Lesson 1 | Patterns and the Coordinate Plane | 5th Grade Mathematics

Objective

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

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).

Foundational Standards

The foundational standards covered in this lesson

2.MD.B.6

Measurement and Data

2.MD.B.6 — Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, …, and represent whole-number sums and differences within 100 on a number line diagram.

Criteria for Success

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

Understand the need for a system in which a point’s location can be described in two dimensions.
Understand that the coordinate plane is a plane in which a point is represented using two coordinates that determine the precise location of that point (MP.6).
Understand that a coordinate plane is defined by two perpendicular lines, called the x-axis and the y-axis, that intersect at the origin, which coincides with the zero on each number line.
Understand that the location of a point in the coordinate plane is defined by its x-coordinate and its y-coordinate, which correspond with how far a point is in the direction of the x-axis and y-axis, respectively.
Given a point on a coordinate plane with intervals of 1 unit, determine its location, and write it as a coordinate pair, which is a type of ordered pair.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Even when lessons do not call for it, students may benefit from using grid paper to aid in their precision (MP.6), though they may not need it. Make it available for students to use but without explicitly requiring the use of the tool, allowing them to use appropriate tools strategically (MP.5).
An ordered pair is a pair of two things written in a certain order. A coordinate pair is a type of ordered pair that consists of two coordinates written in a certain order, x then y. This distinction is not important for Grade 5 students and thus the terms are used interchangeably throughout the unit.

Lesson Materials

Markers or crayons (3 per student) — Need red, yellow, and blue for the Target Task
Template: What’s the Point (1 per pair of students) — This material should be cut into pieces 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

Mr. Ingall, Mrs. Ingall’s husband, spotted a fly on the wall in their house. He wanted to catch it and let it free outside, but he hates bugs. How should he describe to Mrs. Ingall where the fly is on the wall so that she can catch it?

Guiding Questions

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Problem 2

a. Play a round of Guess Which One.

Sit next to your partner.
Partner A: Mentally choose a card (cut out from Template: What’s the Point) without indicating which card you chose. Then, describe the location of the point to your partner.
Partner B: When you have enough information to determine which card your partner chose, guess which one it was.

b. Switch roles and play another round of Guess Which One.

c. Use words to describe the location of the point on the grid below.

Guiding Questions

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References

Illustrative Mathematics IM Grade 5 Unit 7 Lesson 1 Activity 2

IM Grade 5 Unit 7 Lesson 1 Activity 2, accessed on Aug. 31, 2023, 10:13 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Illustrative Mathematics IM Grade 5 Unit 7 Lesson 2 Activity 1

IM Grade 5 Unit 7 Lesson 2 Activity 1, accessed on Aug. 31, 2023, 10:14 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Problem 3

Determine the location of the shapes on the following coordinate plane and write them as an ordered pair:

a. Checkmark: __________

b. Square: __________

c. Star: __________

d. Triangle: __________

e. Circle: __________

Guiding Questions

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References

EngageNY Mathematics Grade 5 Mathematics > Module 6 > Topic A > Lesson 2 — Concept Development

Grade 5 Mathematics > Module 6 > Topic A > Lesson 2 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

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Discussion of Problem Set

I think that point L has coordinates (1, 3) in #1. What mistake did I make?
Share your thinking about #4. What did we learn today that could help the pirate locate his treasure more easily?
What new math vocabulary did we learn today?
Why is a vertical line at the origin the best place for the y-axis?
Why would it be important for us to all follow the same order when we write down the x-axis and y-coordinates?

Target Task

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

Problem 1

Select the two statements that correctly describe the point plotted on the coordinate plane.

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Problem 2

On the coordinate plane above, highlight each of the following features with a marker or colored pencil:

Highlight the origin in red.
Highlight the x-axis in yellow.
Highlight the y-axis in blue.

Student Response

An example response to the Target Task at the level of detail expected of the students.

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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 2

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

Foundational Standards

Measurement and Data

Criteria for Success

Tips for Teachers

Lesson Materials

Anchor Tasks

Problem 1

Guiding Questions

Problem 2

Guiding Questions

References

Problem 3

Guiding Questions

References

Problem Set

Discussion of Problem Set

Target Task

Problem 1

Problem 2

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

Lesson Map

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