Curriculum / Math / 7th Grade / Unit 2: Operations with Rational Numbers / Lesson 13
Math
Unit 2
7th Grade
Lesson 13 of 18
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Lesson Notes
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Multiply signed rational numbers and interpret products in real-world contexts.
The core standards covered in this lesson
7.NS.A.2.A — Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.
7.NS.A.2.C — Apply properties of operations as strategies to multiply and divide rational numbers.
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
Your dog’s veterinarian recommends that you put your dog on a diet to lose some weight. You change your dog’s food and feeding schedule and keep a log of his weight. On average, you notice that your dog’s weight changes by $$-0.8$$ pounds per month. Write an expression to represent the total change in your dog's weight after $$6$$ months. What number represents the change in your dog’s weight?
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List three factors that have a product of $${-{3\over5}}$$? Can you think of another set of three factors?
On the number line below, $${|a| < |b|}$$. Which expressions are negative? Select all that apply.
A. $${ab}$$
B. $$-({ab})$$
C. $${(-a)(-b)}$$
D. $${2a}$$
E. $${2b-a}$$
F. $${2a}-b$$
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15-20 minutes
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5-10 minutes
On Thursday, the temperature was 64 ℉. Since Monday, three days earlier, the temperature had decreased consistently by 2 degrees each day. What multiplication expression represents the change in temperature from Thursday to Monday? Explain what each factor in your expression represents.
Find the product:
$${1{1\over2} \times \left( -{7\over8} \right )}$$
Determine if the statement is always, sometimes, or never true: The product of any two numbers is the product of their opposites.
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Next
Determine the rules for dividing signed numbers.
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
Model the addition of integers using a number line.
7.NS.A.1.B7.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.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
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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