Fishtank Learning

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

Objective

Draw perpendicular lines on a coordinate plane (optional).

Anchor Tasks - 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

How can we use a right-angle template, a corner of a piece of paper, or a protractor to determine if the streets are perpendicular?
How could you use the grid lines on the map to determine if the streets are perpendicular?
Just like in Lesson 6, we’re going to use triangles to determine whether these lines are parallel. Take the two corners of the triangle you have (cut out from Template: Triangle on Coordinate Plane) that are not right angles and fold them inward so that they match up with the right-angle corner. What do you notice? What do you wonder?
Notice that the triangle you have (cut out from Template: Triangle on Coordinate Plane) can be found in the intersection of 5th Avenue and West 34th Street. How does this help us determine if these two streets are perpendicular?

Notes

Students learned how to use tools like a right-angle template or a protractor to determine if lines are perpendicular in Grade 4 Unit 8.
Below is a picture of the triangle cut out from Template: Triangle on Coordinate Plane before and after its acute corners are folded into the right angle corner, proving that together they form a right angle:

Two examples of how to use congruent triangles on grid lines to determine whether the streets are perpendicular are shown below:

To offer more examples and non-examples of perpendicular line segments on a coordinate grid, you could discuss each of the following:

Students will need one triangle cut out from Template: Triangle on Coordinate Plane.

Anchor Tasks - Problem 2

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

Anchor Tasks - 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

How can we determine where to plot $$\overline{JK}$$?
What is the difference (in a subtractive sense) between the x-coordinate in points G and H? What is the difference between the y-coordinate in points G and H?
What is the difference (in a subtractive sense) between the x-coordinate in points J and K? What is the difference between the y-coordinate in points J and K?
What do you notice about the difference in the x- and y-coordinates of both pairs of points? What do you wonder? Will this be true of any pair of perpendicular points? Why or why not?

Notes

Students will start to explore the relationship between x- and y-coordinates in perpendicular line segments. This goes beyond the scope of the standards so is just exploratory and nicely previews 8.EE.6.

Problem Set

View Problem Set

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

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 $$\overleftrightarrow{MN}$$.

Word Problem

A conference consists of 4 50-minute sessions and a 25 minute lunch break. How long, in hours, is the conference?