Curriculum / Math / 7th Grade / Unit 2: Operations with Rational Numbers / Lesson 9
Math
Unit 2
7th Grade
Lesson 9 of 18
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Subtract rational numbers with and without the number line.
The core standards covered in this lesson
7.NS.A.1.C — 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.
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.7 — Understand ordering and absolute value of rational numbers.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Mount Ojos del Salado is the highest mountain in Chile, with a peak at about 6,900 meters above sea level. The Atacama Trench, just off the coast of Peru and Chile, is about 8,100 meters below sea level (at its lowest point).
a. What is the difference in elevations between Mount Ojos del Salado and the Atacama Trench?
b. Is the elevation halfway between the peak of Mount Ojos del Salado and the Atacama Trench above sea level or below sea level? Explain without calculating the exact value.
c. What elevation is halfway between the peak of Mount Ojos del Salado and the Atacama Trench?
Differences of Integers, accessed on Aug. 14, 2017, 11:15 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
Find each sum or difference. Rewrite subtraction problems into addition problems or use a number line as needed.
a. $${18{1\over5}-(-5)}$$
b. $${-40{2\over3}-8{1\over2}}$$
c. $${-9.08+16.52}$$
d. $${-6-(-12)}$$
e. $${-11{1\over6}-(-3)}$$
f. $${52+(-15)}$$
g. $${-36.125+(-14.6)}$$
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Which pair of expressions below are equivalent?
Tasia's bank account was –$25.64. She deposited a check into her bank account and her new total is $152.29. How much was the check that Tasia deposited into her account?
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Lesson 8
Lesson 10
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
Determine efficient ways to add rational numbers with and without the number line.
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
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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