Curriculum  /  Math  /  5th Grade  /  Unit 7: Patterns and the Coordinate Plane  /  Lesson 7

Patterns and the Coordinate Plane

Lesson 7

Math

Unit 7

5th Grade

Lesson 7 of 14

Objective

Draw perpendicular lines on a coordinate plane (optional).

Common Core Standards

Core Standards

  • 5.G.A.1 — Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
  • 5.G.A.2 — Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

Foundational Standards

  • 4.G.A.1

Criteria for Success

  1. Determine whether two line segments drawn on a grid or coordinate plane are perpendicular.
  2. Draw perpendicular line segments on a grid or coordinate plane. 
  3. Identify the coordinates of points on two perpendicular line segments. 
  4. (Optional) Notice patterns in the coordinates of two perpendicular line segments.

Tips for Teachers

  • This lesson is optional. In Lesson 8 when students draw shapes on the coordinate plane (which will include determining whether a shape’s sides are perpendicular or not), all relevant line segments will be along gridlines, making verification of perpendicularity easier.
  • Students have done similar work in Grade 4 Unit 8, particularly Lesson 3, Lesson 15, and Lesson 17. This may still be a challenging lesson, though, so it may be useful to refer to Grade 4 Unit 8 to see the ways in which students worked on similar tasks to inform your instruction of this lesson. 

Lesson Materials

Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Tasks

25-30 minutes

Problem 1

The Empire State Building is at the intersection of 5th Avenue and West 34th Street in New York City. Is the intersection of these streets perpendicular? Use the map below to help.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Student Response

Upgrade to Fishtank Plus to view Sample Response.

References

Google Maps Map: Empire State Building

Map data ©Google. Accessed May 25, 2018, 3:45 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

On the coordinate grid below, draw a line segment that is perpendicular to each given line segment.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Student Response

Upgrade to Fishtank Plus to view Sample Response.

References

EngageNY Mathematics Grade 5 Mathematics > Module 6 > Topic C > Lesson 15 — Concept Development

Grade 5 Mathematics > Module 6 > Topic C > Lesson 15 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

Use the coordinate plane below to answer the questions.

a.   What are the coordinates of points $$G$$ and $$H$$?

b.   Draw another line segment, $${\overline{JK}}$$, on the coordinate plane that is perpendicular to $${\overline{GH}}$$.

c.   What are the coordinates of point $$J$$ and point $$K$$?

d.   Explain how you figured out where to plot $${\overline{JK}}$$.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Student Response

Upgrade to Fishtank Plus to view Sample Response.

References

EngageNY Mathematics Grade 5 Mathematics > Module 6 > Topic C > Lesson 16 — Concept Development

Grade 5 Mathematics > Module 6 > 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 Set

15-20 minutes

Discussion of Problem Set

  • In #1, how did you determine which sets of segments were perpendicular?
  • In #2, do your segments look like your neighbor’s line segments? Are there other lines that are perpendicular to the given segments, or is your figure the only correct response?
  • How is drawing perpendicular lines similar to and different from drawing parallel lines?
  • In #3, are there other segments that are perpendicular to $${\overline{AB}}$$? How do you know?

Target Task

5-10 minutes

Use the coordinate plane below for Parts (a) and (b).

a.   Draw a line through points M and N.

b.   Draw a second line that is perpendicular to $$\overleftrightarrow{MN}$$.

Student Response

Upgrade to Fishtank Plus to view Sample Response.

Additional Practice

The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Word Problems and Fluency Activities

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Next

Draw shapes on a coordinate plane.

Lesson 8
icon/arrow/right/large

Lesson Map

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

Topic A: Introduction to the Coordinate Plane

Topic B: Drawing Figures and Shapes in the Coordinate Plane

Topic C: Real-World Problems and Patterns on the Coordinate Plane

Request a Demo

See all of the features of Fishtank in action and begin the conversation about adoption.

Learn more about Fishtank Learning School Adoption.

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Yes

No

Any other information you would like to provide about your school?

We Handle Materials So You Can Focus on Students

We Handle Materials So You Can Focus on Students

We've got you covered with rigorous, relevant, and adaptable math lesson plans for free