Curriculum / Math / 7th Grade / Unit 2: Operations with Rational Numbers / Lesson 4
Math
Unit 2
7th Grade
Lesson 4 of 18
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Lesson Notes
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Model the addition of integers using a number line.
The core standards covered in this lesson
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.
The foundational standards covered in this lesson
6.NS.C.6 — Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
6.NS.C.7.C — Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of -30 dollars, write |-30| = 30 to describe the size of the debt in dollars.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
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.
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Is $${-7+4}$$ equivalent to $${4+(-7)}$$?
Show the sum for each expression on a number line to justify your answer.
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.
A set of suggested resources or problem types that teachers can turn into a problem set
15-20 minutes
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5-10 minutes
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.
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.
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Determine efficient ways to add rational numbers with and without the number line.
Topic A: Adding and Subtracting Rational Numbers
Represent rational numbers on the number line. Define opposites, absolute value, and rational numbers.
Standards
7.NS.A.1
Compare and order rational numbers. Write and interpret inequalities to describe the order of rational numbers.
Describe situations in which opposite quantities combine to make zero.
7.NS.A.1.A
7.NS.A.1.B7.NS.A.1.D
Efficiently add and reason about sums of rational numbers.
Understand subtraction as addition of the opposite value (or additive inverse).
7.NS.A.1.C7.NS.A.1.D
Find and represent the distance between two rational numbers as the absolute value of their difference.
7.NS.A.1.C
Subtract rational numbers with and without the number line.
Add and subtract rational numbers efficiently using properties of operations.
7.NS.A.1.D
Add and subtract rational numbers using a variety of strategies.
7.NS.A.17.NS.A.1.A7.NS.A.1.B7.NS.A.1.C7.NS.A.1.D
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Topic B: Multiplying and Dividing Rational Numbers
Determine the rules for multiplying signed numbers.
7.NS.A.2.A7.NS.A.2.C
Multiply signed rational numbers and interpret products in real-world contexts.
Determine the rules for dividing signed numbers.
7.NS.A.2.B7.NS.A.2.C
Divide signed rational numbers and interpret quotients in real-world contexts.
Convert rational numbers to decimals using long division and equivalent fractions.
7.NS.A.2.D
Multiply and divide with rational numbers using properties of operations.
7.NS.A.27.NS.A.2.C
Topic C: Using all Four Operations with Rational Numbers
Solve problems with rational numbers and all four operations.
7.NS.A.3
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