Lesson 10 | Operations with Rational Numbers | 7th Grade Mathematics

Objective

Add and subtract rational numbers efficiently using properties of operations.

Common Core Standards

Core Standards

The core standards covered in this lesson

7.NS.A.1.D — Apply properties of operations as strategies to add and subtract rational numbers.

The Number System

7.NS.A.1.D — Apply properties of operations as strategies to add and subtract rational numbers.

Foundational Standards

The foundational standards covered in this lesson

5.NF.A.2

Number and Operations—Fractions

5.NF.A.2 — Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.
1.OA.B.3

Operations and Algebraic Thinking

1.OA.B.3 — Apply properties of operations as strategies to add and subtract. Students need not use formal terms for these properties. To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.)

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Rewrite problems with subtraction as addition problems in order to use the commutative property.
Rewrite mixed numbers as a sum of the whole number and the fraction in order to find efficient ways to solve problems.
Analyze and discuss different approaches to adding and subtracting rational numbers.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

As students become more efficient and less reliant on using the number line to find sums and differences, they also learn how using properties of operations can be valuable in understanding the problem as a whole and increasing efficiency even more (MP.1).
Continue building fluency with mental math and other activities.

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Anchor Problems

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

25-30 minutes

Problem 1

Represent the following using a single rational number.

$${-2{2\over5}+3{1\over4}-{3\over5}}$$

How many different ways to approach this problem can you think of?

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 7 Mathematics > Module 2 > Topic A > Lesson 8 — Exercise 1

Grade 7 Mathematics > Module 2 > Topic A > Lesson 8 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Problem 2

Jamal is completing a math problem and represents the expression $${-5{5\over7}+8-3{2\over7}}$$ with a single rational number as shown in the steps below. Explain what Jamal did in each step and check his work along the way.

$${=-5{5\over7}+8+ \left (-3{2\over7} \right)}$$

$${=-5{5\over7} +\left (-3{2\over7} \right) + 8}$$

$${=-5 + \left( -{5\over7} \right) +(-3)+ \left (-{2\over7} \right) +8}$$

$${=-5 + \left( -{5\over7} \right) + \left (-{2\over7} \right) + (-3) +8}$$

$${= -5 + (-1) + (-3) + 8}$$

$${= -6 + (-3) + 8}$$

$${=(-9)+8}$$

$${=-1}$$

Guiding Questions

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Student Response

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Problem 3

Which expression is equivalent to $${-14.6-(-5.75)-8.4}$$? Use it to find a single rational number to represent the expression.

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Guiding Questions

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Student Response

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Problem Set

A set of suggested resources or problem types that teachers can turn into a problem set

15-20 minutes

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

5-10 minutes

Find a single integer that represents the expression. Explain the strategy you use.

$${-14+8-3+20+(-6)-(-2)+5}$$

Student Response

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Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

Math Mistakes Adding and Subtracting Negative Numbers
EngageNY Mathematics Grade 7 Mathematics > Module 2 > Topic A > Lesson 8 — Problem Set
EngageNY Mathematics Grade 7 Mathematics > Module 2 > Topic A > Lesson 9 — Problem Set
Open Middle Absolute Value 2. — Challenge

Operations with Rational Numbers

Objective

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Common Core Standards

Core Standards

The Number System

Foundational Standards

Number and Operations—Fractions

Operations and Algebraic Thinking

Criteria for Success

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Tips for Teachers

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Anchor Problems

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Problem 1

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Guiding Questions

Student Response

References

Problem 2

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Guiding Questions

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Problem 3

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Guiding Questions

Student Response

Problem Set

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Target Task

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Student Response

Additional Practice

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