Algebra Readiness Curriculum by UCLA-Center
for Mathematics and Teaching, Inc.
Algebra Readiness Curriculum Guide
-Table of ContentsTitle
Page
Overview………………………………………………………………………………………………………………………..
1
Course Outline………………………………………………………………………………………………………………….
2-3
Curriculum Pacing Schedule ……………………………………………………………….…………………………………
4 - 33
Content Standards, Subtopics, Resources and Teaching Strategies
1st Quarter ……………………………………………….….………………………………………………………………….
4 - 10
2nd Quarter ………….………………………………………………………………………………………………………….
11 - 16
3rd Quarter …………………………………………………………………………….……………………………………….
17 - 25
4th Quarter ………………………………………………………………………………………………….….….....................
26 - 33
Appendix 1: California Mathematics Framework Appendix E
Appendix 2: Suggested Benchmark Assessments
Created 7/2008
Note: Weeks referenced in the Vocabulary refer to school weeks, and the weeks referenced in the Materials section refer to the weekly student packets.
i
Curriculum Guide Overview
Underlying Philosophy in the Creation of Curriculum Guides
• California Mathematics Standards are in the curriculum.
• State Testing Blueprints now allow us to know exactly how many test items come from each standard. This knowledge is
what determines how much time is given to each topic.
• Teachers need a guide to ensure teaching proportionately to the standards-this helps not only to improve test scores but also
ensures that all students have access to learning the standards.
• Quarterly benchmark assessments which match the guides and are correlated to CST will be helpful for teachers in:
1. Allowing them to see where their students are so they can modify instruction.
2. Helping them interpret the standard and level of depth expected.
Process of Creating the Curriculum Guides
• Begin with just the standards and decide the most logical way for students to learn them. This includes grouping standards
together. This creates the order of the guide.
• Look at the CST Blueprint to determine the number of weeks to be spent on each standard and pace the guides.
• Split up each topic into teaching weeks to give teachers more detailed support/guidance.
• Analyze each adopted textbook section to determine which, if any, standards are addressed within any part of the lesson.
• List suggested activities, student expectations, and informal assessments that could be used to support teaching.
• Highlight key vocabulary and any supplemental material/literature.
• Analyze the CST released test items to ensure all vocabulary and topics assessed are specifically covered in the curriculum
guide.
Created 7/2008
Note: Weeks referenced in the Vocabulary refer to school weeks, and the weeks referenced in the Materials section refer to the weekly student packets.
1
Algebra Readiness Course Outline
Quarter 1
Topic 1: Integers
Time Frame: 6 Weeks
Subtopics: Whole numbers: Vocabulary, addition and subtraction, multiplication and division, using area model to explain
multiplication, estimating quotients, place value and rounding, division with remainder, expanded form and divisibility, fourfold way;
numbers, pictures and words.
Topic 2: Rational Number Concepts
Time Frame: 4 Weeks
Subtopics: Fractions: parts and whole, fourfold way; growing shapes, factorization, fraction equivalence, fourfold way; conversion
graphs, fractions renaming, number lines; fractions, decimals; place value, rounding, and expanded form, number line; rational numbers,
decimals; ordering, addition and subtraction.
Quarter 2
Topic 3: Expressions and Equations
Time Frame: 4 Weeks
Subtopics: Numerical expressions and equations, fractions; addition and subtraction, balance puzzles, solving equations, input and
output, fractions; multiplication.
Topic 4: Length, Area, and Volume
Time Frame: 4 Weeks
Subtopics: Rectangles: Fixed area, fractions: division, rectangular prism: volume and surface area, decimals; multiplication, circles;
circumference, area, cylinders; volume and surface area.
Created 7/2008
Note: Weeks referenced in the Vocabulary refer to school weeks, and the weeks referenced in the Materials section refer to the weekly student packets.
2
Quarter 3
Topic 5: Ratio, Proportion, and Percent
Time Frame: 5 Week
Subtopics: Statistics: Analyzing Name Scores, data displays, proportional reasoning, understanding percent, ratios, rates, and
proportions, percent increase and decrease, simple interest, percent problems, linking percent and proportion, probability; spinner
puzzle, dimensional analysis, solving proportions, probability; flip and roll.
Topic 6: Conjecture and Justification
Time Frame: 4 Weeks
Subtopics: Areas of polygons, squares and square roots, defining exponent, conjectures about exponents, time-distance graphs, rules for
exponents, probability: fair games, the Pythagorean theorem, applications of Pythagorean theorem, statistics; measures of center.
Quarter 4
Topic 7: Symbolic Algebra
Time Frame: 4 Weeks
Subtopics: Using algebra to prove conjectures, order of operations, solving equations, algebra applications; perimeter problems,
simplifying expressions, algebra applications; number problems, inequalities, algebra applications; train problems, algebra applications.
Topic 8: Linear functions
Time Frame: 4 Weeks
Subtopics: Introduction to Slope, rate graph, properties of arithmetic and equality, inputs and outputs, introduction to lines, finding
slopes of lines, introduction to systems of equations, using multiple strategies to solve problems, writing equation of lines, stacking cups,
lefty-righty experiment, review.
Standards Numbering Key Used in the Guide
Created 7/2008
Materials
Example:
Example:
NS 4.2.1 = Number Sense
Fourth Grade
Standard 2.1
Week 1- SP = Weekly Packet
Student Packet
Note: Weeks referenced in the Vocabulary refer to school weeks, and the weeks referenced in the Materials section refer to the weekly student packets.
3
Topic 1
1 Quarter
Integers
st
6 Weeks
Subtopics:
Whole Numbers:
•
•
•
•
•
•
•
•
•
Vocabulary
Addition and
subtraction
Multiplication
and division
Using area models
to explain
multiplication
Estimating
quotients
Place value and
rounding
Division with
remainder
Expanded form
and divisibility
Fourfold way:
Numbers,
pictures, and
words
Materials:
Week 0 – SP
Week 1 – SP
Week 2 – SP
Week 3 – SP
Week 4 - SP
Algebra Readiness
Standards
CUSD
Resources/Teaching Strategies
Week 1 & 2 (Suggested 10 days): Semester One Startup - Week 0 Student Packet
NS 4.2.1
NS 4.2.1, MR 7.2.6
Estimate and compute the sum and difference
of whole numbers and positive decimals to two Lessons: Week 0 Student Packet - 0.1, 0.2, 0.3
places.
MR 7.2.6
Express the solution clearly and logically by
using the appropriate mathematical notation
and terms and clear language; support solution
with evidence in both verbal and symbolic
work.
NS 2.3.1
Use repeated addition, arrays, and counting by
multiples to do multiplication.
NS 4.1.3
Round whole numbers through the millions to
the nearest ten, hundred, thousand, ten
thousand, or hundred thousand.
MR 4.2.1
Use estimation to verify the reasonableness of
calculator results.
Key Vocabulary – Week 1 & 2
Algebraic Expressions
Geometry
Proportions
Area
Integers
Ratios
Decimals
Length
Statistics
Equations
Linear Functions
Volume
Exponents
Percents
Whole Numbers
Fractions
Probability
Week 3 (Suggested 5 days): Unit 1: Integers - Week 1 Student Packet
NS 2.3.1, NS 4.1.3, MR 4.2.1
Lessons: Week 1 Student Packet - 1.1, 1.2, 1.3
Associative Property
of Multiplication
Commutative Property
of Multiplication
Digit
Distributive Property
Key Vocabulary – Week 3
Dividend
Divisor
Quotient
Rounding
Estimate
Expanded Form
Topic Continues…
Created 7/2008
Note: Weeks referenced in the Vocabulary refer to school weeks, and the weeks referenced in the Materials section refer to the weekly student packets.
4
Topic 1
1 Quarter
Integers
st
6 Weeks
Subtopics:
Whole Numbers:
•
•
•
•
•
•
•
•
•
Vocabulary
Addition and
subtraction
Multiplication
and division
Using area models
to explain
multiplication
Estimating
quotients
Place value and
rounding
Division with
remainder
Expanded form
and divisibility
Fourfold way:
Numbers,
pictures, and
words
Algebra Readiness
Standards
NS 2.3.2
Use repeated subtraction, equal sharing, and
forming equal groups with remainder to do
division.
NS 3.1.5
Use expanded notation to represent numbers
(e.g., 3,206 = 3,000 + 200 + 6).
NS 4.1.4
Decide when a rounded solution is called for
and explain why such a solution may be
appropriate.
CUSD
Resources/Teaching Strategies
Week 4 (Suggested 5 days): Unit 1: Integers - Week 2 Student Packet
NS 2.3.2, NS 3.1.5, NS 4.1.4, NS 4.1.8, NS 6.2.3
Lessons: Week 2 Student Packet - 2.1, 2.2, 2.3
Key Vocabulary – Week 4
Absolute Value
Algorithm
Divisor
Estimate
Dividend
Expanded Form
Divisible
Quotient
Remainder
Standard Form
NS 4.1.8
Use concept of negative numbers (e.g., on a
number line, in counting, in temperature, in
“owning”).
NS 6.2.3
Solve addition, subtraction, multiplication, and
division problems, including those arising in
concrete situations that use positive and
negative integers and combinations of these
operations.
Materials:
Week 0 – SP
Week 1 – SP
Week 2 – SP
Week 3 – SP
Week 4 - SP
Topic Continues…
Created 7/2008
Note: Weeks referenced in the Vocabulary refer to school weeks, and the weeks referenced in the Materials section refer to the weekly student packets.
5
Topic 1
1 Quarter
Integers
st
6 Weeks
Subtopics:
Whole Numbers:
•
•
•
•
•
•
•
•
•
Vocabulary
Addition and
subtraction
Multiplication
and division
Using area models
to explain
multiplication
Estimating
quotients
Place value and
rounding
Division with
remainder
Expanded form
and divisibility
Fourfold way:
Numbers,
pictures, and
words
Materials:
Week 0 – SP
Week 1 – SP
Week 2 – SP
Week 3 – SP
Week 4 - SP
Created 7/2008
Algebra Readiness
Standards
CUSD
Resources/Teaching Strategies
Week 5 (Suggested 5 days): Unit 1: Integers - Week 3 Student Packet
NS 6.2.3
Solve addition, subtraction, multiplication, and NS 6.2.3, NS 7.1.2, MG 4.2.0, SDP 2.2.1
Lessons: Week 3 Student Packet - 3.1, 3.2, 3.3
division problems, including those arising in
concrete situations that use positive and
negative integers and combinations of these
operations.
Key Vocabulary – Week 5
NS 7.1.2
Add, subtract, multiply, and divide rational
numbers (integers, fractions, and terminating
decimals) and take positive rational number to
whole-number powers.
Absolute Value
Integers
Addends
Minuend
Difference
Subtrahend
Sum
SDP 2.2.1
Recognize, describe, and extended pattern and
determine a next term in linear pattern (e.g., 4,
8, 12…; the number of ears on one horse, two
horses, three horses, four horses).
NS 6.2.3
Week 6 (Suggested 5 days): Unit 1: Integers - Week 4 Student Packet
Solve addition, subtraction, multiplication, and
NS 6.2.3, MG 4.2.1, MR 7.2.5
division problems, including those arising in
Lessons: Week 4 Student Packet - 4.1, 4.2, 4.3
concrete situations, that use positive and
negative integers and combinations of these
operations
Key Vocabulary – Week 6
MG 4.2.1
Draw the points corresponding to linear
relationships on graph paper (e.g., draw 10
points on the graph of the equation y = 3x and
connect them by using a straight line).
Fourfold Way
Product
Explicit
Recursive
Integers
Symbols
Quotient
MR 7.2.5
Use a variety of methods, such as words,
numbers, symbols, charts, graphs, tables,
diagrams, and models, to explain mathematical
reasoning.
Note: Weeks referenced in the Vocabulary refer to school weeks, and the weeks referenced in the Materials section refer to the weekly student packets.
6
Topic 2
1 Quarter
Rational
Number
Concepts
st
4 Weeks
Subtopics:
•
•
•
•
•
•
•
•
•
•
Fractions: Parts
and wholes
Fourfold way:
Growing Shapes
Factorization
Fractions:
Equivalence
Fourfold way:
Conversion
graphs
Fraction:
Renaming
Number lines:
Fractions
Decimals: Place
value, rounding,
and expanded
form
Number line:
Rational numbers
Decimals:
Ordering,
addition, and
subtraction
Algebra Readiness
CUSD
Standards
Resources/Teaching Strategies
NS 3.3.1
Compare fractions represented by drawing or
concrete material to show equivalence and to
add and subtract simple fractions in context
(e.g., ½ of pizza is the same amount as 2/4 of
another pizza that is the same size; show that
3/8 is larger than 1/4).
Week 7 (Suggested 5 days): Unit 2 – Rational Number Concepts - Week 5 Student
Packet
NS 3.3.1, NS 3.3.2, NS 4.4.2, NS 5.1.4, MG 4.2.1, MR 7.2.5
Lessons: Week 5 Student Packet - 5.1, 5.2, 5.3
NS 3.3.2
Add and subtract simple fractions (e.g.,
determine that 1/8 + 3/8 is the same as 1/2).
NS 4.4.2
Know that numbers such as 2, 3, 5, 7 and 11 do
not have factors except 1 and themselves and
that such numbers are called prime numbers.
NS 5.1.4
Determine the prime factors of all numbers
through 50 and write the number as the product
of their prime factors by using exponents to
show multiples of a factor (e.g., 24 = 2 x 2 x2 x
3 = 23 x 3).
Area
Composite Number
Key Vocabulary – Week 7
Equivalent
Factors
Congruent
Multiple
Equal
Natural
Perimeter
Prime Number
Whole
Materials:
Week 5 – SP
Week 6 – SP
Week 7 – SP
Week 8 – SP
MG 4.2.1
Draw the points corresponding to linear
relationships on graph paper (e.g., draw 10
points on the graph of the equation y = 3x and
connect them by using a straight line).
MR 7.2.5
Use a variety of methods, such as words,
numbers, symbols, charts, graphs, tables,
diagrams, and models, to explain mathematical
reasoning.
Topic continues…
Created 7/2008
Note: Weeks referenced in the Vocabulary refer to school weeks, and the weeks referenced in the Materials section refer to the weekly student packets.
7
Topic 2
1 Quarter
Rational
Number
Concepts
st
4 Weeks
Subtopics:
•
•
•
•
•
•
•
•
•
•
Fractions: Parts
and wholes
Fourfold way:
Growing Shapes
Factorization
Fractions:
Equivalence
Fourfold way:
Conversion
graphs
Fraction:
Renaming
Number lines:
Fractions
Decimals: Place
value, rounding,
and expanded
form
Number line:
Rational numbers
Decimals:
Ordering,
addition, and
subtraction
Algebra Readiness
CUSD
Standards
Resources/Teaching Strategies
NS 3.3.1
Compare fractions represented by drawing or
concrete material to show equivalence and to
add and subtract simple fractions in context
(e.g., ½ of pizza is the same amount as 2/4 of
another pizza that is the same size; show that
3/8 is larger than 1/4).
Week 8 (Suggested 5 days): Unit 2: Rational Number Concepts - Week 6 Student
Packet
NS 3.3.1, NS 4.1.5, AF 5.1.5, MG 4.2.1
Lessons: Week 6 Student Packet - 6.1, 6.2, 6.3
NS 4.1.5
Explain different interpretations of fractions,
for example, parts of a whole, parts of a set,
and division of whole numbers by whole
numbers; explain equivalents of fractions.
AF 5.1.5
Solve problems involving linear function with
integer values; write the equation; and graph
the resulting ordered pair of integers on a grid.
MG 4.2.1
Draw the points corresponding to linear
relationships on graph paper (e.g., draw 10
points on the graph of the equation y = 3x and
connect them by using a straight line).
Key Vocabulary – Week 8
Denominator
Equivalent fraction
Improper Fraction
Mixed Number
Fourfold Way
Multiplication Property of
One
Proper Fraction
Rational Number
Materials:
Week 5 – SP
Week 6 – SP
Week 7 – SP
Week 8 – SP
Topic Continued…
Created 7/2008
Note: Weeks referenced in the Vocabulary refer to school weeks, and the weeks referenced in the Materials section refer to the weekly student packets.
8
Topic 2
1 Quarter
Rational
Number
Concepts
st
4 Weeks
Subtopics:
•
•
•
•
•
•
•
•
•
•
Fractions: Parts
and wholes
Fourfold way:
Growing Shapes
Factorization
Fractions:
Equivalence
Fourfold way:
Conversion
graphs
Fraction:
Renaming
Number lines:
Fractions
Decimals: Place
value, rounding,
and expanded
form
Number line:
Rational numbers
Decimals:
Ordering,
addition, and
subtraction
Algebra Readiness
Standards
NS 3.1.5
Use expanded notation to represent numbers
(e.g., 3,206 = 3,000 + 200 + 6).
NS 5.1.1
Estimate, round, and manipulate very large
(e.g., millions) and very small (e.g.,
thousandths) numbers.
NS 5.1.2
Interpret percents as a part of a hundred; find
decimal and percent equivalents for common
fractions and explain why they represent the
same value; compute a given percent of a
whole number.
NS 6.1.1
Compare and order positive and negative
fractions, decimals, and mixed numbers and
place them on a number line.
CUSD
Resources/Teaching Strategies
Week 9 (Suggested 5 days): Unit 2: Rational Number Concepts - Week 7 Student
Packet
NS 3.1.5, NS 5.1.1, NS 5.1.2, NS 6.1.1
Lessons: Week 7 Student Packet - 7.1, 7.2, 7.3
Key Vocabulary – Week 9
Benchmark Fraction
Compound Fraction
Multiplication Property of 1
Percent
Improper Fraction
Proper Fraction
Rational Number
Terminating
Decimal
Unit Fraction
Materials:
Week 5 – SP
Week 6 – SP
Week 7 – SP
Week 8 – SP
Topic Continued…
Created 7/2008
Note: Weeks referenced in the Vocabulary refer to school weeks, and the weeks referenced in the Materials section refer to the weekly student packets.
9
Topic 2
1 Quarter
Rational
Number
Concepts
st
4 Weeks
Subtopics:
•
•
•
•
•
•
•
•
•
•
Fractions: Parts
and wholes
Fourfold way:
Growing Shapes
Factorization
Fractions:
Equivalence
Fourfold way:
Conversion
graphs
Fraction:
Renaming
Number lines:
Fractions
Decimals: Place
value, rounding,
and expanded
form
Number line:
Rational numbers
Decimals:
Ordering,
addition, and
subtraction
Created 7/2008
Algebra Readiness
Standards
CUSD
Resources/Teaching Strategies
NS 5.1.2
Interpret percents as a part of a hundred; find
decimal and percent equivalents for common
fractions and explain why they represent the
same value; compute a given percent of a
whole number.
Week 10 (Suggested 5 days): Unit 2: Rational Number Concepts - Week 8
Student Packet
NS 5.1.2, NS 6.1.1, NS 7.1.3
Lessons: Week 8 Student Packet - 8.1, 8.2, 8.3
NS 6.1.1
Compare and order positive and negative
fractions, decimals, and mixed numbers and
place them on a number line.
Key Vocabulary – Week 10
NS 7.1.3
Convert Fractions to decimals and percents
and use there representations in estimations,
computations, and applications.
Absolute Value
Decimal
Rational Numbers
Benchmark Fraction
Integers
Repeating
Counting
Natural Number
Whole Numbers
Materials:
Week 5 – SP
Week 6 – SP
Week 7 – SP
Week 8 – SP
End of 1st Quarter
Note: Weeks referenced in the Vocabulary refer to school weeks, and the weeks referenced in the Materials section refer to the weekly student packets.
10
Topic 3
2 Quarter
Expressions
and Equations
nd
4 Weeks
Subtopics:
•
•
•
•
•
•
•
Numerical
Expressions and
Equations
Fractions:
Addition and
Subtraction
Algebraic
Expression and
Equation
Balance Puzzles
Solving Equations
Inputs and
Outputs
Fractions:
Multiplication
Algebra Readiness
Standards
NS 3.3.1
Compare fractions represented by drawing or
concrete material to show equivalence and to
add and subtract simple fractions in context
(e.g., ½ of pizza is the same amount as 2/4 of
another pizza that is the same size; show that
3/8 is larger than 1/4).
NS 6.2.1
Solve problems involving addition,
Subtraction, multiplication, and division of
positive fractions and explain why a particular
operation was used for a given situation.
NS 7.1.2
Add, subtract, multiply, and divide rational
numbers (integers, fractions, and terminating
decimals) and take positive rational number to
whole-number powers.
NS 7.2.2
Add and subtract fractions by using factoring
to find common denominator.
CUSD
Resources/Teaching Strategies
Week 11 (Suggested 5 days) : Unit 3 – Expressions and Equations - Week 9
Student Packet
NS 3.3.1, NS 6.2.1, NS 7.1.2, NS 7.2.2, AF 4.1.1, AF 4.1.2
Lessons: Week 9 Student Packet - 9.1, 9.2, 9.3
Common
Denominators
Equation
Equivalent Fractions
Expression
Key Vocabulary – Week 11
Improper Fractions
Multiple
Proper Fractions
Solve an Equation
Multiplication Property of
One
Numerator
Materials:
Week 09 – SP
Week 10 – SP
Week 11 – SP
Week 12 – SP
AF 4.1.1
Use letters, boxes, or other symbols to stand
for any number in simple expression or
equation (e.g., demonstrate an understanding
and the use of the concept of a variable).
AF 4.1.2
Interpret and evaluate mathematical
expressions that now use parentheses.
Topic Continues…
Created 7/2008
Note: Weeks referenced in the Vocabulary refer to school weeks, and the weeks referenced in the Materials section refer to the weekly student packets.
11
Topic 3
2 Quarter
Expressions
and Equations
nd
4 Weeks
Subtopics:
•
•
•
•
•
•
•
Numerical
Expressions and
Equations
Fractions:
Addition and
Subtraction
Algebraic
Expression and
Equation
Balance Puzzles
Solving Equations
Inputs and
Outputs
Fractions:
Multiplication
Materials:
Week 09 – SP
Week 10 – SP
Week 11 – SP
Week 12 – SP
Algebra Readiness
Standards
NS 6.2.1
Solve problems involving addition,
Subtraction, multiplication, and division of
positive fractions and explain why a particular
operation was used for a given situation.
AF 4.2.1
Know and understand that equals added to
equals are equal.
AF 4.1.1
Use letters, boxes, or other symbols to stand
for any number in simple expression or
equation (e.g., demonstrate and understanding
and the use of the concept of a variable).
AF 4.2.1
Know and understand that equals added to
equals are equal.
NS 6.2.1
Solve problems involving addition,
Subtraction, multiplication, and division of
positive fractions and explain why a particular
operation was used for a given situation.
CUSD
Resources/Teaching Strategies
Week 12 (Suggested 5 days): Unit 3: Expressions and Equations - Week 10
Student Packet
NS 6.2.1, AF 4.2.1, AF 4.1.1,
Lessons: Week 10 Student Packet - 10.1, 10.2, 10.3
Equal Sign
Equation
Evaluate an
Expression
Expression
Key Vocabulary – Week 12
Improper Fraction
Mixed Number
Solve an Equation
Variable
Proper Fraction
Rational Number
Week 13 (Suggested 5 days): Unit 3: Expressions and Equations - Week 11
Student Packet
AF 4.2.1, NS 6.2.1, AF 6.1.1, NS 7.1.2
Lessons: Week 11 Student Packet - 11.1, 11.2, 11.3
Key Vocabulary – Week 13
Distributive Property
Equal Sign
Expression
Simplify an Expression
Equation
Solve an Equation
Zero Pair
AF 6.1.1
Write and solve one-step linear equations in
one variable.
NS 7.1.2
Add, subtract, multiply, and divide rational
numbers (integers, fractions, and terminating
decimals) and take positive rational numbers to
whole-number powers.
Topic continues…
Created 7/2008
Note: Weeks referenced in the Vocabulary refer to school weeks, and the weeks referenced in the Materials section refer to the weekly student packets.
12
Topic 3
2 Quarter
Expressions
and Equations
nd
4 Weeks
Subtopics:
•
•
•
•
•
•
•
Numerical
Expressions and
Equations
Fractions:
Addition and
Subtraction
Algebraic
Expression and
Equation
Balance Puzzles
Solving Equations
Inputs and
Outputs
Fractions:
Multiplication
Algebra Readiness
Standards
NS 2.3.1
Use repeated addition, arrays, and counting by
multiples to do multiplication.
NS 6.2.2
Explain the meaning of multiplication and
division of positive fractions and perform the
calculations (e.g., 5/8 + 15/16 = 5/8 x 16/15 =
2/3).
NS 7.1.2
Add, subtract, multiply, and divide rational
numbers (integers, fractions, and terminating
decimals) and take positive rational number to
whole-number powers.
AF 4.1.5
Understand that an equation such as y = 3x + 5
is a prescription for determining a second
number when the first number is given.
CUSD
Resources/Teaching Strategies
Week 14 (Suggested 5 days): Unit 3: Expressions and Equations - Week 12
Student Packet
NS 2.3.1, NS 6.2.2, NS 7.1.2, AF 4.1.5, AF 5.1.5, AF 7.1.5
Lessons: Week 12 Student Packet - 12.1, 12.2, 12.3
Key Vocabulary – Week 14
Area Model
Improper Fraction
Product
Explicit Rule
Input-Output Rule
Proper Fraction
Factor
Linear Function
Variable
Fraction
Mixed Number
Materials:
Week 09 – SP
Week 10 – SP
Week 11 – SP
Week 12 – SP
AF 5.1.5
Solve problems involving linear functions with
integer values; write the equation; and graph
the resulting ordered pairs of integers on a grid.
AF 7.1.5
Represent quantitative relationships
graphically and interpret the meaning of a
specific part of a graph in the situation
represented by the graph.
Created 7/2008
Note: Weeks referenced in the Vocabulary refer to school weeks, and the weeks referenced in the Materials section refer to the weekly student packets.
13
Topic 4
2 Quarter
Length, Area,
and Volume
nd
Algebra Readiness
Standards
NS 2.3.2
Use repeated subtraction, equal sharing, and
forming equal groups with remainder to do
division.
CUSD
Resources/Teaching Strategies
Week 15 (5days): Unit 4 – Length, Area, and Volume - Week 13 Student Packet
NS 2.3.1, NS 6.2.2, AF 7.1.5
Lessons: Week 13 Student Packet - 13.1, 13.2, 13.3
4 Weeks
Subtopics:
•
•
•
•
•
•
•
•
Rectangles:
Fixed Area
Fractions:
Division
Rectangular
Prism: Volume
and Surface
Area
Decimals:
Multiplication
Circles:
Circumference
Decimals:
divisions
Circles: Area
Cylinder:
Volume and
Surface Area
Key Vocabulary – Week 15
NS 6.2.2
Explain the meaning of multiplication and
division of positive fractions and perform the
calculations (e.g., 5/8 + 15/16 = 5/8 x 16/15 =
2/3).
Area of a Rectangle
Division
Multiplicative Inverse
Common Denominator
Maximum Point
Perimeter
AF 7.1.5
Represent quantitative relationships
graphically and interpret the meaning of a
specific part of a graph in the situation
represented by the graph.
Materials:
Week 13 – SP
Week 14 – SP
Week 15 – SP
Week 16 – SP
Topic continues…
Created 7/2008
Note: Weeks referenced in the Vocabulary refer to school weeks, and the weeks referenced in the Materials section refer to the weekly student packets.
14
Topic 4
2 Quarter
Length, Area,
and Volume
nd
4 Weeks
Subtopics:
•
•
•
•
•
•
•
•
Rectangles:
Fixed Area
Fractions:
Division
Rectangular
Prism: Volume
and Surface
Area
Decimals:
Multiplication
Circles:
Circumference
Decimals:
Divisions
Circles: Area
Cylinder:
Volume and
Surface Area
Algebra Readiness
Standards
NS 2.3.1
Use repeated addition, arrays, and counting by
multiples to do multiplication.
Resources/Teaching Strategies
Week 16 (Suggested 5 days): Unit 4: Length, Area, and Volume - Week 14
Student Packet
NS 2.3.1, NS 7.1.2, MG 7.2.1, AF 7.1.3
Lessons: Week 14 Student Packet - 14.1, 14.2, 14.3
NS 7.1.2
Add, subtract, multiply, and divide rational
numbers (integers, fractions, and terminating
decimals) and take positive rational number to
whole-number powers.
MG 7.2.1
Use formulas routinely for finding the
perimeter and area of basic two-dimensional
figure and the surface area and volume of basic
three-dimensional figure, including rectangles,
parallelogram, trapezoids, squares, triangles,
circles, prisms, and cylinders.
AF 7.1.3
Simplify numerical expressions by applying
properties of rational numbers (e.g., identity,
inverse, distributive, associative,
commutative) and justify the process used.
CUSD
Key Vocabulary – Week 16
Rectangular Prism
Area Model
Factors
Bases
Net
Decimal
Place value
Edge
Prism
Face
Product
Right Prism
Surface Area
Vertex
Volume
Materials:
Week 13 – SP
Week 14 – SP
Week 15 – SP
Week 16 – SP
Topic continues…
Created 7/2008
Note: Weeks referenced in the Vocabulary refer to school weeks, and the weeks referenced in the Materials section refer to the weekly student packets.
15
Topic 4
2 Quarter
Length, Area,
and Volume
nd
4 Weeks
Subtopics:
•
•
•
•
•
•
•
•
Rectangles:
Fixed Area
Fractions:
Division
Rectangular
Prism: Volume
and Surface
Area
Decimals:
Multiplication
Circles:
Circumference
Decimals:
Divisions
Circles: Area
Cylinder:
Volume and
Surface Area
Materials:
Week 13 – SP
Week 14 – SP
Week 15 – SP
Week 16 – SP
Created 7/2008
Algebra Readiness
Standards
CUSD
Resources/Teaching Strategies
Week 17 (Suggested 5 days): Unit 4: Length, Area, and Volume - Week 15
MG 6.1.2
Know common estimate of п (3.14; 22/7) and Student Packet
MG 6.1.2, NS 7.1.2, MR 7.3.2
use the value to estimate and calculate the
circumference and the area of circles; compare Lessons: Week 15 Student Packet - 15.1, 15.2, 15.3
the actual measurements.
NS 7.1.2
Add, subtract, multiply, and divide rational
numbers (integers, fractions, and terminating
decimals) and take positive rational number to
whole-number powers.
MR 7.3.2
Note a method of deriving the solution and
demonstrate a conceptual understanding of the
derivation by solving similar problems.
Key Vocabulary – Week 17
Area of a Circle
Circle
Pi
Center
Circumference
Radius
Chord
Diameter
MG 6.1.2
Week 18 (Suggested 5 days): Unit 4: Length, Area, and Volume - Week 16
Know common estimate of п (3.14; 22/7) and Student Packet
use the value to estimate and calculate the
MG 6.1.2, MG 7.2.1
circumference and the area of circles; compare Lessons: Week 16 Student Packet - 16.1, 16.2, 16.3
the actual measurements.
MG 7.2.1
Use formulas routinely for finding the
perimeter and area of basic two-dimensional
figure and the surface area and volume of basic
three-dimensional figure, including rectangles,
parallelogram, trapezoids, squares, triangles,
circles, prisms, and cylinders.
Key Vocabulary – Week 18
Area of a Circle
Cylinder
Surface Area
Base
Radius
Volume
End of 2nd Quarter
Note: Weeks referenced in the Vocabulary refer to school weeks, and the weeks referenced in the Materials section refer to the weekly student packets.
16
Topic 5
3 Quarter
Ratio,
Proportion,
and Percent
rd
5 Weeks
Subtopics:
•
•
•
•
•
•
•
•
•
•
•
•
•
Statistics:
Analyzing Name
Scores
Statistics: Data
Display
Proportional
Reasoning
Understanding
Percent
Ratios, Rates, and
Proportions
Percent Increase
and Decrease
Simple Interest
Percent Problems
Linking Percents
and Proportions
Probability:
Spinner Puzzle
Dimensional
Analysis
Solving
Proportions
Probability: Flip
and Roll
Algebra Readiness
Standards
SDP 6.1.1
Compute the range, mean, median, and mode
of a data set.
SDP 7.1.1
Know various forms of displays for data sets
including stem-and-leaf or box-and-whiskers;
use the forms to display a single set of data or
to compare two sets of data.
SDP 7.1.3
Understand the meaning of, and be able to
compute the minimum, the lower quartile, the
median, the upper quartile, and the maximum
of a data set.
CUSD
Resources/Teaching Strategies
Week 19 (5days): Semester Two Startup - Week 00 Student Packet
SDP 6.1.1, SDP 7.1.1, SDP 7.1.3
Lessons: Week 00 Student Packet - 00.1, 00.2, 00.3
Key Vocabulary – Week 19
Data set
Median
Quartile
Five-number Summary
Mode
Range
Mean
Outlier
Materials:
Week 00 – SP
Week 17 – SP
Week 18 – SP
Week 19 – SP
Week 20 – SP
Topic Continues…
Created 7/2008
Note: Weeks referenced in the Vocabulary refer to school weeks, and the weeks referenced in the Materials section refer to the weekly student packets.
17
Topic 5
3 Quarter
Ratio,
Proportion,
and Percent
rd
5 Weeks
Subtopics:
•
•
•
•
•
•
•
•
•
•
•
•
•
Statistics:
Analyzing Name
Scores
Statistics: Data
Display
Proportional
Reasoning
Understanding
Percent
Ratios, Rates, and
Proportions
Percent Increase
and Decrease
Simple Interest
Percent Problems
Linking Percents
and Proportions
Probability:
Spinner Puzzle
Dimensional
Analysis
Solving
Proportions
Probability: Flip
and Roll
Algebra Readiness
Standards
NS 5.1.2
Interpret percent as a part of a hundred; find
decimal and percent equivalent for common
fractions and explain why they represent the
same value; compute a given percent of a
whole number.
CUSD
Resources/Teaching Strategies
Week 20 (Suggested 5 days): Unit 5: Ratio, Proportion, and Percent - Week 17
Student Packet
NS 5.1.2, NS 6.1.2, NS 6.1.3, NS 7.1.3, AF 7.4.2,
Lessons: Week 17 Student Packet - 17.1, 17.2, 17.3
Key Vocabulary – Week 20
NS 6.1.2
Interpret and use ratios in different contexts
(e.g., batting average, miles per hour) to show
the relative sizes of two quantities, use
appropriate notation (a/b, a to b, a:b).
NS 6.1.3
Use proportion to solve problems (e.g.,
determine the value of N if 4/7 = N/21, find the
length of a side of a polygon similar to a
known polygon). Use cross-multiplication as a
method for solving such problems,
understanding it as the multiplication of both
sides of an equation by multiplicative inverse.
Percent
Rate
Proportion
Unit Price
Unit Rate
Materials:
Week 00 – SP
Week 17 – SP
Week 18 – SP
Week 19 – SP
Week 20 – SP
NS 7.1.3
Convert fractions to decimals and percents and
use these representations in estimations,
computations, and applications.
AF 7.4.2
Solve multi-step problems involving rate,
average speed, distance, and time or a direct
variation.
Topic Continues…
Created 7/2008
Note: Weeks referenced in the Vocabulary refer to school weeks, and the weeks referenced in the Materials section refer to the weekly student packets.
18
Topic 5
3 Quarter
Ratio,
Proportion,
and Percent
rd
5 Weeks
Subtopics:
•
•
•
•
•
•
•
•
•
•
•
•
•
Statistics:
Analyzing Name
Scores
Statistics: Data
Display
Proportional
Reasoning
Understanding
Percent
Ratios, Rates, and
Proportions
Percent Increase
and Decrease
Simple Interest
Percent Problems
Linking Percents
and Proportions
Probability:
Spinner Puzzle
Dimensional
Analysis
Solving
Proportions
Probability: Flip
and Roll
Algebra Readiness
Standards
NS 6.1.4
Calculate given percentages of quantities and
solve problems involving discounts of sales,
interest earned, and tips.
NS 7.1.3
Convert fractions to decimals and percents and
use these representations in estimations,
computations, and applications.
NS 7.1.6
Calculate the percentage of increases and
decreases of a quantity.
CUSD
Resources/Teaching Strategies
Week 21 (Suggested 5 days): Unit 5: Ratio, Proportion, and Percent - Week 18
Student Packet
NS 6.1.4, NS 7.1.3, NS 7.1.6, NS 7.1.7, MR 7.2.1
Lessons: Week 18 Student Packet - 18.1, 18.2, 18.3
Key Vocabulary – Week 21
Compound Interest
Markup
Principal
Discount Interest
Percent Decrease
Simple Interest
Interest
Percent Increase
NS 7.1.7
Solve problems that involve discounts,
markups, commissions, and profit and
compute simple and compound interest.
MR 7.2.1
Use estimation to verify the reasonableness of
calculated results.
Materials:
Week 00 – SP
Week 17 – SP
Week 18 – SP
Week 19 – SP
Week 20 – SP
Topic Continues…
Created 7/2008
Note: Weeks referenced in the Vocabulary refer to school weeks, and the weeks referenced in the Materials section refer to the weekly student packets.
19
Topic 5
3 Quarter
Ratio,
Proportion,
and Percent
rd
5 Weeks
Subtopics:
•
•
•
•
•
•
•
•
•
•
•
•
•
Statistics:
Analyzing Name
Scores
Statistics: Data
Display
Proportional
Reasoning
Understanding
Percent
Ratios, Rates, and
Proportions
Percent Increase
and Decrease
Simple Interest
Percent Problems
Linking Percents
and Proportions
Probability:
Spinner Puzzle
Dimensional
Analysis
Solving
Proportions
Probability: Flip
and Roll
Algebra Readiness
Standards
NS 5.1.2
Interpret percents as part of a hundred: find
decimal and percent equivalents for common
fractions and explain why they represent the
same value; compute a given percent of a
whole number.
NS 7.1.3
Convert fractions to decimals and percents and
use these representations in estimations,
computations, and applications.
MG 7.1.1
Compare weights, capacities, geometric
measures, times, and temperature within and
between measurement systems (e.g., miles per
hour and feet per second, cubic inches to cubic
centimeters).
MG 7.1.3
Use measures expressed as rates (e.g., speed,
density) and measures expressed as products
(e.g., person-days) to solve problems; check
the units of the solutions; and use dimensional
analysis to check the reasonableness of the
answer.
CUSD
Resources/Teaching Strategies
Week 22 (Suggested 5 days): Unit 5: Ratio, Proportion, and Percent - Week 19
Student Packet
NS 5.1.2, NS 7.1.3, MG 7.1.1, MG 7.1.3, SDP 6.3.3
Lessons: Week 19 Student Packet - 19.1, 19.2, 19.3
Key Vocabulary – Week 22
Event
Percent
Ratio
Experiment
Probability
Sample Space
Outcome
Proportion
Trial
Materials:
Week 00 – SP
Week 17 – SP
Week 18 – SP
Week 19 – SP
Week 20 – SP
SDP 6.3.3
Represent probability as ratios, proportions,
decimals between 0 and 1, and percentages
between 0 and 100 and verify that the
probabilities computed are reasonable; know
that if P is the probability of an event, 1 – P is
the probability of an event not occurring.
Topic Continues…
Created 7/2008
Note: Weeks referenced in the Vocabulary refer to school weeks, and the weeks referenced in the Materials section refer to the weekly student packets.
20
Topic 5
3 Quarter
Ratio,
Proportion,
and Percent
rd
5 Weeks
Subtopics:
•
•
•
•
•
•
•
•
•
•
•
•
•
Statistics:
Analyzing Name
Scores
Statistics: Data
Display
Proportional
Reasoning
Understanding
Percent
Ratios, Rates, and
Proportions
Percent Increase
and Decrease
Simple Interest
Percent Problems
Linking Percents
and Proportions
Probability:
Spinner Puzzle
Dimensional
Analysis
Solving
Proportions
Probability: Flip
and Roll
Created 7/2008
Algebra Readiness
Standards
NS 6.1.2
Interpret and use ratios in different contexts
(e.g., batting average, miles per hour) to show
the relative sizes of two quantities, use
appropriate notation (a/b, a to b, a: b).
CUSD
Resources/Teaching Strategies
Week 23 (Suggested 5 days): Unit 5: Ratio, Proportion, and Percent - Week 20
Student Packet
NS 6.1.2, NS 6.1.3, NS 7.1.3, SDP 6.3.1, SDP 6.3.3, MR 7.2.6
Lessons: Week 20 Student Packet - 20.1, 20.2, 20.3
Key Vocabulary – Week 23
NS 6.1.3
Use proportion to solve problems (e.g.,
determine the value of N if 4/7 = N/21, find the
length of a side of a polygon similar to a
known polygon). Use cross-multiplication as a
method for solving such problems,
understanding it as the multiplication of both
sides of an equation by multiplicative inverse.
NS 7.1.3
Convert fractions to decimals and percents and
use these representations in estimations,
computations, and applications.
SDP 6.3.1
Represent all possible outcomes for compound
events in an organized way (e.g., tables, grids,
tree diagram) and express the theoretical
probability of each outcome.
Experimental Probability
Probability Experiment
Theoretical Probability
Outcome
Sample Space
Trial
Materials:
Week 00 – SP
Week 17 – SP
Week 18 – SP
Week 19 – SP
Week 20 – SP
SDP 6.3.3
Represent probability as ratios, proportions,
decimals between 0 and 1, and percentages
between 0 and 100 and verify that the
probabilities computed are reasonable; know
that if P is the probability of an event, 1 – P is
the probability of an event not occurring.
MR 7.2.6
Express the solution clearly and logically by using
the appropriate mathematical notation and terms
and clear language; support solutions with evidence
in both verbal and symbolic work.
Note: Weeks referenced in the Vocabulary refer to school weeks, and the weeks referenced in the Materials section refer to the weekly student packets.
21
Topic 6
rd
3 Quarter
Conjecture and
Justification
4 Weeks
Subtopics:
•
•
•
•
•
•
•
•
•
•
Areas of Polygons
Squares and
Square Roots
Defining
Exponents
Conjectures
About Exponents
Time-Distance
Graphs
Rules for
Exponents
Probability: Fair
Games
The Pythagorean
Theorem
Applications of
the Pythagorean
Theorem
Statistics:
Measures of
Center
Algebra Readiness
Standards
Resources/Teaching Strategies
Week 24 (Suggested 5days): Unit 6: Conjecture and Justification - Week 21
NS 7.2.4
Use the inverse relationship between raising to Student Packet
NS 7.2.4, AF 6.3.1, AF 7.2.1, MG 7.2.1, MG 7.2.2
a power and extracting the root of a perfect
Lessons: Week 21 Student Packet - 21.1, 21.2, 21.3
square integer; for an integer that is not a
square, determine without a calculator the two
integers between which its square root lies and
Key Vocabulary – Week 24
explain why.
Base
Linear Interpolation
Product
AF 6.3.1
Use variables in expressions describing
Exponent
Multiplicative Identity
Square of a Number
geometric quantities (e.g., P=2w + 2l, A=
Property
1/2bh, C= пd- the formulas for the perimeter of
Exponential Notation
Positive Square Root
Square Root
a rectangle, the area of a triangle, and the
circumference of a circle, respectively).
AF 7.2.1
Interpret positive whole-number powers as
repeated multiplication and negative
whole-number powers as repeated division or
multiplication by the multiplicative inverse.
Simplify and evaluate expressions that include
exponents.
Materials:
Week 21 – SP
Week 22 – SP
Week 23 – SP
Week 24 – SP
MG 7.2.1
Use formulas routinely for finding the
perimeter and area of basic two-dimensional
figure and the surface area and volume of basic
three-dimensional figure, including rectangles,
parallelogram, trapezoids, squares, triangles,
circles, prisms, and cylinders.
MG 7.2.2
Estimate and compute the area of more
complex or irregular
two-and-three-dimensional figures by
breaking the figures down into more basic
geometric objects.
Created 7/2008
CUSD
Topic Continues…
Note: Weeks referenced in the Vocabulary refer to school weeks, and the weeks referenced in the Materials section refer to the weekly student packets.
22
Topic 6
3 Quarter
Conjecture and
Justification
rd
Algebra Readiness
Standards
NS 5.1.1
Estimate, round, and manipulate very large
(e.g., millions) and very small (e.g.,
thousandths) numbers
CUSD
Resources/Teaching Strategies
Week 25 (Suggested 5 days): Unit 5: Ratio, Proportion, and Percent - Week 22
Student Packet
NS 5.1.1, NS 7.1.2, AF 7.2.1, MR 7.1.2, MR 7.2.3
Lessons: Week 22 Student Packet - 22.1, 22.2, 22.3
4 Weeks
Subtopics:
•
•
•
•
•
•
•
•
•
•
Areas of Polygons
Squares and
Square Roots
Defining
Exponents
Conjectures
About Exponents
Time-Distance
Graphs
Rules for
Exponents
Probability: Fair
Games
The Pythagorean
Theorem
Applications of
the Pythagorean
Theorem
Statistics:
Measures of
Center
NS 7.1.2
Add, subtract, multiply, and divide rational
numbers (integers, fractions, and terminating
decimals) and take positive rational number to
whole-number powers.
AF 7.2.1
Interpret positive whole-number powers as
repeated multiplication and negative
whole-number powers as repeated division or
multiplication by the multiplicative inverse.
Simplify and evaluate expressions that include
exponents.
MR 7.1.2
Formulate and justify mathematical
conjectures based on a general description of
the mathematical question or problem posed.
Key Vocabulary – Week 25
Base
Factors
Scientific Notation
Exponent
Product
Slope of a line
Exponential Notation
Rate
Materials:
Week 21 – SP
Week 22 – SP
Week 23 – SP
Week 24 – SP
MR 7.2.3
Estimate unknown quantities graphically and
solve for them by using logical reasoning and
arithmetic and algebraic techniques.
Topic Continues…
Created 7/2008
Note: Weeks referenced in the Vocabulary refer to school weeks, and the weeks referenced in the Materials section refer to the weekly student packets.
23
Topic 6
3 Quarter
Conjecture and
Justification
rd
Algebra Readiness
Standards
NS 7.1.1
Estimate unknown quantities graphically and
solve for them by using logical reasoning and
arithmetic and algebraic techniques.
CUSD
Resources/Teaching Strategies
Week 26 (Suggested 5 days): Unit 5: Ratio, Proportion, and Percent – Week 23
Student Packet
NS 7.1.1, NS 7.1.3, NS 7.1.5, NS 7.2.1, AF 7.2.1, SPD 6.3.5
Lessons: Week 23 Student Packet - 23.1, 23.2, 23.3
4 Weeks
Subtopics:
•
•
•
•
•
•
•
•
•
•
Areas of Polygons
Squares and
Square Roots
Defining
Exponents
Conjectures
About Exponents
Time-Distance
Graphs
Rules for
Exponents
Probability: Fair
Games
The Pythagorean
Theorem
Applications of
the Pythagorean
Theorem
Statistics:
Measures of
Center
NS 7.1.3
Convert fractions to decimals and percents and
use these representations in estimations,
computations, and applications.
NS 7.1.5
Know that every rational number is either
terminating or repeating decimal and be able to
convert terminating decimals into reduced
fractions.
NS 7.2.1
Understand negative whole-number
exponents. Multiply and divide expressions
involving exponents with a common base.
AF 7.2.1
Interpret positive whole-number powers as
repeated multiplication and negative
whole-number powers as repeated division or
multiplication by the multiplicative inverse.
Simplify and evaluate expressions that include
exponents.
Key Vocabulary – Week 26
Base
Independent Events
Dependent Events
Repeating Decimal
Exponent
Scientific Notation
Terminating Decimal
Materials:
Week 21 – SP
Week 22 – SP
Week 23 – SP
Week 24 – SP
SDP 6.3.5
Understand the difference between
independent and dependent events.
Topic Continues…
Created 7/2008
Note: Weeks referenced in the Vocabulary refer to school weeks, and the weeks referenced in the Materials section refer to the weekly student packets.
24
Topic 6
3 Quarter
Conjecture and
Justification
rd
4 Weeks
Subtopics:
•
•
•
•
•
•
•
•
•
•
Areas of Polygons
Squares and
Square Roots
Defining
Exponents
Conjectures
About Exponents
Time-Distance
Graphs
Rules for
Exponents
Probability: Fair
Games
The Pythagorean
Theorem
Applications of
the Pythagorean
Theorem
Statistics:
Measures of
Center
Created 7/2008
Algebra Readiness
Standards
CUSD
Resources/Teaching Strategies
Week 27 (Suggested 5 days): Unit 5: Ratio, Proportion, and Percent - Week 24
AF 6.3.1
Use variables in expressions describing
Student Packet
AF 6.3.1, MG 7.2.1, MG 7.3.3, SDP 6.1.1, MR 7.1.2
geometric quantities (e.g., P=2w + 2l, A=
1/2bh, C= пd- the formulas for the perimeter of Lessons: Week 24 Student Packet - 24.1, 24.2, 24.3
a rectangle, the area of a triangle, and the
circumference of a circle, respectively).
Key Vocabulary – Week 27
MG 7.2.1
Hypotenuse
Median
Pythagorean
Use formulas routinely for finding the
Theorem
perimeter and area of basic two-dimensional
Legs
Mode
Range
figure and the surface area and volume of basic
three-dimensional figure, including rectangles,
Mean
Outlier
Right Triangle
parallelogram, trapezoids, squares, triangles,
circles, prisms, and cylinders.
MG 7.3.3
Know and understand the Pythagorean
theorem and its converse and use it to find the
length of the missing side of a right triangle
and the lengths of the other line segments and,
in some situations, empirically verify the
Pythagorean theorem by direct measurement.
Materials:
Week 21 – SP
Week 22 – SP
Week 23 – SP
Week 24 – SP
SDP 6.1.1
Compute the range, mean, median, and mode
of data sets.
MR 7.1.2
Formulate and justify mathematical
conjectures based on a general description of
the mathematical question or problem posed.
End of 3rd Quarter
Note: Weeks referenced in the Vocabulary refer to school weeks, and the weeks referenced in the Materials section refer to the weekly student packets.
25
Topic 7
th
4 Quarter
Symbolic
Algebra
4 Weeks
Subtopics:
•
•
•
•
•
•
•
•
•
Using Algebra to
Prove
Conjectures
Order of
Operation
Solving Equations
Algebra
Applications:
Perimeter
Problems
Simplifying
Expressions
Algebra
Applications:
Number
Problems
Inequalities
Algebra
Applications:
Train Problems
Algebra
Applications
Algebra Readiness
CUSD
Standards
Resources/Teaching Strategies
AF 7.1.2
Use the correct order of operations to evaluate
algebraic expressions such as 3(2x + 5)2
Week 28 (Suggested 5days): Unit 7: Symbolic Algebra – Week 25 Student Packet
AF 7.1.2, AF 7.1.3, MR 7.1.2, MR 7.2.4, MR 7.3.3
Lessons: Week 25 Student Packet – 25.1, 25.2, 25.3
AF 7.1.3
Simplify numerical expressions by applying
properties of rational numbers (e.g., identity,
inverse, distributive, associative,
commutative) and justify the process used.
MR 7.1.2
Formulate and justify mathematical
conjectures based on a general description of
the mathematical question or problem posed.
MR 7.2.4
Make and test conjectures by using both
inductive and deductive reasoning.
Key Vocabulary – Week 28
Conjecture
Generalization
Mathematical Proof
Expression
Inductive Reasoning
Terms
Materials:
Week 25 – SP
Week 26 – SP
Week 27 – SP
Week 28 – SP
MR 7.3.3
Develop generalizations of the results obtained
and the strategies used to apply them to new
problem situations.
Topic Continues…
Created 7/2008
Note: Weeks referenced in the Vocabulary refer to school weeks, and the weeks referenced in the Materials section refer to the weekly student packets.
26
Topic 7
4 Quarter
Symbolic
Algebra
th
4 Weeks
Subtopics:
•
•
•
•
•
•
•
•
•
Using Algebra to
Prove
Conjectures
Order of
Operation
Solving Equations
Algebra
Applications:
Perimeter
Problems
Simplifying
Expressions
Algebra
Applications:
Number
Problems
Inequalities
Algebra
Applications:
Train Problems
Algebra
Applications
Algebra Readiness
Standards
Resources/Teaching Strategies
Week 29 (Suggested 5 days): Unit 7: Symbolic Algebra - Week 26 Student Packet
AF 7.1.1
AF 7.1.1, AF 7.1.3, MG 7.3.3, MR 7.2.5, MR 7.2.6, MR 7.2.8, ALG 4.0
Use variables and appropriate operations to
write an expression, an equation, an inequality, Lessons: Week 26 Student Packet - 26.1, 26.2, 26.3
or a system of equations or inequalities that
represents a verbal description (e.g., three less
than a number, half as large as area A).
Key Vocabulary – Week 29
AF 7.1.3
Simplify numerical expressions by applying
Addition Property of
Associative Property of
Distributive Property
properties of rational numbers (e.g., identity,
Equality
Multiplication
inverse, distributive, associative,
Additive Inverse Property Commutative Property of Multiplication Property of
commutative) and justify the process used.
Addition
Equality
Associative property of
Commutative Property of
Multiplicative Identity
MG 7.3.3
Addition
Multiplication
Property
Know and understand the Pythagorean
theorem and its converse and use it to find the
length of the missing side of a right triangle
and the lengths of the other line segments and,
Materials:
in some situations, empirically verify the
Week 25 – SP
Pythagorean theorem by direct measurement.
Week 26 – SP
Week 27 – SP
MR 7.2.5
Week 28 – SP
Use a variety of methods, such as words,
numbers, symbols, charts, graphs, tables,
diagrams, and models, to explain mathematical
reasoning.
MR 7.2.6
Express the solution clearly and logically by
using the appropriate mathematical notation
and terms and clear language; support solution
with evidence in both verbal and symbolic
work.
MR 7.2.8
Make precise calculations and check that
validity of the results from the context of the
problem.
Created 7/2008
CUSD
Topic Continues…
Note: Weeks referenced in the Vocabulary refer to school weeks, and the weeks referenced in the Materials section refer to the weekly student packets.
27
Topic 7
4 Quarter
Symbolic
Algebra
th
4 Weeks
Algebra Readiness
Standards
CUSD
Resources/Teaching Strategies
ALG 4.0
Students simplify expressions before solving
linear equations and inequalities in one
variable, such as 3(2x – 5) + 4 (x-2) = 12.
[excluding inequalities]
Subtopics:
•
•
•
•
•
•
•
•
•
Using Algebra to
Prove
Conjectures
Order of
Operation
Solving Equations
Algebra
Applications:
Perimeter
Problems
Simplifying
Expressions
Algebra
Applications:
Number
Problems
Inequalities
Algebra
Applications:
Train Problems
Algebra
Applications
AF 7.1.3
Simplify numerical expressions by applying
properties of rational numbers (e.g., identity,
inverse, distributive, associative,
commutative) and justify the process used.
AF 7.4.1
Solve two-step linear equations and
inequalities in one variable over the rational
numbers, interpret the solution or solutions in
the context from which they arose, and verify
the reasonableness of the results.
ALG 4.0
Students simplify expressions before solving
linear equations and inequalities in one
variable, such as 3(2x – 5) + 4 (x-2) = 12.
[excluding inequalities]
ALG 5.0
Students solve multi-step problems, including
word problems, including linear equations and
linear inequalities in one variable and provide
justification fro each step. [excluding
inequalities]
Week 30 (Suggested 5 days): Unit 7: Symbolic Algebra – Week 27 Student Packet
AF 7.1.3, AF 7.4.1, ALG 4.0, ALG 5.0
Lessons: Week 27 Student Packet - 27.1, 27.2, 27.3
Key Vocabulary – Week 30
Addends
Additive Inverse Property
Associative Property of
Multiplication
Commutative Property of
Addition
Commutative Property of
Multiplication
Difference
Equation
Multiplication Property of
Equality
Materials:
Week 25 – SP
Week 26 – SP
Week 27 – SP
Week 28 – SP
Topic Continues…
Created 7/2008
Note: Weeks referenced in the Vocabulary refer to school weeks, and the weeks referenced in the Materials section refer to the weekly student packets.
28
Topic 7
4 Quarter
Symbolic
Algebra
th
4 Weeks
Subtopics:
•
•
•
•
•
•
•
•
•
Using Algebra to
Prove
Conjectures
Order of
Operation
Solving Equations
Algebra
Applications:
Perimeter
Problems
Simplifying
Expressions
Algebra
Applications:
Number
Problems
Inequalities
Algebra
Applications:
Train Problems
Algebra
Applications
Algebra Readiness
Standards
CUSD
Resources/Teaching Strategies
Week 31 (Suggested 5 days): Unit 7: Symbolic Algebra - Week 28 Student Packet
AF 7.1.1
AF 7.1.1, AF 7.4.1, AF 7.4.2, ALG 2.0, ALG 5.0
Use variables and appropriate operations to
write an expression, an equation, an inequality, Lessons: Week 28 Student Packet - 28.1, 28.2, 28.3
or a system of equations or inequalities that
represents a verbal description (e.g., three less
Key Vocabulary – Week 31
than a number, half as large as area A).
Boundary Point
Inductive Reasoning
Symmetric Property of
AF 7.4.1
Equality
Solve two-step linear equations and
Empirical data
Inequality
Transitive Property of
inequalities in one variable over the rational
Equality
numbers, interpret the solution or solutions in
Empirical Evidence
Interval
the context from which they arose, and verify
the reasonableness of the results.
AF 7.4.2
Solve multi-step problems involving rate,
average speed, distance, and time or a direct
variation.
ALG 2.0
Students understand and use such operations as
taking the opposite, finding the reciprocal,
taking a root, and raising to a fractional power.
They understand and use the rule of exponents.
[excluding fractional power].
Materials:
Week 25 – SP
Week 26 – SP
Week 27 – SP
Week 28 – SP
ALG 5.0
Students solve multi-step problems, including
word problems, including linear equations and
linear inequalities in one variable and provide
justification fro each step. [excluding
inequalities]
Topic Continues…
Created 7/2008
Note: Weeks referenced in the Vocabulary refer to school weeks, and the weeks referenced in the Materials section refer to the weekly student packets.
29
Topic 8
th
4 Quarter
Linear
Functions
4 Weeks
Subtopics:
•
•
•
•
•
•
•
•
•
•
•
•
Introduction to
Slope
Rate Graphs
Properties of
Arithmetic and
Equality
Inputs and
Outputs
Introduction to
Lines
Finding Slopes of
Lines
Introduction to
Systems of
Equations
Using Multiple
Strategies to Solve
Problems
Writing
Equations of
Lines
Stacking Cups
Lefty-Righty
Experiment
Review 2
Algebra Readiness
Standards
AF 7.1.3
Simplify numerical expressions by applying
properties of rational numbers (e.g., identity,
inverse, distributive, associative,
commutative) and justify the process used.
AF 7.1.5
Represent quantitative relationships
graphically and interpret the meaning of a
specific part of a graph in the situation
represented by the graph.
AF 7.3.3
Graph linear functions, noting that the vertical
change (change in y-value) per unit of
horizontal change (change in x-value) is
always the same and know that the ratio (“rise
over run”) is called the slope of a graph.
CUSD
Resources/Teaching Strategies
Week 32 ( Suggested 5 days): Unit 8: Linear Functions - Week 29 Student Packet
AF 7.1.3, AF 7.1.5, AF 7.3.3, MG 4.2.2, MG 4.2.3, ALG 4.0
Lessons: Week 29 Student Packet – 29.1, 29.2, 29.3
Key Vocabulary – Week 32
Factors
Quotient
Slope of a Line
Ordered Pair
Rate
Unit Rate
Materials:
Week 29 – SP
Week 30 – SP
Week 31 – SP
Week 32 – SP
MG 4.2.2
Understand that the length of a horizontal line
segment equals the difference of the
x-coordinates.
MG 4.2.3
Understand that the length of a vertical line
segment equals the difference of the
y-coordinates.
ALG 4.0
Students simplify expressions before solving
linear equations and inequalities in one
variable, such as 3(2x – 5) + 4 (x-2) = 12.
[excluding inequalities]
Topic Continues…
Created 7/2008
Note: Weeks referenced in the Vocabulary refer to school weeks, and the weeks referenced in the Materials section refer to the weekly student packets.
30
Topic 8
4 Quarter
Linear
Functions
th
Algebra Readiness
Standards
CUSD
Resources/Teaching Strategies
Week 33 (Suggested 5 days): Unit 8 : Linear Functions - Week 30 Student Packet
AF 4.1.5
Understand that an equation such as y = 3x + 5 AF 4.1.5, AF 7.1.5, AF 7.3.3
Lessons: Week 30 Student Packet - 30.1, 30.2, 30.3
is a prescription for determining a second
number when the first number is given.
4 Weeks
Subtopics:
•
•
•
•
•
•
•
•
•
•
•
•
Introduction to
Slope
Rate Graphs
Properties of
Arithmetic and
Equality
Inputs and
Outputs
Introduction to
Lines
Finding Slopes of
Lines
Introduction to
Systems of
Equations
Using Multiple
Strategies to Solve
Problems
Writing
Equations of
Lines
Stacking Cups
Lefty-Righty
Experiment
Review 2
AF 7.1.5
Represent quantitative relationships
graphically and interpret the meaning of a
specific part of a graph in the situation
represented by the graph.
AF 7.3.3
Graph linear functions, noting that the vertical
change (change in y-value) per unit of
horizontal change (change in x-value) is
always the same and know that the ratio (“rise
over run”) is called the slope of a graph.
Key Vocabulary – Week 33
Explicit Rule
Linear function
x-Intercept
Input-Output Rule
Slope of a Line
y-Intercept
Materials:
Week 29 – SP
Week 30 – SP
Week 31 – SP
Week 32 – SP
Topic Continues…
Created 7/2008
Note: Weeks referenced in the Vocabulary refer to school weeks, and the weeks referenced in the Materials section refer to the weekly student packets.
31
Topic 8
4 Quarter
Linear
Functions
th
Algebra Readiness
Standards
CUSD
Resources/Teaching Strategies
Week 34 (Suggested 5 days): Unit 8: Linear Functions – Week 31 Student Packet
AF 4.1.5
Understand that an equation such as y = 3x + 5 AF 4.1.5, AF 7.1.1, AF 7.1.5, AF 7.3.3, AF 7.4.2, MR 7.2.5
Lessons: Week 31 Student Packet - 31.1, 31.2, 31.3
is a prescription for determining a second
number when the first number is given.
4 Weeks
Subtopics:
•
•
•
•
•
•
•
•
•
•
•
•
Introduction to
Slope
Rate Graphs
Properties of
Arithmetic and
Equality
Inputs and
Outputs
Introduction to
Lines
Finding Slopes of
Lines
Introduction to
Systems of
Equations
Using Multiple
Strategies to Solve
Problems
Writing
Equations of
Lines
Stacking Cups
Lefty-Righty
Experiment
Review 2
Created 7/2008
AF 7.1.1
Use variables and appropriate operations to
write an expression, an equation, an inequality,
or a system of equations or inequalities that
represents a verbal description (e.g., three less
than a number, half as large as area A).
AF 7.1.5
Represent quantitative relationships
graphically and interpret the meaning of a
specific part of a graph in the situation
represented by the graph.
AF 7.3.3
Graph linear functions, noting that the vertical
change (change in y-value) per unit of
horizontal change (change in x-value) is
always the same and know that the ratio (“rise
over run”) is called the slope of a graph.
Key Vocabulary – Week 34
Dimensional Analysis
Point of Intersection
Linear Function
System of Linear Equations
Materials:
Week 29 – SP
Week 30 – SP
Week 31 – SP
Week 32 – SP
AF 7.4.2
Solve multi-step problems involving rate,
average speed, distance, and time or a direct
variation.
MR 7.2.5
Use a variety of methods, such as words,
numbers, symbols, charts, graphs, tables,
diagrams, and models, to explain mathematical
reasoning.
Note: Weeks referenced in the Vocabulary refer to school weeks, and the weeks referenced in the Materials section refer to the weekly student packets.
32
Topic 8
4 Quarter
Linear
Functions
th
4 Weeks
Subtopics:
•
•
•
•
•
•
•
•
•
•
•
•
Introduction to
Slope
Rate Graphs
Properties of
Arithmetic and
Equality
Inputs and
Outputs
Introduction to
Lines
Finding Slopes of
Lines
Introduction to
Systems of
Equations
Using Multiple
Strategies to Solve
Problems
Writing
Equations of
Lines
Stacking Cups
Lefty-Righty
Experiment
Review 2
Created 7/2008
Algebra Readiness
CUSD
Standards
Resources/Teaching Strategies
AF 7.3.3
Graph linear functions, noting that the vertical
change (change in y-value) per unit of
horizontal change (change in x-value) is
always the same and know that the ratio (“rise
over run”) is called the slope of a graph.
Week 35 (Suggested 5 days): Unit 8: Linear Functions - Week 32 Student Packet
AF 7.3.3, SDP 7.1.2
Lessons: Week 32 Student Packet - 32.1, 32.2, 32.3
SDP 7.1.2
Represent two numerical variables on a scatter
plot and informally describe how the data
points are distributed and any apparent
relationship that exists between the two
variables (e.g., between time spent on
homework and grade level).
Key Vocabulary – Week 35
Conjecture
Generalization
Interval
Expression
Inequality
Lines of Best Fit
Terms
Materials:
Week 29 – SP
Week 30 – SP
Week 31 – SP
Week 32 – SP
End of 4th Quarter
Note: Weeks referenced in the Vocabulary refer to school weeks, and the weeks referenced in the Materials section refer to the weekly student packets.
33