Rational Numbers

Lesson 13

Math

Unit 4

6th Grade

Lesson 13 of 13

Objective


Calculate vertical and horizontal distances on a coordinate plane using absolute value in real-world and mathematical problems.

Common Core Standards


Core Standards

  • 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.
  • 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.

Foundational Standards

  • 5.G.A.1
  • 5.G.A.2

Criteria for Success


  1. Find vertical and horizontal distances between two points on the same vertical or horizontal line by reasoning about absolute value.
  2. Find the length of horizontal and vertical line segments in the coordinate plane when given two coordinate points. 
  3. Find possible endpoints of horizontal and vertical line segments when given one endpoint of the line segment and the length of the line segment.

Tips for Teachers


  • Visual representations (maps or coordinate planes) can support student understanding of how distances are calculated and can enable students to verify by counting (MP.5). It is also important for students to understand what is happening beyond just counting the units. Ask students to represent their thinking using absolute value, and encourage them to try problems without using a visual once they’ve gotten the concept down.
  • The question of diagonal distance may come up. It isn’t until eighth grade that students learn how to use the Pythagorean Theorem to find distance between any two points in the coordinate plane; however, you could blow up a unit square and do a quick measurement activity to show students that the diagonal distance across a unit square is greater than 1 and thus can’t be counted in the same way as vertical or horizontal distances.

Lesson Materials

  • Graph Paper (2-3 sheets per student)
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Anchor Problems

25-30 minutes


Problem 1

Four friends are driving. They come to an intersection of two roads; the road they are on continues straight, and the other road is perpendicular to it. The sign at the intersection shows the distances to several towns.

a.   Draw a map of the roads.

b.   What is the distance between Albertsville and Dewey Falls? How can you represent this distance using absolute value?

c.   What is the distance between Blossville and Cheyenne? How can you represent this using absolute value?

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 6 Mathematics > Module 3 > Topic C > Lesson 18Opening Exercise

Grade 6 Mathematics > Module 3 > Topic C > Lesson 18 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

Consider the line segment with endpoints $${(-3, 3)}$$ and $${(-3, -5)}$$. Find the length of the line segment by finding the distance between the endpoints.

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 6 Mathematics > Module 3 > Topic C > Lesson 18Example 3

Grade 6 Mathematics > Module 3 > Topic C > Lesson 18 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem 3

A horizontal line segment has one endpoint at the point $${(2, -3)}$$. If the line segment is $$7$$ units long, then what are possible coordinates for the other endpoint? Use the coordinate plane below if needed.

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 6 Mathematics > Module 3 > Topic C > Lesson 19Exercise 2

Grade 6 Mathematics > Module 3 > Topic C > Lesson 19 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem Set

15-20 minutes


Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes


Problem 1

The coordinates of five points are shown below.

Point $$A$$: $$(-4,6)$$

Point $$B$$: $$(2,0)$$

Point $$C$$: $$(0,2)$$

Point $$D$$: $$(4,6)$$

Point $$E$$: $$(2,4)$$

a.   Find two points that lie on the same horizontal line. Explain your reasoning.

b.   Find two points that lie on the same vertical line. Explain your reasoning.

Student Response

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Problem 2

A line segment drawn in the coordinate plane has endpoints at $$(-3,4)$$ and $$(-3,-6)$$. What is the length of the line segment?

Student Response

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Additional Practice


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 Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Understanding Positive and Negative Rational Numbers

Topic B: Order and Absolute Value

Topic C: Rational Numbers in the Coordinate Plane

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