Operations with Rational Numbers

Lesson 4

Math

Unit 2

7th Grade

Lesson 4 of 18

Objective


Model the addition of integers using a number line.

Common Core Standards


Core Standards

  • 7.NS.A.1.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 real-world contexts.
  • 7.NS.A.1.D — Apply properties of operations as strategies to add and subtract rational numbers.

Foundational Standards

  • 6.NS.C.6
  • 6.NS.C.7.C

Criteria for Success


  1. Model addition on a number line using concepts of absolute value and the sign of the number to determine magnitude and direction.
  2. Determine that the commutative property of addition holds for the addition of integers.
  3. Represent integer addition problems on a number line.
  4. Write integer addition problems from models on a number line. 
  5. Model with mathematics using number lines, equations, and descriptions to show the relationships between the representations (MP.4).

Tips for Teachers


  • In the next three lessons, students begin to operate with signed numbers. In this lesson, they start by building a conceptual understanding of the operation of addition using a number line and familiar contexts. Then in later lessons, students determine efficient ways to add rational numbers without the use of a number line. 
  • This lesson only uses integers to allow for students to focus on the concepts and not calculations with fractions or decimals. Other rational numbers will be used in Lessons 5 and 6. 

Lesson Materials

  • Laminated number line (1 per student)
  • Dry erase marker (1 per student)
  • Game piece or token (1 per student)
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Anchor Problems


Problem 1

The number line below represents the road that Joshua lives on, with his home located at point 0. The numbers on the number line represent the number of miles from Joshua’s house, either east or west. Throughout the week, Joshua goes on trips and errands along this road. 

For each day described in the chart, model Joshua’s trip and determine where on the number line he ends up each day. Write an addition equation to represent it.

Day Trip Addition Equation
Sun 5 miles east to the grocery store, then 2 miles east to the bank  
Mon 5 miles east to the grocery store, then 3 miles west to the post office  
Tues 5 miles east to the grocery store, then 8 miles west to the school  
Wed 3 miles west to the school, then 2 miles west to the park  
Thu 3 miles west to the school, then 1 mile east to the gas station  
Fri 3 miles west to the school, then 10 miles east to the bank  
Sat 5 miles west to the park, then 5 miles east to home  

Guiding Questions

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Problem 2

Is $${-7+4}$$ equivalent to $${4+(-7)}$$

Show the sum for each expression on a number line to justify your answer.

 

 

Guiding Questions

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Problem 3

In part (a), model the addition problem on the number line to find the sum. In part (b), write an addition equation to represent what is shown on the number line.

a.      $${5+(-4)+(-3)}$$

 

b.   

Guiding Questions

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Problem Set

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Target Task


Represent each addition problem in parts A through C on a number line and find each sum.

a.   $${-9+5}$$

b.   $${8+(-7)}$$

c.   $${-3+(-6)}$$

d.   Choose one problem from A through C and write a real-world situation that could be modeled by the problem.

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.

  • Include problems where students go between addition equations and number line models (e.g., given one, write the other).
  • Include error analysis problems where addition equations have been incorrectly written to represent a number line diagram (see notes in Anchor Problem #3).
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Lesson 3

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Lesson 5

Lesson Map

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Topic A: Adding and Subtracting Rational Numbers

Topic B: Multiplying and Dividing Rational Numbers

Topic C: Using all Four Operations with Rational Numbers

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