Curriculum  /  Math  /  6th Grade  /  Unit 4: Rational Numbers  /  Lesson 12

Rational Numbers

Lesson 12

Math

Unit 4

6th Grade

Lesson 12 of 13

Objective

Reflect points across axes and determine the impact of reflections on the signs of ordered pairs.

Common Core Standards

Core Standards

  • 6.NS.C.6.B — Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.

Foundational Standards

  • 4.G.A.3
  • 5.G.A.1

Criteria for Success

  1. Understand that when two points differ only in the signs of the coordinates, the points are related to each other by reflections over the axes. 
  2. Recognize two points that are reflections over the $${{{x-}}}$$axis as having the same $${{{x-}}}$$coordinate and opposite values for the $${{{y-}}}$$coordinate. 
  3. Recognize two points that are reflections over the $${{{y-}}}$$axis as having the same $${{{y-}}}$$coordinate and opposite values for the $${{{x-}}}$$coordinate. 
  4. Locate and identify coordinate points after reflections over one or both axes.

Tips for Teachers

Students learned about lines of symmetry in fourth grade but may need a review before applying this concept to the coordinate plane. The concept of reflection is important to work that students will do with transformations in eighth grade.

Lesson Materials

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

25-30 minutes

Problem 1

Two pairs of coordinate points are shown in the table below. For each pair of points:

a.   Locate and label the points in the coordinate plane. 

b.   Record your observations for each row in the table.

​​​​​​

  $$(3, 4)$$ and $$(-3,4)$$ $$(3,4)$$ and $$(3, -4)$$
How are the coordinate points similar?    
How are the coordinate points different?    
What do you notice about their locations?    
How far is each point from each axis?    
Which axis could you fold along to make the points match up?    

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 6 Mathematics > Module 3 > Topic C > Lesson 16 — Example 1

Grade 6 Mathematics > Module 3 > Topic C > Lesson 16 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

Four points are graphed in the coordinate plane below.

a.   Point $$A$$ is reflected over the $${{{x-}}}$$axis. What are the coordinates of the reflected point?

b.   Point $$A$$ is reflected over the $${{y-}}$$axis. What are the coordinates of the reflected point?

c.   A point located at $${(-5, -1)}$$ is reflected over the $${{{x-}}}$$axis. Which point in the plane above will represent this point?

d.   Point $$C$$ is reflected over both the $${{{x-}}}$$axis and the $${{y-}}$$axis. What are its new coordinates?

Guiding Questions

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Student Response

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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

Point $$Q$$ is located at $$(-3,2)$$. It is reflected over at least one axis and is now located at $$(-3,-2)$$. Describe the reflection that took place.

Student Response

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Problem 2

Riley reflects point $$L$$, located at $$(5,4)$$, over the $$y$$-axis. They determine its new location is at $$(4,-5)$$. Did Riley correctly identify the coordinates of the reflected point? Explain your reasoning.

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.

  • Multiple-choice questions such as:

The point $${(-2, 4)}$$ is reflected over one axis. Which could be the coordinates of the point after the reflection?

  1. $${(-4, 2)}$$
  2. ​​​​​​​​​​​​​​​​​​​​​$${(-2, -4)}$$
  3.  $${(2, -4)}$$
  4.  $${(4, -2)}$$

The point $${(5, -8)}$$ is reflected over both axes. Which coordinate represents the location of the point after the reflections?

  1. $${(-8, 5)}$$
  2.  $${(-5, 8)}$$
  3.   $${(5, 8)}$$
  4.  $${(8, -5)}$$

Next

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

Lesson 13
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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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