Grade 7
Unit 1
Table of Contents
Integers and Rational Numbers
Section
Page Number
Unit Description
Unit Standards
Unit Essential Questions
Unit Proficiencies (Learning Targets)
Unit Vocabulary
Sample Unit Calendar and Possible Supporting Materials
Student Proficiencies Handout
Unit Assessments and Rubric/Commentary
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This Unit Developed by: Althea Beam, Robert Shearer, and Brad
Agenbroad (June, 2014)
Unit Title:
Stage 1
Unit
Description:
Standards:
Grade 7
Content Unit 1
Integers and rational numbers
Identify Desired Results
Dates of Unit:
Students will solve real-world and mathematical problems involving the four operations with rational numbers. They will learn
to add, subtract, multiply, and divide with integers and extend that knowledge to include rational numbers .
7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent
addition and subtraction on a horizontal or vertical number line diagram.
a. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two
constituents are oppositely charged.
b. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is
positive or negative.
Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing realworld contexts.
c. Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two
rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.
d. Apply properties of operations as strategies to add and subtract rational numbers.
7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational
numbers.
a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy
the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for
multiplying signed numbers. Interpret products
of rational numbers by describing real-world contexts.
b. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero
divisor) is a rational number.
If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real-world contexts.
c. Apply properties of operations as strategies to multiply and divide rational numbers.
d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or
eventually repeats
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This Unit Developed by: Althea Beam, Robert Shearer, and Brad Agenbroad (June, 2014)
7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with
rational numbers extend the rules for manipulating fractions to complex fractions.)
7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form
(whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations as strategies to calculate with
numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation
and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her
salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is
27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact
computation.
Essential
Questions:
Standard
Proficiencies
1. How is an understanding of positive and negative rational numbers useful in problem solving?
2. How does the ability to use multiple methods and tools to compute fluently—and make reasonable estimates—help to simplify
mathematical tasks involving integers and rational numbers?
7.NS.1
7.NS.2
7.NS.3
7.EE.3
I can describe situations in which opposite
quantities combine to make zero.
(Learning Targets)
a) I can demonstrate and explain how the
sum of q + p will be the absolute value of q
units in the negative or positive direction of
p, depending on the sign of q.
b) I can demonstrate and explain how the
distance between two rational numbers is
the absolute value of their difference.
c) I can demonstrate and explain
how subtraction of rational numbers is the
same as adding the additive inverse.
d) I can use properties of operations to
add and subtract rational numbers.
I can use the properties of
operations, including
distributive property, to multiply
rational numbers.
a) I can describe and model
real life situations for
multiplying and dividing
rational numbers.
I can solve problems involving
adding, subtracting, multiplying
and dividing rational numbers
including complex fractions.
I can solve multi-step real-life
problems posed with positive
and negative rational numbers
in any form.
I can use properties of
operations to calculate with
numbers in any form and
determine if my answers are
reasonable.
b) I can explain why integers
can be divided, except when
the divisor is zero.
c) I can describe why the
quotient is always rational, and
why –(p/q) = (–p)/q= p/(–q).
d) I know and can describe
the rules for multiplying and
dividing integers (signed
numbers).
I can describe and model real life situations
for adding and subtracting rational
numbers.
I can use properties of
operations to multiply and
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This Unit Developed by: Althea Beam, Robert Shearer, and Brad Agenbroad (June, 2014)
divide rational numbers.
I can use long division to
convert a rational number to a
decimal.
I can explain how the decimal
form of a rational number
either terminates or repeats.
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This Unit Developed by: Althea Beam, Robert Shearer, and Brad Agenbroad (June, 2014)
Stage 2
Determine Assessment Evidence
Academic Language (What language will students need to sound like experts?)
Academic Vocabulary:
-additive inverse
-equation
-equivalent ratio
-expression
-formula
-divisor
-absolute value
-negative
-integer
-quotient
-product
-positive
-fraction
-inequality
-rational number
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This Unit Developed by: Althea Beam, Robert Shearer, and Brad Agenbroad (June, 2014)
Unit of Study Assessment Checklist
Stage 3
Plan Learning Experiences and Instruction
Pacing Calendar
Proficiency
Materials
Time Allotment
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This Unit Developed by: Althea Beam, Robert Shearer, and Brad Agenbroad (June, 2014)
INTEGERS & RATIONAL
NUMBERS PROFICIENCIES
Name ______________________________
Date ________________________ Period _____
My Proficiency Assessment Scores
Proficiency #1 – “I can use properties of operations to add and
subtract rational numbers.
Proficiency #2 – “I can demonstrate and explain how the sum of
q + p will be the absolute value of q units in the negative or
positive direction of p, depending on the sign of q.”
Proficiency #3 – “I can demonstrate and explain how the distance
between two rational numbers is the absolute value of their
difference.
Proficiency #4 – “I can demonstrate and explain how subtraction
of rational numbers is the same as adding the additive inverse.
Proficiency #5 – “I can use properties of operations to add and
subtract rational numbers.
Proficiency #6 – “I can describe and model real life situations for
adding and subtracting rational numbers.
Proficiency #7 – “I can use the properties of operations, including
distributive property, to multiply rational numbers.”
.
Proficiency #8 – “I can describe and model real life situations for
multiplying and dividing rational numbers.
Proficiency #9 – “I can explain why integers can be divided,
except when the divisor is zero.
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This Unit Developed by: Althea Beam, Robert Shearer, and Brad
Agenbroad (June, 2014)
Proficiency #10 – “I can use positive and negative numbers to
describe real life situations .”
Proficiency #11 – “I can explain the meaning of zero in real life
situations.”
Proficiency #12 – “I can find the mean of a set of numbers.”
Proficiency #13 – “I can find the median of a set of numbers .”
Proficiency #14 – “I can find the mode of a set of numbers .”
Proficiency #15 – “I can find the range of a numbers .”
Proficiency #16 – “I can understand and use mathematical
vocabulary .”
additive inverse
equation
equivalent ratio
expression
formula
divisor
absolute value
negative
integer
quotient
product
positive
fraction
inequality
rational number
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This Unit Developed by: Althea Beam, Robert Shearer, and Brad
Agenbroad (June, 2014)
Proficiency Assessment…
Name _________________________________
Date _______________________ Period ____
Proficiency # – “I can ….”
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This Unit Developed by: Althea Beam, Robert Shearer, and Brad
Agenbroad (June, 2014)
Proficiency
Score
4
Percentage
3
83%
2
67%
1
50%
100%
Description
WOW!
I have shown proficiency and deeper understanding by:

You got it 
I have shown proficiency by:

Help is needed
I have shown partial understanding by:

Uh-oh…
I have not yet shown my understanding of the math.
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This Unit Developed by: Althea Beam, Robert Shearer, and Brad
Agenbroad (June, 2014)