Lesson 7 | Patterns and the Coordinate Plane | 5th Grade Mathematics

Objective

Draw perpendicular lines on a coordinate plane (optional).

Common Core Standards

Core Standards

The core standards covered in this lesson

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).

Geometry

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.

Geometry

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

The foundational standards covered in this lesson

4.G.A.1

Geometry

4.G.A.1 — Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

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

Tips for Teachers

Suggestions for teachers to help them teach this lesson

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

Template: Triangle on Coordinate Plane (1 copy per 6 students) — These need to be cut out before the lesson.

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Anchor Tasks

Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding

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

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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

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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

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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

Problem Set

Answer Keys

Unlock the answer keys for this lesson's problem set and extra practice problems to save time and support student learning.

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

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

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

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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.

Extra Practice Problems

Extra Practice Problems

Answer Keys

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Word Problems and Fluency Activities

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Lesson 6

Lesson 8

Lesson Map

Topic A: Introduction to the Coordinate Plane

Define a coordinate plane and identify the coordinates of given points.

5.G.A.1

Construct a coordinate plane and plot points given their coordinates.

5.G.A.1

Construct a coordinate plane with non-unit intervals and use it to plot and identify points.

5.G.A.1

Determine the interval needed to plot various points and practice plotting and identifying points on coordinate grids with various axes.

5.G.A.1

Topic B: Drawing Figures and Shapes in the Coordinate Plane

Plot horizontal and vertical lines on a coordinate plane and find patterns in their coordinates.

5.G.A.1 5.G.A.2

Draw parallel lines on a coordinate plane (optional).

5.G.A.1 5.G.A.2

Draw perpendicular lines on a coordinate plane (optional).

5.G.A.1 5.G.A.2

Draw shapes on a coordinate plane.

5.G.A.1 5.G.A.2

Draw symmetric figures on a coordinate plane.

5.G.A.1 5.G.A.2

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

Understand that a coordinate plane can be used to represent real-world information and interpret coordinate values of points in the context of a situation.

5.G.A.2

Represent real-world problems by graphing information represented on a table in the coordinate plane and interpret coordinate values of points in the context of a situation.

5.G.A.2

Represent real-world problems by graphing information given as a description of a situation in the coordinate plane and interpret coordinate values of points in the context of a situation.

5.G.A.2 5.OA.B.3

Generate two numerical patterns using two given rules, plotting the points, and identify multiplicative relationships between corresponding terms.

5.OA.B.3

Generate two numerical patterns using two given rules, plotting the points, and identify more complex relationships between corresponding terms.

5.OA.B.3

Patterns and the Coordinate Plane

Objective

Common Core Standards

Core Standards

Geometry

Geometry

Foundational Standards

Geometry

Criteria for Success

Tips for Teachers

Lesson Materials

Anchor Tasks

Problem 1

Guiding Questions

References

Problem 2

Guiding Questions

References

Problem 3

Guiding Questions

References

Problem Set

Discussion of Problem Set

Target Task

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

Lesson Map

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