7th Grade Math Unit 1 Information
Operations With Rational Numbers
Milestones Domain & Weight: Numbers & Operations 21%
Flip Book For Rational Numbers
Overview : Unit 1
Prerequisites : Unit 1
Vocabulary : Unit 1
Unit Length: Approximately 31 days
Checklist : Unit 1
Study Guide for Unit 1
Study Guide KEY for Unit 1
No Calculators are Allowed in This Unit
Click on the links below for resources by Concept:
Concept One – Multiplying & Dividing Rational Numbers
Concept Two – Adding & Subtracting Rational Numbers
TCSS 7th Math ~ Operations With Rational Numbers
Concept One ~ Adding & Subtracting Rational Numbers
Standard(s) &
Essential Questions
MGSE7.NS.1b
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. Interpret sums
of rational numbers by
describing real world
contexts.
MGSE7.NS.1c
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.
EQ: How do I use a
number line to model
addition or subtraction of
rational numbers?
MGSE7.NS.1d Apply
properties of operations
as strategies to add and
subtract rational
numbers.
TCSS
Vocabulary
Resources
Assessment
Activator:
 Spotlight Task ~ Deep Freeze
Note: Includes 30 sec. video & weather maps

Negative Numbers

Positive Numbers
Eureka Resources
 Concept One ~ TE | SE
License
CC.7.NS.1
Integer Resources (Addition/Subtraction)

Rational Numbers

Smart Board/Promethean Flip Chart Intro to Integers

ZERO Pair

Smart Board/Promethean Flip Chart Add Integers

Additive Inverse

Smart Board/Promethean Flip Chart Add & Subtract

CCGPS Frameworks: Models: Teaching Operations of Integers

Discovery Subtraction Questions

“Subitize” Cards (Good idea if you omit the word subitize.)

Largest Sum Wins – 2 Players
o Instructions

Largest Difference Wins – 2 Players
o Instructions

Integer Word Problems

CCGPS Frameworks Helicopters & Submarines SE | TE

CCGPS Frameworks Hot Air Balloons

CCGPS Frameworks Debits & Credits

Create Three - NEW
SE | TE
SE | TE
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Continued on next page…
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TCSS 7th Math ~ Operations With Rational Numbers
…continued from previous page
EQ: What models can
be used to show addition
and subtraction of
positive and negative
rational numbers?
MGSE7.NS.3 Solve
real-world and
mathematical problems
involving the four
operations with rational
numbers.


Additive Inverse

Multiplicative
Inverse

Rational Numbers

ZERO Pair
Differentiation: Assign specific stations as needed & work in
small group while others do stations.
th
o 7 Station Activity [abs value] (Walch)
 Stations 1, 2, and 4 whole number integers.
 Station 3 includes decimals.
o
o
EQ: What strategies are
most useful in helping
me develop algorithms
for adding, subtracting,
multiplying, and dividing
positive and negative
rational numbers?
o
o
CC.7.NS.3
7 Station Activity [ + & - ] (Walch)
 Station 1 requires integer chips.
 Stations 2 and 3 whole number integers
 Station 4 includes decimals.
Glencoe Differentiation Integers / Absolute Value
 Reteach
 Enrich
 Word Problems
Glencoe Differentiation Addition
 Reteach
 Enrich
 Word Problems
Glencoe Differentiation Subtraction
 Reteach
 Word Problems
Additional Integer Resources (Addition/Subtraction)

Glencoe CCGPS Math Text(McGraw-Hill2013) p199-228

Integer Card Games – Addition & subtraction

Integer Rules Flowchart

Push Your Luck Integers
Additional Fraction Resources (Addition/Subtraction)
7th must add negatives to each operation. Positives done in 4th & 5th.
 Glencoe Math Text (McGraw-Hill, 2013) p.271 - 306
TCSS

CCGPS Frameworks: What Does It Cost?
o Note: Multi-step, real-world problems

CCGPS Frameworks: Field Trip Funding
o Note: Multi-step, real-world problem
o Calculate costs of different trips.
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3
TCSS 7th Math ~ Operations With Rational Numbers
Concept Two ~ Multiplying & Dividing Rational Numbers
Standard(s) & Essential
Questions
MGSE7.NS.2 Apply and extend
previous understandings of
multiplication and division and of
fractions to multiply and divide rational
numbers.
MGSE7.NS.2a 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 realworld contexts.
MGSE7.NS.2c Apply properties of
operations as strategies to multiply
and divide rational numbers.
MGSE7.NS.2b 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.
EQ: What strategies are most useful
in helping me develop algorithms for
adding, subtracting, multiplying, and
dividing positive and negative rational
numbers?
Vocabulary
Integers
positive
numbers
negative
numbers
Assessment
Examples
Resources
Eureka Resources
 Eureka Math (2014 Common Core)
Concept Two ~ TE | SE
License
Integer Resources(Multiplication/Division)
 Smart Board/Promethean Flip Chart Multiplication & Division

Glencoe CCGPS Math Text (McGraw-Hill) p. 229 – 250

Differentiation: Assign specific stations as needed & work in
small group while others do stations.
th
o 7 Station Activity Book [ x &÷] (Walch)
 Stations 1 & 4, whole number integers
 Station 2 is good, but requires integer chips.
 Station 3 involves fractions
rational
numbers
o
Glencoe Differentiation Multiplication
 Reteach
 Enrich
 Word Problems
o
Glencoe Differentiation Division
 Reteach
 Enrich
 Word Problems
Multiplicative
Inverse

Integer Thoughtful Questions
Additional Integer Resources(Multiplication/Division
 Integer War Card Game w/worksheet

C.7.NS.2
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Integer Card Games - Multiplying
Continued on next page…
TCSS
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TCSS 7th Math ~ Operations With Rational Numbers
…continued from previous page.
MGSE7.NS.2d 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.
E.Q. What are the steps to converting
a rational number to a decimal using
long division?
Fractions to Decimals
 Eureka Resources TE | SE

Glencoe Math Text (McGraw-Hill, 2013) p. 257-271

Converting Fractions to Decimals
License
Additional Fraction Resources(Multiplication/Division)
FOR REVIEW / REMEDIATION: 7th grade should be adding
negatives to each operation. Operations with positive fractions were
done in earlier grades.
 Glencoe Math Text (McGraw-Hill, 2013) - Multiplying - p.
311-318
TCSS
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