. (5 9) (20 12)
23. 10 [8 (16)] 2
Source: www.worldoffacts.com
6,194
42
28
Europe
86
5,642
12
Australia
South America
2,228
400
Asia
North America
8,850
156
Africa
22. 29 (4) (15) 48
36
21. Find the difference between the
lowest point in South America and
the lowest point in Africa. 114 m
20. How far below the highest point in
North America is the lowest point
in Asia? 6,594 m
19. How far below the highest point in
Australia is the lowest point in
Australia? 2,240 m
Highest
Point (m)
5,895
Lowest
Point (m)
Continent
18. g d f 22
17. d f g 8
16. d f 3
GEOGRAPHY For Exercises 1921, use
the table that shows the elevations
above sea level of the lowest and
highest points on six continents.
15. d g 15
14. g 15 4
13. d 10 14
Evaluate each expression if d 4, f 7, and g 11.
11. 12 19 7
9. 8 (22) 30
8. 19 (13) 6
7. 14 (18) 4
10. 1 15 16
6. 8 (9) 1
5. 18 (7) 25
3. 8 9 17
4. 4 (12) 16
Subtracting Integers
2. 3 12 9
Simplify.
1-5
Subtracting Integers
Chapter 1
5. WATER The boiling point of water is
212°F, while 460°F is its absolute
lowest temperature. Find the
difference between these two
temperatures. 672°F
3. TEMPERATURE The highest recorded
temperature on Earth was recorded in
Africa at 136°F, while the lowest was
129°F in Antarctica. What is the
range of temperatures recorded
on Earth? 265°F
1. Find the difference in elevation
between the top of Mt. McKinley and
and the top of Mt. Everest. 8,715 ft
Death Valley
39
29,035
$5
Glencoe California Mathematics, Grade 7
6. STOCK MARKET During the course of
one day, the price of a stock fluctuated
between a high of $3 above the
previous day’s closing price and a low of
$2 below the previous day’s closing
price. What was the difference between
the high and low prices for that day?
4. WEATHER If the overnight temperature
at the Arctic Circle was 14°F, but the
temperature rose to 8°F during the day,
what was the difference between these
high and low temperatures? 22°F
2. Find the difference in elevation
between Death Valley and the
Dead Sea. 1,066 ft
282
1,348
28,232
Mt. Everest
Dead Sea
20,320
Puerto Rican Trench
Elevation (feet)
Mt. McKinley
Place
elevations of several places on Earth.
GEOGRAPHY For Exercises 1 and 2, use the table. The table shows the
7NS1.2
Word Problem Practice
7NS1.2
Practice
1. 15 7 8
Subtract.
1-5
NAME ________________________________________ DATE ______________ PERIOD _____
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-5)
Lesson 1–5
Chapter 1
7
6
5
4
A17
X
7
6
5
4
7
6
5
4
2
1
0
2
Y
1
3
2
1
|5 (5)| 10
3
0
0
|(7) (1)| 6
3
|(4) 2| 6
1
1
1
2
2
2
G
3
3
3
4
4
4
5
A
5
5
6
6
6
7
6
5
4
3
2
1
0
1
2
3
M
4
5
7
Chapter 1
8
6
5
4
3
2
1
y1
40
0
1
2
8
4
5
6
6
7
7
7
7
8
8
8
8
Glencoe California Mathematics, Grade 7
Answers
Glencoe California Mathematics, Grade 7
3
y2
5. Graph the two solutions to the equation |y 2| 3. Call the points y1
and y2.
8
N
4. Graph two points, M and N, that are each 5 units from 2. Make M N.
Use the number lines to solve the problems.
8
B
3. A at 5 and B at 5
8
2. X at 7 and Y at 1
8
H
1. H at 4 and G at 2
Graph each pair of points on the number line. Then write an
expression using absolute value to find the distance between the
points.
7
Multiplying and Dividing Integers
Lesson Reading Guide
7NS1.2, 7AF1.3
negative
7. The quotient of two integers with different signs is __________ .
negative; 8
Chapter 1
41
Glencoe California Mathematics, Grade 7
divide by the number of numbers in the set; average.
17. Explain how to find the mean of a set of numbers. What is another name
for the mean? Sample answer: Find the sum of the numbers and then
Remember What You Learned
8
64
16. 21
15. positive; 7
14. 35 (7) positive; 5
13. 12 (4) negative; 3
3
12. 6(7) positive; 42
10. 3 5 negative; 15
11. 9(2) negative; 18
9. 4 8 positive; 32
Determine whether each product or quotient is positive or negative.
Then evaluate the expression.
positive
positive
6. The product of two integers with the same signs is __________ .
8. The quotient of two integers with the same signs is __________ .
negative
5. The product of two integers with different signs is __________ .
Complete each sentence with either positive or negative.
4. Identify each number in the multiplication sentence 3(120) 360 as
either a factor or a product. 3: factor; 120: factor; 360: product
Read the Lesson
10(120); 1,200
3. Write a multiplication sentence that could be used to find the
submersible’s depth after 10 minutes. Then find the product.
three times.
2. Write a multiplication sentence that could be used to find this same
depth. Explain your reasoning. 3(120); you are adding 120
answers: 240 (120) or 120 (120) (120); 360
1. Write two different addition sentences that could be used to find the
submersible’s depth after 3 minutes. Then find their sums. Sample
Read the introduction at the top of page 51 in your textbook.
Write your answers below.
1-6
Get Ready for the Lesson
7NS2.5
The absolute value of the difference between two integers can be interpreted
as the distance between two points on a number line. That is, if point A has a
as a coordinate and point B has b as a coordinate, then |a b| is the distance
between points A and B.
Enrichment
NAME ________________________________________ DATE ______________ PERIOD _____
Distance on the Number Line
1-5
NAME ________________________________________ DATE ______________ PERIOD _____
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Answers (Lessons 1-5 and 1-6)
Lesson 1–6
Chapter 1
Multiplying and Dividing Integers
Study Guide and Intervention
7NS1.2, 7AF1.3
A18
15
75
10. 5
6. 25 5 5
11. 6(3)(5) 90
7. 48 4 12
3. 9(4) 36
Chapter 1
13. 3c b 17
Glencoe California Mathematics, Grade 7
42
96
1
11
Glencoe California Mathematics, Grade 7
a6
16. c
13
143
12. 8. 63 (7) 9
4. 12(8)
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
14. a(b c) 3
15. c2 5b 29
Evaluate each expression if a 1, b 4, and c 7.
9. (4)2 16
5. 33 (3) 11
1. 8(8) 64
2. 3(7) 21
The dividend and divisor have the same sign. The quotient is positive.
Find 54 (6).
The dividend and divisor have different signs. The quotient is negative.
Find 15 (3).
The factors have the same sign. The product is positive.
Find 5(6).
The factors have different signs. The product is negative.
Find 7(4).
Multiply or divide.
Exercises
54 (6) 9
Example 4
15 (3) 5
Example 3
5(6) 30
Example 2
7(4) 28
Example 1
Use the following rules to determine whether the product or quotient of two integers is positive or
negative.
• The product of two integers with different signs is negative.
• The product of two integers with the same sign is positive.
• The quotient of two integers with different signs is negative.
• The quotient of two integers with the same sign is positive.
1-6
NAME ________________________________________ DATE ______________ PERIOD _____
3
16
48
22. 8
18. 40 (5)
12
14. 1(3)(4)
100
10. (10)2
3
19
57
23. 9
19. 63 (7)
1,000
15. (10)3
144
11. 6(8)(3)
45
7. 15(3)
8
3. 4(2)
Chapter 1
ab
29. c 2
25. abc 60
b
2a c
30. 2
26. 2b c 4
43
31. b2 5a
a
2b c
27. 5
32. (c)2 36
28. ab c 4
15
75
24. 19
20. 76 4
84
16. 3(4)(7)
64
12. (4)3
91
8. 7(13)
35
4. 5 7
7NS1.2, 7AF1.3
Glencoe California Mathematics, Grade 7
35
8
Evaluate each expression if a 2, b 5, and c 6.
14
4
56
21. 5
17. 15 3
Divide.
81
13. (9)2
70
9. 5(2)(7)
72
132
6. 11 12
5. 9(8)
6
2. 3(3)
9
Multiplying and Dividing Integers
Skills Practice
1. 2 3
Multiply.
1-6
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-6)
Lesson 1–6
Chapter 1
56
11. 8
7
A19
17. r2 16 32
42
16. 14
rt
122
12
27. 12
24. 3(5)2 75
4 12
28. 6
8
Chapter 1
44
Glencoe California Mathematics, Grade 7
Answers
Glencoe California Mathematics, Grade 7
30. WEATHER During a six hour period, the temperature dropped 18F. Find the average
hourly change in the temperature. 3F
29. MONEY If you have $216 and you spend $12 each day, how long would it be until you
had no money left? 18 days
10(15)
26. 25
6
23. (3)2 (4)2 144
25. 5(2)(4)(3) 120
22. 22, 19, 14, 17, 18 18
21. 5, 4, 8, 12, 10 1
Find each product or quotient.
20. 11, 15, 16, 17, 20, 18, 22 9
18. (2t 4)2 4 25
5s
15. 5
t4
80
12. 16
5
9. 48 (6) 8
6. 2(5)(3) 30
3. 8(9) 72
7NS1.2, 7AF1.3
19. 8, 5, 3, 9, 5, 2 2
Find the mean of each set of integers.
14. 10 rt 18
13. s + 5t 24
Evaluate each expression if r 4, s 11, and t 7.
66
10. 11
6
7. 14 2 7
8. 35 (7) 5
5. (7)2 49
4. 4(12) 48
Divide.
2. 3 12 36
Multiplying and Dividing Integers
Practice
1. 5(7) 35
Multiply.
1-6
NAME ________________________________________ DATE ______________ PERIOD _____
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
14 F
Chapter 1
6 yr
45
7. DEPRECIATION The value of a piece of
office equipment is changing at a rate
of $175 per year. How long will it take
for the change in value to be $1,050?
7h
5. WEATHER On a certain day, the
temperature changed at a rate
of 2ºF per hour. How long did
it take for the change in
temperature to be 14ºF?
G 10 20 30 40 50 40 30 20 10 G
3. FOOTBALL A football team lost 9 yards
on each of three consecutive plays.
What was the team’s total change in
position for the three plays? 27 yd
Glencoe California Mathematics, Grade 7
8. POPULATION The population of a small
town is changing at a rate of 255
people per year. How long will it take
for the change in population to be
2,040 people? 8 yr
6. GEOLOGY The length of an island is
changing at the rate of 17 inches per
year. How long will it take for the
change in the length of the island to be
255 inches? 15 years
2,400 ft
4. HIKING A group of hikers is descending
a mountain at a rate of 400 feet per
hour. What is the change in the
elevation of the hikers after 6 hours?
15 in.
7NS1.2, 7AF1.3
2. EVAPORATION The height of the water
in a tank decreases 3 inches each week
due to evaporation. What is the change
in the height of the water over a fiveweek period due to evaporation?
Multiplying and Dividing Integers
Word Problem Practice
1. STOCK MARKET The price of a stock
decreased $2 per day for four
consecutive days. What was the total
change in value of the stock over the
four-day period? $8
1-6
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-6)
Lesson 1–6
Chapter 1
Enrichment
7NS1.2, 7AF1.3
2
6. 609 1,218
5. 57 114
A20
18. 364 182
17. 116 58
16. 54 27
30. 57 40 57 2 2 10
32. 93 125 93 1,000 2 2 2
46
29. 472 50 472 100 2
31. 138 25 138 100 2 2
Chapter 1
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Glencoe California Mathematics, Grade 7
28. 613 5 613 10 2
27. 256 20 256 10 2
Transform each product into an expression that uses doubling or
halving. Change only the second factor.
26. 20 317 6,340
25. 20 361 7,220
24. 20 93 1,860
4,360
23. 5 (872)
22. 5 234 1,170
21. 5 126 630
Compute mentally.
15. 38 19
14. 56 28
13. 72 36
12. 1,484 742
8. 6,523 13,046
4. 2,512 5,024
19. 5,296 2,648 20. 7,436 3,718
11. 690 345
7. 383 766
3. 48 96
10. 468 234
9. 64 32
Halve each number. Use mental math.
2. 214 428
1. 13 26
Double each number. Use mental math.
2
10
1
5
; 5 10 ; 87 5 87 10 2 870 2 435
Most numbers are easy to double or halve mentally. And, many types of
multiplication problems can be done mentally by using doubling and halving.
In working problems of this type, it is helpful to remember that 5 equals 10
divided by 2. And, dividing by 2 is the same as multiplying by one-half. So,
multiplying by 5 is the same as first multiplying by 10 and then halving.
Doubles and Halves
1-6
NAME ________________________________________ DATE ______________ PERIOD _____
Calculating with Integers
TI-83/84 Plus Activity
(–)
10
(–)
24 (–)
ENTER
4
8
(–)
4
—
(–)
1
ENTER
3
So, g t 3 when g 4 and t 1.
Enter:
16
8. 36 (11) 47
5. 48 (3)
2. 4 (11) 7
0
Chapter 1
19. x (z) 4
16. x y 1
13. 0 y
10. 15 x 11
47
20. x y (2) 10
17. y z 5
14. z (6) 7
11. y (4) 1
Evaluate each expression if x 4, y 5, and z 1.
7. 12 (11) 132
4. 6 12 6
1. 8 16 8
3
ENTER
Evaluate g t if g 4 and t 1.
So, 24 (3) 8.
Enter:
Find 24 (3).
So, 6 (10) 5 (4).
Enter: 6 +
Find 6 (10).
Perform the indicated operation.
Exercises
Example 3
Example 2
Example 1
28
Glencoe California Mathematics, Grade 7
21. x y z 20
18. x y z 9
15. 14 (z) 14
12. 10 z 10
9. 84 (3)
6. 3 (9) 6
3. 5 17 85
You can solve problems involving integers on a graphing calculator.
When a number is positive, you do not need to enter a sign. But when
a number is negative, use the (–) key before you enter the number.
1-6
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-6)
1–6
Lesson X–6
Chapter 1
Writing Equations
Lesson Reading Guide
7AF1.1, 7AF1.4
A21
Writing Equations
Study Guide and Intervention
4n
a number divided by 3
the quotient of z and 3
the ratio of z and 3
Chapter 1
48
Glencoe California Mathematics, Grade 7
Answers
Glencoe California Mathematics, Grade 7
sentence is translated as an equation with the verb
representing .
12. Devise your own way to determine how a verbal description should be
translated as an algebraic equation. Sample answer: A complete
Remember What You Learned
division
11. Find the ratio of the amount of gasoline used and the distance traveled.
10. Find the high temperature on Wednesday if this temperature is 3º less
than the high temperature on Tuesday. subtraction
9. Find the product of the price of a calculator and the number of students
in the class. multiplication
addition
8. Find the flight time after the time has been increased by 15 minutes.
6. the difference of 32 and x
Chapter 1
49
12. 5 shirts at $d each is $105.65. 5d 105.65
32 x
Glencoe California Mathematics, Grade 7
11. The original price decreased by $5 is $34. p 5 34
x
7
10. The quotient of x and 7 is equal to 13. 13
9. The sum of r and 45 is 79. r 45 79
8. The product of 7 and b is equal to 63. 7b 63
7. 5 more than a number is 6. n 5 6
Write each verbal sentence as an algebraic equation.
5. 14 less than f f 14
4. p increased by 10 p 10
3. the product of 5 and b 5b
addition
7. Find how much an executive spent on breakfast, lunch, and dinner.
g
15
2. the quotient of g and 15 n 9 45
Equation
1. the sum of 8 and t 8 t
Write each verbal phrase as an algebraic expression.
Exercises
Sentences
9 less than a number is equal to 45.
The difference of a number and 9 is 45.
A number decreased by 9 is 45.
45 is equal to a number minus 9.
z
3
Expression
r6
Phrases
Expression
Phrases
the difference of r and 6
6 subtracted from a number
6 less than a number
r minus 6
7AF1.1, 7AF1.4
The table shows several verbal sentences that represent the same equation.
4 multiplied by n
4 times a number
the product of 4 and n
Expression
x8
Phrases
Expression
Phrases
8 more than a number
the sum of 8 and a number
x plus 8
x increased by 8
The table shows several verbal phrases for each algebraic expression.
1-7
NAME ________________________________________ DATE ______________ PERIOD _____
6. Find the price of an airline ticket after the price has been decreased by
$50. subtraction
5. Find the cost per person when the price of a pizza is split among several
people. division
4. Find the difference between the cost of a gallon of premium gasoline and
the cost of a gallon of regular gasoline. subtraction
Look at the steps for writing an algebraic equation on page 57. Then
determine whether each situation requires addition, subtraction,
multiplication, or division.
Read the Lesson
number of guest times $8 per guest is a party cost of $120.
3. What does the equation g 8 120 represent in this situation? The
8 g or 8g
2. Write an expression representing the cost of a party with g guests.
1. What is the relationship between the number of guests and the cost of
the party? The cost is equal to 8 times the number of guests.
Read the introduction at the top of page 57 in your textbook.
Write your answers below.
Get Ready for the Lesson
1-7
NAME ________________________________________ DATE ______________ PERIOD _____
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Answers (Lesson 1-7)
Lesson 1-7
Chapter 1
Writing Equations
Skills Practice
4. the difference of t and 1 t 1
3. the product of 10 and c 10c
25s
12. 25 times the number of students
s 75
A22
Chapter 1
Glencoe California Mathematics, Grade 7
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
50
24. Carla’s height plus 4 inches is 68 inches. h 4 68
23. The cost of 10 books at $d each is $159.50. 10d 159.50
22. The total area decreased by 75 square feet is 250 square feet. a 75 250
21. 65 is 5 times a number. 65 5n
20. The total of Joshua’s savings and $350 is $925. s 350 925
19. The number of members divided by 6 is 15. 15
m
6
18. 17 more than some number is equal to 85. n 17 85
17. $12 less than the original price is $48. p 12 48
16. The quotient of z and 10 is equal to 32. 32
z
10
15. The difference of 100 and x is 57. 100 x 57
14. The product of 6 and m is 216. 6m 216
13. The sum of a number and 16 is equal to 45. n 16 45
Write each verbal sentence as an algebraic equation.
e2
11. 2 hours more than the estimate
p 500
10. the total of Ben’s score and 75
8. the height decreased by 2 inches h 2
7. the cost of 7 CDs at $d each 7d
9. $500 less than the sticker price
6. the cost split among 4 people
5. the score increased by 8 points p 8
c
4
2. the sum of d and 7
d7
7AF1.1, 7AF1.4
1. a number divided by 5 n
5
Write each verbal phrase as an algebraic expression.
1-7
NAME ________________________________________ DATE ______________ PERIOD _____
Writing Equations
Practice
7AF1.1, 7AF1.4
n
4
3
15
5
p
2,000
3,000
4,000
2
3
4
g 1,000k
g
1,000
1
k
Grams, g
Kilograms, k
9.
Chapter 1
a 3h
51
10. MONEY Carlotta earns $3 for every hour
that she baby sits. Complete the table of
values showing the amount she earns for
baby sitting 1, 2, 3, 4, and h hours. Given
h, a number of hours, write an equation to
find a, the amount that Carlotta earns.
8.
3
4
9
12
3
6
9
12
3h
Amount, a
Glencoe California Mathematics, Grade 7
1
2
3
4
h
Hours, h
f
y 3
2
6
y
1
3
f
Yards, y
Feet, f
Write an equation to model the relationship between the quantities
in each table.
p
15
p number of plays; 5 or
7. FOOTBALL A team had a total gain of 15 yards over several plays with
an average gain of 5 yards per play. How many plays are represented?
6. GEOMETRY A rectangle's width is one-third its length. If the width is 8
1
inches, what is the length of the rectangle? length; 8
score; m 6 88
5. GRADES Kelly’s test score was 6 points higher than Michelle’s. If Kelly’s
test score was 88, what was Michelle’s test score? m Michelle’s test
Define a variable. Then write an equation that could be used to solve
each problem.
b
6
4. When the bananas were divided evenly among the 6 monkeys, each
monkey received 4 bananas. b the total number of bananas;
3. A class of 30 students separated into equal sized teams results in 5
30
students per team. n the number of teams; 5
m Michael’s age, m 3 14
Latisha had before her birthday; m 25 115
2. At 14 years old, Adam is 3 years younger than his brother Michael.
1. After receiving $25 for her birthday, Latisha had $115. m = the money
Define a variable. Then write an equation to model each situation.
1-7
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-7)
Lesson 1-7
Chapter 1
A23
Chapter 1
p population of Oakland;
p 9,477 390,007
52
Glencoe California Mathematics, Grade 7
Answers
Glencoe California Mathematics, Grade 7
h height of Kings Peak;
h 8,667 4,861
8. GEOGRAPHY Kings Peak in Utah is
8,667 feet taller than Spruce Knob in
West Virginia. Spruce Knob is 4,861
feet tall. Define a variable and write an
equation to find the height of Kings
Peak.
d distance of Mars from the
Sun; 6d 1,429,400,000
7. POPULATION The population of
Oakland, California, is 9,477 more than
the population of Omaha, Nebraska.
Omaha has a population of 390,007.
Define a variable and write an equation
to find the population of Oakland.
b number of San Diego
branches; 79 b 44
6. ASTRONOMY Saturn is 6 times farther
from the Sun than Mars. Define a
variable and write an equation to find
the distance of Mars from the Sun if
Saturn is about 1,429,400,000 km from
the sun.
2
5. LIBRARIES The San Diego Public Library
has 44 fewer branches than the Chicago
Public Library. Define a variable and
write an equation for the number of
branches in the San Diego Public
Library if Chicago has 79 branches.
e the amount of energy Brazil
used; 4e 12,000
number of curium; 48 1c
4. CHEMISTRY The atomic number of
cadmium is half the atomic number of
curium. The atomic number for
cadmium is 48. Define a variable and
write an equation to find the atomic
number of curium. c atomic
a Julia’s age; 13 j 3
3. ENERGY One year, China consumed
4 times as much energy as Brazil.
Define a variable and write an equation
to find the amount of energy Brazil
used that year if China used 12,000
kilowatt-hours.
v Tennessee’s votes;
23 v 34
7AF1.1, 7AF1.4
2. CIVICS In the 2004 presidential election,
Texas had 23 more electoral votes than
Tennessee. Define a variable and write
an equation to find the number of
Tennessee’s electoral votes if Texas had
34 votes.
Writing Equations
Word Problem Practice
1. AGE Julia is 3 years younger than
Kevin. Kevin is 13. Define a variable
and write an equation to find Julia’s
age.
1-7
NAME ________________________________________ DATE ______________ PERIOD _____
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Enrichment
7AF1.1
1
4
2
8
3
12
4
16
5
20
7
28
6
24
8
32
Multiply the previous term by
three; 729, 2187, 6561
D. 3, 9, 27, 81, 243, ___, ___, ___
Subtract three from the previous
term; 21, 24, 27
B. 3, 6, 9,12, 15, 18, ___, ___, ___
Add to the previous term two more
than was added one term before;
49, 64, 81
t 62300 0.1n
5. Sequence E
2. Sequence B t 3n
6. Sequence F t n
Chapter 1
t n 10; 110
11. 11, 12, 13, 14, 15, …
t 2n 2; 198
9. 0, 2, 4, 6, 8, …
t 3n 1; 301
7. 4, 7, 10, 13, 16, …
t 0.75n; 75
Glencoe California Mathematics, Grade 7
See students’ work.
12. Write your own sequence rule and
find the first 5 terms.
10. 0.75, 1.5, 2.25, 3, 3.75, …
t n2 1; 10,001
8. 2, 5, 10, 17, 26, …
53
2
3. Sequence C t 2n 1
Write an equation rule for each of the sequences below. Then use the
equation to find the 100th term.
4. Sequence D t 3
n
1. Sequence A t 2n
Write an equation rule for each of the sequences in exercises 1–6. Be
careful that your rule gives the correct first term.
Look again at the beginning example. The rule is multiply the position number by four.
If we call the position numbers n, the algebraic expression for the rule is 4n. For each
term t 4n.
The rule of a sequence can be generalized into an equation so that it is possible to find the
10th term, 100th term, or nth term without writing out of the terms in between. The rule of
the sequence shows the relationship between a term and its position number.
Divide the previous term by ten;
0.0623, 0.00623, 0.000623
E. 6,230, 623, 62.3, 6.23, 0.623, ___, ___, ___ F. 1, 4, 9, 16, 25, 36, ___, ___, ___
Add two to the previous term;
15, 17, 19
C. 3, 5, 7, 9, 11, 13, ___, ___, ___
Add two to the previous term;
14, 16, 18
A. 2, 4, 6, 8, 10, 12, ___, ___, ___
Pattern
4
4
4
4
Describe the pattern in words and write the next three terms in each of the
following sequences.
Position
Term
A sequence can be extended by finding the pattern, describing it, and then applying the
description to produce successive terms. To describe the pattern in words, we could write,
“Add four to the previous term to find the next term.” Determine the pattern rule for the
sequence below. What are the next three terms?
Writing Equations to Describe Sequences
1-7
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-7)
Lesson 1-7
Chapter 1
7MR1.1, 7NS1.2
Problem-Solving Investigation: Work Backward
Study Guide and Intervention
• Select a strategy including a possible estimate.
• Solve the problem by carrying out your plan.
• Examine your answer to see if it seems reasonable.
Plan
Solve
Check
A24
Start with $110 for the first week and work forward. On the second week she
deposited twice as much money in the bank than on the first week, which is
$220. On the third week, she deposited $40 less than the second week, which is
$180. On the fourth week she deposited $20 more than on the third week, or
$200. This is what you know she deposited on the fourth week.
Chapter 1
Glencoe California Mathematics, Grade 7
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
54
Xing is 18 years old; Eliot is 9 years old; Sam is 13 years old.
2. AGE Sam is 4 years older than Eliot. Eliot is 9 years younger than Xing. Xing is 3 years
older than Damien. If Damien is 15 years old, how old are each of the other boys?
1. SHOPPING Jack spent a total of $87.58 when he went shopping for camping supplies. He
spent $36.89 on food, $23.24 on a sleeping bag, and bought lunch. When he got home,
he had $15.70. How much did he spend on lunch? $11.75
Use the work backward strategy to solve each problem.
Exercises
Check
2
Work
backward.
Divide by
2.
First Week
$110
Start with the $200 Mari put in the bank on the fourth week.
Solve
Third Week
Second Week
$20
$180
$40
$220
Work
This is $40 less
Work
This is twice as
backward. than the second backward.
much as the
Subtract
week.
Add $40.
first week.
$20.
Start with the amount she put in the bank on the last week and work
backward.
Plan
Fourth Week
$200
This is $20
more than the
third week.
You know that Mari put $200 in the bank on the fourth week. You need to know
how much money she put in the bank on the first week.
Explore
Mari put money in her savings account each week. She put a certain amount of money in
the bank on the first week. On the second week she put twice as much money in the bank
as the first week. On the third week, she put $40 less in the bank than on the second week.
On the fourth week, she put $20 more in the bank than on the third week. Mari put $200 in
the bank on the fourth week. How much money did Mari put in the bank on the first week?
Example 1
• Determine what information is given in the problem and what you need to find.
Explore
You may need to work backward to solve a problems.
1-8
NAME ________________________________________ DATE ______________ PERIOD _____
7MR1.1, 7NS1.2
Problem-Solving Investigation: Work Backward
Skills Practice
Arrival Time
10:37 A.M.
1:45 P.M.
3:30 P.M.
Chapter 1
55
Glencoe California Mathematics, Grade 7
6. Mrs. Gonzales left her office at 7:25 a.m. She planned that it would take her 30
minutes to get to the airport, but the traffic was so heavy it took an additional 20
minutes. It takes 30 minutes to check her baggage and walk to the boarding gate. What
is the first flight she can take to Dallas? Flight 142
5. Charles needs to take Flight 295. He needs 45 minutes to eat breakfast and pack. It
takes 25 minutes to get to the airport. To be at the airport 90 minutes early, what is
the latest time he can start eating breakfast? 9:20 A.M.
Flight Number
253
142
295
Airline Schedule
Minneapolis, MN to Dallas, TX
Departure Time
8:20 A.M.
11:52 A.M.
12:00 P.M.
Use the table to solve each problem.
4. JOGGING Edmund is training for a marathon. He ran a certain number of miles on
Monday. On Wednesday, he ran 2 more miles than on Monday. On Saturday, he ran
twice as far as on Wednesday. On Sunday, he ran 6 miles less than on Saturday. He ran
8 miles on Sunday. How many miles did Edmund run on Monday? 5 miles
3. NUMBERS Jana is thinking of a number. If she divides her number by 12 and then
multiplies the quotient by 8, the result is 520. What number is Jana thinking of? 780
2. SHIPPING An overseas cargo ship was being loaded. At the end of each day, a scale
showed the total weight of the ship’s cargo. On Monday, 48 tons of cargo were loaded
onto the ship. On Tuesday, three times as much cargo was loaded on to the ship as on
Monday. On Wednesday, 68 tons of cargo were loaded onto the ship. On Thursday, 0.75
as much cargo was loaded onto the ship as on Wednesday. On Friday, 120 tons of cargo
were loaded onto the ship. At the end of the day on Friday, the scale showed that the
ship was carrying 690 tons of cargo. How much cargo was the ship carrying when it
first came into port on Monday? 259 tons
1. SKATEBOARDS On Monday, David’s skateboard shop received its first shipment of
skateboards. David sold 12 skateboards that day. On Thursday, he sold 9 skateboards.
On Friday, he received a shipment of 30 more skateboards and sold 10 skateboards. He
then had a total of 32 skateboards in his shop. How many skateboards were delivered
on Monday? 33
Use the work backward strategy to solve each problem.
1-8
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-8)
Lesson 1-8
Chapter 1
A25
3. BAKING Isabel doubled her recipe for
chocolate chip cookies. After her
brothers ate 8 cookies, she set aside half
of the remaining cookies for a school
party. Isabel then gave 2 dozen cookies
to her neighbor. She had 12 cookies left
over. How many cookies does one recipe
make? 40 cookies
• Use the four-step plan.
• Work backward.
Problem-Solving Strategies
Use any strategy to solve Exercises 3
and 4. Some strategies are shown below.
2. GRADES Kumiko had an average of 92
on her first three math tests. Her scores
on the second and third tests were 97
and 89. What was her score on the first
test? 90
1. TRAVEL Rajiv and his family left home
on a trip and drove for 2 hours before
they stopped to eat. After 1.5 hours,
they were back on the road. They
arrived at their destination 3 hours
later at 5:00 P.M. What time did they
leave home? 10:30 A.M.
Use the work backward strategy to
solve Exercises 1 and 2.
Chapter 1
7MR1.1, 7NS1.2
33 min
72 min
255 min
213 min
56
Glencoe California Mathematics, Grade 7
Answers
Glencoe California Mathematics, Grade 7
Subtract; 1972 1944 28;
88 28 60; 60 years old
6. U.S. PRESIDENTS Harry S Truman was
elected president in 1944. He died in
1972 at the age of 88. How old was he at
the time he was elected?
Subtraction; division; addition;
775 97 678;
678 2 339; 339 97 436;
$436 million
5. MOVIES The two animated films with
the highest box office receipts brought
in a total of $775 million. If one film
brought in $97 million more than the
other, how much did the film with the
highest receipts bring in?
For Exercises 5 and 6, select an
appropriate operation to solve the
problem. Justify your solution and
solve the problem.
Select the Operation
How many more minutes per week do
boys spend using the Internet for
purposes other than school work than
girls? 81 min
Boys
Girls
Gender Time Used for Total Time
School Work per Week
4. ANALYZE TABLES The table below gives
the results from a poll taken at school
about the times in minutes that boys
and girls spend using the Internet for
school work and the total time spent
using the Internet each week.
Problem-Solving Investigation: Work Backward
Practice
Mixed Problem Solving
1-8
NAME ________________________________________ DATE ______________ PERIOD _____
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
7MR1.1, 7NS1.2
Problem-Solving Investigation: Work Backward
Word Problem Practice
Tuesday
20 minutes
more than
Monday
Chapter 1
2 hours and 20 minutes
5. WEATHER On Monday, Eliza read her
book. On Tuesday, she read three times
as long as she read on Monday. On
Wednesday she read 20 minutes less
than Tuesday. On Thursday she read
for 20 minutes, which was half as long
as she read on Wednesday How many
minutes did Eliza read over the 4-day
period?
17 minutes
3. HOCKEY During a hockey game,
Brandon played 7 less minutes than
Nick. Zach played 12 minutes more
than Brandon. Hunter played twice as
long as Zach. Hunter played for 44
minutes. How many minutes did Nick
play in the hockey game?
30 minutes
57
Saturday
Twice as
long as
Thursday
Sunday
15 minutes
less than
Saturday–
45 minutes
Glencoe California Mathematics, Grade 7
30 stamps
6. STAMPS Zoe added 23 stamps to her
collection. Three months later her
collection had tripled in number to a
total of 159 stamps. How many stamp
did Zoe have to start her collection?
4. PACKAGES In the morning, a delivery
truck delivers 24 of it packages to a
factory. It then goes to a distribution
lot, where the remaining packages are
separated into 4 equal groups and put
on other trucks. There were 18
packages in each of the groups. How
many packages were on the delivery
truck to begin with? 96 packages
20 minutes
2. How many minutes did Elena practice
on Monday?
Thursday
10 minutes
less than
Tuesday
1. How many minutes did Elena practice
the clarinet on Thursday?
Monday
?
record of the amount of time Elena practiced her clarinet in a week.
CLARINET PRACTICE For Exercises 1 and 2, use the table at the right. It is a
Use the work backward strategy to solve each problem.
1-8
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-8)
Lesson 1-8
Chapter 1
⫽
⫽
1
x 1
1. x 1 4 3
4
1
1
1
1
x 3
x
1
⫽
⫽
1
1
1
7
1
1
1
1
⫺1 ⫺1
x (4)
x
⫺1 ⫺1
c. Add 3 to each side.
d. Add 5 to each side.
_____ d
_____ c
s 5 14
4 3 p
11 m 33 _____ a
A26
Add 7 to each side.
13
Chapter 1
Glencoe California Mathematics, Grade 7
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
58
Chapter 1
13. 62 b 45 17
7. 17 c 41 24
4. x 5 8
1. s 4 12 16
59
14. x 39 65
11. 13 t 29
26
42
8. v 36 25 61
5. b 10 34 24
2. d 2 21 19
9. y 29 51
6. f 22 6
22
16
3. h 6 15 9
Glencoe California Mathematics, Grade 7
15. 56 47 n 9
12. 55 39 k 16
51 25 51 (25) or 76
Replace h with 51. Is this sentence true?
Write the original equation.
25 25 0 and 76 25 51. h is by itself.
Add 25 to each side.
Write the equation.
Solve each equation. Check your solution.
10. 19 z 32 51
11. 9 g 14 5
h 25¬ 76
51 25¬ 76
76¬ 76 ✓
Exercises
Check
26 19 45
Replace w with 26. Is this sentence true?
Write the original equation.
Solve h 25 76. Check your solution.
w 19¬ 45
26 19¬ 45
45¬ 45 ✓
h 25¬ 76
h 25 25¬ 76 25
h¬ 51
Example 2
Check
19 19 0 and 45 19 26. w is by itself.
Subtract 19 from each side.
Write the equation.
Solve w 19 45. Check your solution.
w 19 45
w 19 19 45 19
w 26
Example 1
12. Write two addition and two subtraction equations of your own. Trade
your equations with a partner and solve. Explain to each other the
method you used to solve the equations. See students’ work.
10. 3 7 r 10
5
⫺1
⫺1 ⫺1
6AF1.1
Solving Addition and Subtraction Equations
Study Guide and Intervention
You can use the following properties to solve addition and subtraction equations.
• Addition Property of Equality — If you add the same number to each side of an equation, the two
sides remain equal.
• Subtraction Property of Equality — If you subtract the same number from each side of an equation,
the two sides remain equal.
1-9
NAME ________________________________________ DATE ______________ PERIOD _____
Remember What You Learned
9. z 8 2 6
Solve each equation.
Subtract 11 from each side.
_________________________ Subtract 3 from each side.
8. 17 11 k _________________________
7. c 3 9
6. w 7 2 _________________________
For Exercises 6–8, explain how to solve each equation.
b. Subtract 6 from each side.
_____ b
x69
a. Subtract 11 from each side.
5. Match the method of solving with the appropriate equation.
Read the Lesson
⫽
⫽
⫺1 ⫺1
3. x (4) 5 1
4. Explain how you would find a value of x that makes x (3) 8 true
without using models. Subtract 3 from each side.
1
1
2. x 3 7 4
Solve each equation using algebra tiles.
Complete the Mini Lab at the top of page 65 in your textbook.
Write your answers below.
x
6AF1.1
Solving Addition and Subtraction Equations
Lesson Reading Guide
Get Ready for the Lesson
1-9
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-9)
Lesson 1-9
Chapter 1
A27
60
Glencoe California Mathematics, Grade 7
Answers
Glencoe California Mathematics, Grade 7
24. 27 z 47 74
23. 54 32 w 22
22. 111 x 68 43
Chapter 1
21. g 35 62 27
18. m 65 11 54
15. f 25 35 60
20. n 75 42 117
36
19. r 53 19 72
14. 17 19 x
12. 22 y 29 7
17. s 46 72 26
8
11. 19 z 21 2
16. y 37 59 22
13. 16 24 p
10. 17 b 8 25
8. 8 d 14
7. u 4 1 3
9. 19 x 7 12
6. h 3 6
5. a 4 3 7
4. z 5 1 6
6
3. t 2 2 4
2. y 6 5 1
1. x 3 4 1
3
6AF1.1
Solving Addition and Subtraction Equations
Skills Practice
Solve each equation. Check your solution.
1-9
NAME ________________________________________ DATE ______________ PERIOD _____
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
6AF1.1
8. 15 n 10 5
7. 14 2 d 16
140
R S
12. 12 c 16 4
9. 8 r 6 2
6. y 10 3 7
Chapter 1
31 p 14; 45 points
61
16. ANALYZE TABLES The total points scored by both
teams in the 2006 Super Bowl was 14 less than
the total points for 2005. Write and solve an
equation to find the total points for 2005.
p
31
2005
2006
Glencoe California Mathematics, Grade 7
Source: www.superbowl.com
Points
Year
Total Points Scored by Both
Teams in Super Bowl
45; Add the numbers on the left and then subtract the total
from each side, or subtract each number on the left from
each side one at a time; 14 boxes.
15. FUND RAISING During a five-day fund raiser, Shantell sold 8 boxes of
greeting cards the first day, 6 boxes the second day, 10 boxes the third
day, and 7 boxes the fourth day. If she sold a total of 45 boxes of greeting
cards during the five days, write an equation that can be used to find the
number of boxes Shantell sold the fifth day. Explain two methods of
solving this equation. Then solve the equation. 8 6 10 7 f 14. ARCHITECTURE The Sears Tower in Chicago was the tallest building in the
world when it was completed. Twenty-three years later, a taller building
was completed in 1996 on Taiwan. Write and solve an equation to find the
year that the Sears Tower was completed. y 23 1996; 1973
13. GEOMETRY Two angles are supplementary if
the sum of their measures is 180. The two
angles shown are supplementary. Write and
solve an equation to find the measure of
angle R. m 140 180; 40
11. 9 g 9 18
5. m 9 7 16
4. k 4 14 10
10. 11 w 5 16
2. h 3 8 11
1. t 7 12 5
3. 8 b 9 17
Solving Addition and Subtraction Equations
Practice
Solve each equation. Check your solution.
1-9
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-9)
Lesson 1-9
Chapter 1
6AF1.1
A28
62
a 67 80; 13
Chapter 1
Glencoe California Mathematics, Grade 7
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
h 543 8; 535 ft
p 832,598 6,823,568;
p 7,656,166
8. POPULATION In 2005, the population of
Honduras is the population of Haiti
decreased by 832,598. The population of
Honduras is 6,823,568. Write and solve
a subtraction equation to find the
population of Haiti.
t 12 7; 5°F
7. ELEVATION The lowest point in
Louisiana is 543 feet lower than the
highest point in Louisiana. The
elevation of the lowest point is 8 feet.
Write and solve a subtraction equation
to find the elevation of the highest
point in Louisiana.
mA ⫽ 78˚
6. CHEMISTRY The atomic number of
mercury is the sum of the atomic
number of aluminum and 67. The
atomic number of mercury is 80. Write
and solve an addition equation to find
the atomic number of aluminum.
B A
5. WEATHER After the temperature
had risen 12°F, the temperature
was 7°F. Write and solve an
addition equation to find the
7 F
starting temperature.
180˚
m 78° 180°;
102°
b 40 287; $327
4. BANKING After you withdraw $40 from
your checking account, the balance is
$287. Write and solve a subtraction
equation to find your balance before
this withdrawal.
r 24 29; 53 representatives
3. GEOMETRY Two angles are
supplementary if the sum of their
measures is 180°. Angles A and B are
supplementary. If the measure of
angle A is 78°, write and solve an
addition equation to find the measure
of angle B.
a 2 79; 77 years old
2. CIVICS New York has 24 fewer members
in the House of Representatives than
California. New York has 29
representatives. Write and solve a
subtraction equation to find the
number of California representatives.
Solving Addition and Subtraction Equations
Word Problem Practice
1. AGE Walter lived 2 years longer than
his brother Martin. Walter was 79 at
the time of his death. Write and solve
an addition equation to find Martin’s
age at the time of his death.
1-9
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment
Chapter 1
D.
A.
45˚
2(45°) x° 180°
63
Glencoe California Mathematics, Grade 7
45°
90°
D
360° x° 150° 90°
F
120°
B
x° 72° 180°
30° x° 15° 90°
75°
108°
E
A
90° x° 15°
125°
30˚
Angle Measurement (x)
15˚
x˚
15˚
C
x˚
F.
Letter of Figure
45˚
E.
35˚
x˚
Equation
x˚
150˚
x˚ 90˚
C.
35° 20° x° 180°
72˚
x˚
B.
Match each equation in the chart at the bottom of the page with a
figure that could be used to solve for the missing angle measurement.
Then solve for that measurement.
Angles are complementary if their measures add to 90°. If their measures
add to 180°, they are supplementary. The total number of degrees in the
measures of the central angles of a circle is 360°. The sum of the measures of
the angles in a triangle is 180°. A straight angle measures 180°.
20˚
7AF1.1
Equations are often used to solve geometric problems. To work the problems
on this page, you will need to use the following facts.
Geometric Equations
1-9
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-9)
Lesson 1-9
Chapter 1
6AF1.1
Solving Multiplication and Division Equations
Lesson Reading Guide
multiply
divide
A29
135 15 9
64
Glencoe California Mathematics, Grade 7
Answers
Glencoe California Mathematics, Grade 7
3
14
Chapter 1
9. 29t 145 5
132
7. 17c 68 4
Chapter 1
10. 125 5z 25
65
11. 13t 182
Glencoe California Mathematics, Grade 7
12. 117 39k
10
8. h 12
11
8
6. x 7 70
3. 7h 21 3
5. f 6 48
5
2. 2d 12 6
Solve each equation. Check your solution.
Exercises
9¬ 9 ✓
Replace d with 135.
Write the original equation.
d 135
Multiply each side of the equation by 15.
4. 8x 40 5
11. 9 9g 1
Check
d
¬ 9
15
135
¬ 9
15
d
(15) 9(15)
15
d
9
15
15
This sentence is true.
Replace w with 6.
Solve d 9. Check your solution.
114¬ 114 ✓
Write the original equation.
Identity Property; 1w w
1. r 6 30
21
19w¬ 114
w6
19 19 1 and 114 19 6.
Divide each side of the equation by 19.
19w
114
19
19
1w 6
Write the equation.
19w 114
Solve 19w 104. Check your solution.
19(6)¬ 114
Example 2
Check
Example 1
• Multiplication Property of Equality — If you multiply each side of an equation by the same number, the
two sides remain equal.
• Division Property of Equality — If you divide each side of an equation by the same nonzero number,
the two sides remain equal.
12. Write two multiplication and two division equations of your own. Trade
your equations with a partner and solve. Explain to each other the
method you used to solve the equations. See students’ work.
10. 3 x
7
Divide each side by 16.
6AF1.1
Solving Multiplication and Division Equations
Study Guide and Intervention
You can use the following properties to solve multiplication and division equations.
1-10
NAME ________________________________________ DATE ______________ PERIOD _____
Remember What You Learned
9. 8r 32 4
Solve each equation.
8. 64 16k
_________________________
_________________________ Divide each side by 2.
7. 2c 14
6
_________________________ Multiply each side by 6.
multiply
6. u 13
Explain how to solve each equation.
5. To solve 7 d, __________ each side by 6.
6
4. To solve 65 5t, __________ each side by 5. divide
3. To solve b 4, __________ each side by 2.
2
2. To solve 3x 51, __________ each side by 3.
Complete each sentence.
Read the Lesson
1. If d represents the number of days the bamboo has been growing, write a
multiplication equation you could use to find how long it would take for
the bamboo to reach a height of 210 inches. 35d 210
Read the introduction at the top of page 70 in your textbook.
Write your answers below.
Get Ready for the Lesson
1-10
NAME ________________________________________ DATE ______________ PERIOD _____
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Answers (Lesson 1-10)
Lesson 1-10
Chapter 1
A30
Chapter 1
22. 23 506
g
22
31
Glencoe California Mathematics, Grade 7
4
210
Glencoe California Mathematics, Grade 7
24. 47k 517 11
14
21. 15 z
19
18. s 9 171
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
66
23. 16 400
y
25
20. 16q 272 17
19. m 7 217
98
17. 21a 126 6
153
y
14. 14 7
16. 17c 136 8
13. w 17
9
11. 11d 143
8
99
15. 112 8v 14
12. 116 29k
13
10. 135 9z 15
9. 18y 144
7. 14g 56 4
12
8. t 11 132
4. 7z 49 7
21
6. a 11
9
5. n 7
3
3
3. 5x 15
21
2. 3c 12 4
1. u 3
7
6AF1.1
Solving Multiplication and Division Equations
Skills Practice
Solve each equation. Check your solution.
1-10
NAME ________________________________________ DATE ______________ PERIOD _____
n
11. 9 72
8
a
12. 3 75
25
c
9. 43 86
2
6. 56 7d 8
3. 36 9b 4
Chapter 1
Solve each equation.
84
17. 3 28
g
8g 104; 13 gallons
67
4
18. 8 0.5
x
16. the number of gallons in 104 pints
2q 24; 12 quarts
Glencoe California Mathematics, Grade 7
144
19. 16 9
r
1 gallon 8 pints
1 gallon 4 quarts
1 quart 4 cups
1 quart 2 pints
1 pint 2 cups
MEASUREMENT For Exercises 15 and 16, refer to the table. Write and
solve an equation to find each quantity.
Customary System
15. the number of quarts in 24 pints
Conversions (capacity)
14. POPULATION The population of South Africa is four times the population of Greece. If
the population of South Africa is 44 million, write and solve a multiplication equation to
find the population of Greece. 44 4g; 11 million
13. CARS Mrs. Alvarez bought a new car. Her monthly payments are $525. If she will pay a
total of $25,200 in payments, write and solve a multiplication equation to find the
number of payments.
525n 25,200; 48 payments
y
10. 16 48
3
v
8. 20 80
4
5. 12m 72 6
4. 3p 24 8
55
2. 8h 64 8
1. 5s 45 9
x
7. 11
5
6AF1.1
Solving Multiplication and Division Equations
Practice
Solve each equation. Check your solution.
1-10
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-10)
Lesson
Lesson 1-10
X–4
Chapter 1
A31
26a 338; 13 yr
7. AGE The product of Bart’s age and 26 is
338. Write and solve a multiplication
equation to find Bart’s age.
20m 120; 6 min
5. ROBOTS The smallest robot can travel
20 inches per minute through a pipe.
Write and solve a multiplication
equation to find how long it will take
this robot to travel through 10 feet of
pipe.
3d 57; 19 days
3. EXERCISE Jasmine jogs 3 miles each day.
Write and solve a multiplication
equation to find how many days it will
take her to jog 57 miles.
9h 54; 6 h
Chapter 1
6AF1.1
68
Glencoe California Mathematics, Grade 7
Answers
Glencoe California Mathematics, Grade 7
325p 6,825; 21 yr
8. POPULATION The population of a small
town is increasing at a rate of 325
people per year. Write and solve a
multiplication equation to find how
long it will take the population to
increase by 6,825.
40w 680; 17 days
6. BANKING Nate withdraws $40 from his
checking account each day. Write and
solve a multiplication equation to find
how long it will take him to withdraw
$680.
62h 558; 9 h
4. TRAVEL On a trip, the Rollins family
drove at an average rate of 62 miles per
hour. Write and solve a multiplication
equation to find how long it took them
to drive 558 miles.
0.50b 5; 10 bars
2. SHOPPING Granola bars are on sale
for $0.50 each. If Brad paid $5 for
granola bars, write and solve a
multiplication equation to find how
many bars he bought.
Solving Multiplication and Division Equations
Word Problem Practice
1. WAGES Felipe earns $9 per hour for
helping his grandmother with her yard
work. Write and solve a multiplication
equation to find how many hours he
must help his grandmother in order to
earn $54.
1-10
NAME ________________________________________ DATE ______________ PERIOD _____
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Enrichment
7AF1.1
Chapter 1
69
n 6 2n; n 6; integers are 6, 8, 10, 12
Glencoe California Mathematics, Grade 7
7. Find four consecutive even integers such that the largest is twice the
smallest.
n 2 3n 6; n 4; integers are 4 and 6
6. The larger of two consecutive even integers is 6 less than 3 times the
smaller. Find the integers.
n (n 2) (n 4) (n 6) 80;
n 23; integers are 23, 21, 19, 17
5. Find the four consecutive odd integers with a sum of 80.
n (n 1) (n 2) 12; n 5; integers are 5, 4, 3
4. Find the three consecutive integers that have a sum of 12.
Write an equation to solve each problem.
9, 11, 13, 15, 17
3. What five consecutive odd integers does Expression C produce when
n 9?
0, 2, 4, 6, 8
2. What five consecutive even integers does Expression B produce when
n 0?
8, 9, 10, 11, 12
1. What five consecutive integers does Expression A produce when n 8?
Use Expressions A, B, and C for these problems.
Phrase C
“five consecutive odd integers”
Expression C n, n 2, n 4, n 6, n 8
Phrase B
“five consecutive even integers”
Expression B n, n 2, n 4, n 6, n 8
Phrase A
“five consecutive integers”
Expression A n, n 1, n 2, n 3, n 4
Equations can be used to solve problems that involve consecutive integers. In
solving these problems, you will need to translate certain phrases into
algebraic expressions. Here are some examples.
Consecutive Integers
1-10
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-10)
Lesson
Lesson 1-10
X–4
Chapter 1 Assessment Answer Key
2 pencils and
1 eraser
1.
2.
7
3.
32
4.
8
5.
9
Quiz 2 (Lesson 1-4 and 1-5)
Page 73
1.
4
2.
27
3.
33
4.
18
5.
3
6.
13
7.
22
8.
4
9.
9
10.
19
Quiz 3 (Lesson 1-6 through 1-8)
Page 74
1.
24
2.
35
3.
25
4.
9
5.
2
6.
17
7.
n (5)
8.
c3
9.
n 9 24
10.
Mid-Chapter Test
Page 75
1.
D
2.
H
3.
A
4.
F
5.
D
6.
4 3 2 1 0 1 2
a 15 12.50
Quiz 4 (Lesson 1-9 and 1-10)
Page 74
1.
2
2.
21
3.
28
4.
12
5.
$25
7.
3
8.
5 7; 2 cards
9.
10.
2 buses
(continued on the next page)
Chapter 1
A32
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Quiz 1 (Lesson 1-1 through 1-3)
Page 73
Chapter 1 Assessment Answer Key
Vocabulary Test
Page 76
1.
inverse
operations
2.
coordinate
3.
absolute value
4. negative number
Form 1
Page 77
Page 78
1.
B
12.
J
2.
J
13.
A
3.
C
14.
G
4.
G
15.
D
5.
A
16.
J
6.
H
7.
D
17.
A
8.
F
18.
H
19.
A
20.
G
5. counterexample
7.
powers
8.
solutions
9.
evaluate
10.
inequality
an educated guess
used in some
problem-solving
strategies where,
for example, you
guess that the
numbers in the
problem follow
11. some pattern
an open sentence
that is true for any
numbers, such as
a b b a,
the Commutative
Property of
Addition
12.
Chapter 1
9.
D
10.
F
11.
C
B:
A33
Glencoe California Mathematics, Grade 7
Answers
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
6. additive inverses
Chapter 1 Assessment Answer Key
1.
A
2.
F
3.
C
4.
5.
F
Page 80
11.
D
12.
F
13.
C
14.
J
A
15.
6.
D
2.
G
3.
A
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10.
Chapter 1
B
15.
7.
G
11.
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C
Page 82
4.
6.
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8.
1.
A
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16.
7.
Form 2B
Page 81
19.
D
20.
G
B:
8,000
F
B:
A34
5
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Form 2A
Page 79
Chapter 1 Assessment Answer Key
Form 2C
Page 83
2.
3.
4.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5.
7.5 in.
14
15.
17
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28
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8
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Chapter 1
14.
A35
Glencoe California Mathematics, Grade 7
Answers
1.
Page 84
Chapter 1 Assessment Answer Key
Form 2D
Page 85
Page 86
1. 12 cucumbers &
2 green peppers
3.
4.
5.
16.
80
17.
140
18.
8
19.
8
20.
n 14
21.
9 lawns
22.
22
23.
7
24.
13
25.
144
B:
2A
b
12
4
7.
4
8.
3
9.
2
2
40
12.
18
13.
18
Chapter 1
16
23
10
11.
15.
6
6.
10.
22
A36
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2.
14.
Chapter 1 Assessment Answer Key
Form 3
Page 87
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
No; 9.99 12.95 1. 6.75 10.39 40
2.
360
3.
105
13.
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15.
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B:
2A
b
h
Chapter 1
A37
Glencoe California Mathematics, Grade 7
Answers
Page 88
Chapter 1 Assessment Answer Key
Extended-Response Test, Page 89
Scoring Rubric
Specific Criteria
4
The student demonstrates a thorough understanding of the mathematics
concepts and/or procedures embodied in the task. The student has
responded correctly to the task, used mathematically sound procedures,
and provided clear and complete explanations and interpretations. The
response may contain minor flaws that do not detract from the
demonstration of a thorough understanding.
3
The student demonstrates an understanding of the mathematics concepts
and/or procedures embodied in the task. The student’s response to the
task is essentially correct with the mathematical procedures used and the
explanations and interpretations provided demonstrating an essential but
less than thorough understanding. The response may contain minor errors
that reflect inattentive execution of the mathematical procedures or
indications of some misunderstanding of the underlying mathematics
concepts and/or procedures.
2
The student has demonstrated only a partial understanding of the
mathematics concepts and/or procedures embodied in the task. Although
the student may have used the correct approach to obtaining a solution or
may have provided a correct solution, the student’s work lacks an essential
understanding of the underlying mathematical concepts. The response
contains errors related to misunderstanding important aspects of the task,
misuse of mathematical procedures, or faulty interpretations of results.
1
The student has demonstrated a very limited understanding of the
mathematics concepts and/or procedures embodied in the task. The
student’s response to the task is incomplete and exhibits many flaws.
Although the student has addressed some of the conditions of the task, the
student reached an inadequate conclusion and/or provided reasoning that
was faulty or incomplete. The response exhibits many errors or may be
incomplete.
0
The student has provided a completely incorrect solution or
uninterpretable response, or no response at all.
Chapter 1
A38
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Level
Chapter 1 Assessment Answer Key
Extended-Response Test, Page 89
Sample Answers
In addition to the scoring rubric found on page A38, the following sample answers
may be used as guidance in evaluating open-ended assessment items.
b. The equation is s 80.
1. a. To find the average of Theo’s test
scores, add the five scores and then
divide the sum by 5, the number of
scores.
5
s
¬ 80
5
s
(5)¬ 80(5)
5
415
76 87 82 91 79
5
5
s¬ 400
83
The sum of Tiffany’s scores is 400.
Theo’s average is 83.
c. 85 73 87 84 329
The sum of Tiffany’s scores is 400.
The equation is m 329 400.
b.
72 74 76 78 80 82 84 86 88 90 92 94
83
83
83
83
83
7
4
1
8
4
The missing score is 71.
d. 71
85
73
87
84
d. Sample answer: The negative
differences correspond to the scores
that are less than the average score.
The negative differences correspond
to the scores that are to the left of
the average score on the number
line.
80
80
80
80
80
9
5
7
7
4
e. The sums are both 0. The sum of
the differences between a student’s
actual test scores and average score
is always 0.
e. 7 4 (1) 8 (4) 0
2. a. Theo’s average is three more than
Tiffany’s average. Let t represent
Tiffany’s average. Then the equation
is 83 t 3.
83 t 3
83 3 t 3 3
80 t
Tiffany’s average score is 80.
Chapter 1
A39
Glencoe California Mathematics, Grade 7
Answers
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
c. 76
87
82
91
79
m 329 400
m 329 329 400 329
m 71
Chapter 1 Assessment Answer Key
Standardized Test Practice
Page 90
Page 91
1.
A
B
C
D
12.
F
G
H
J
2.
F
G
H
J
13.
A
B
C
D
3.
A
B
C
D
14.
F
G
H
J
15.
A
B
C
D
16.
F
G
H
J
17.
A
B
C
D
18.
F
G
H
J
19.
A
B
C
D
F
G
H
J
5.
A
B
C
D
6.
F
G
H
J
7.
A
B
C
D
8.
F
G
H
J
9.
A
B
C
D
10.
F
G
H
J
11.
A
B
C
D
Chapter 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4.
A40
Glencoe California Mathematics, Grade 7
Chapter 1 Assessment Answer Key
Standardized Test
Page 92
24
20.
21.
{10, 3,
1, 1, 14}
22.
12
S Samantha’s
age; s 4
23.
24.
n 12 6;
n 18
25.
r = 15
26a.
When the
numbers are
graphed on a
number line, the
numbers appear
in order from least
to greatest from
left to right.
26b.
26c.
Chapter 1
Answers
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
⫺2 ⫺1 0 1 2 3
2, 0, 1, 3
A41
Glencoe California Mathematics, Grade 7
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