Curriculum / Math / 7th Grade / Unit 2: Operations with Rational Numbers / Lesson 8
Math
Unit 2
7th Grade
Lesson 8 of 18
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Find and represent the distance between two rational numbers as the absolute value of their difference.
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.
The foundational standards covered in this lesson
6.NS.C.7 — Understand ordering and absolute value of rational numbers.
6.NS.C.8 — Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
This may be a good lesson to do the How Much to 0? mental math activity, described in the 7th Grade Math Fluency Building Exercises included in this unit's materials.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
A man on a boat is sitting 9 feet above sea level. A bird flies at an altitude of 54 feet above sea level, and a fish swims below at an altitude of 8 feet below sea level. The ocean floor sits 75 feet below the surface of the ocean.
Find each distance described below. Then write a number sentence to represent each distance you find.
a. Between the bird and the man
b. Between the man and the surface of the ocean
c. Between the man and the fish
d. Between the ocean floor and the fish
e. Between the ocean floor and the bird
Aakash, Bao Ying, Chris, and Donna all live on the same street as their school, which runs from east to west.
a. Draw a picture that represents the positions of their houses along the street.
b. How far is each house from every other house?
c. Represent the relative position of the houses on a number line, with the school at zero, points to the west represented by negative numbers, and points to the east represented by positive numbers.
d. How can you see the answers to part B on the number line? Using the numbers (some of which are positive and some negative) that label the positions of houses on the number line, represent these distances using sums or differences.
Distances between Houses, accessed on Aug. 14, 2017, 10:24 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.
The distance between point Q and point R is 5.3. Give possible values for Q and R in each situation, and represent the distance on a number line.​​​​​​
a. Q and R are both positive numbers.
b. Either Q or R is negative.
c. Both Q and R are negative.
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
The highest temperature on a winter day in New York City was $$11$$°C. The lowest temperature on the same day in the same city was $$-8$$°C.
Jordan says that over the course of the day, the temperature decreased by $$3$$°C. Do you agree with Jordan? Justify your response.
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 7
Lesson 9
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
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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