Curriculum / Math / 7th Grade / Unit 2: Operations with Rational Numbers / Lesson 5
Math
Unit 2
7th Grade
Lesson 5 of 18
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Determine efficient ways to add rational numbers with and without the 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
Suggestions for teachers to help them teach this lesson
Though it is important for students to develop efficient methods to compute with rational numbers, it is equally important that they understand the reasoning behind these methods. The first two Anchor Problems aim to guide students toward understanding how to add rational numbers in general, by modeling travel along a number line (MP.4).
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Revisit Joshua’s road from Lesson 4 Anchor Problem #1 to answer the questions that follow.
a. Joshua travels 5 miles east and then 2 miles east, represented by the equation $${5+2=7}$$.
b. Joshua travels 5 miles west and then 2 miles west, represented by the equation $${-5+(-2)=-7}$$.
The number line below represents Joshua’s road. Use it to answer the questions below.
a. Joshua takes two trips and represents them using the addition problem $${-5+2}$$.
b. Joshua takes another two trips, starting from home, and represents them using the addition problem $${6+(-8)}$$. Answer the same questions (i.)–(iv.) from part A.
c. Explain how you can find the sum of two numbers with opposite signs without using a number line.
For problems A - H, determine if the sum will be positive, negative, or zero. You do not need to find the sum. For problems I - L, find the sum.
a. $${4+(-1)}$$
b. $${-14+(-10)}$$
c. $${7+(-8)}$$
d. $${12.25+13.7}$$
e. $${-22+20}$$
f. $${-5 {1\over2}+7}$$
g. $${-4+4}$$
h. $${-7+(-7)}$$
i. Find the sum. $${42+(-10)}$$
j. Find the sum: $${-15+23}$$
k. Find the sum: $${-18 {1\over2}+\left ( -4 {3\over4} \right )}$$
l. Find the sum: $${100+(-164)}$$
A set of suggested resources or problem types that teachers can turn into a problem set
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Which addition problems below will have a positive sum? Select all that apply.
Write an addition problem that has a sum of $${-24}$$. Include one positive number and one negative number in your problem.
An example response to the Target Task at the level of detail expected of the students.
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.
Lesson 4
Lesson 6
Topic A: Adding and Subtracting Rational Numbers
Represent rational numbers on the number line. Define opposites, absolute value, and rational numbers
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
Model the addition of integers using a number line.
7.NS.A.1.B 7.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.C 7.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.1 7.NS.A.1.A 7.NS.A.1.B 7.NS.A.1.C 7.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.A 7.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.B 7.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.2 7.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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