Lesson 2 | Patterns and the Coordinate Plane | 5th Grade Mathematics

Objective

Construct a coordinate plane and plot points given their coordinates.

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

Construct a coordinate plane on graph paper.
Given the coordinates of a point, plot it on a coordinate plane with intervals of 1 unit.
Understand that there are two different ways of interpreting a point, e.g., (2, 3): (1) as instructions (right 2, up 3) and (2) as the point defined by being a distance 2 from the y-axis and a distance 3 from the x-axis.
Given instructions from another point on a coordinate plane, plot a point on a coordinate plane with intervals of 1 unit.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Here is a neat Desmos activity you can use to supplement today's lesson.

Lesson Materials

Graph Paper (1 per student)
Optional: Quarter inch graph paper (1 per student) — This is optional in case you don't have graph paper.

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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

Construct a coordinate plane on grid paper.

Guiding Questions

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Problem 2

a. Plot a point on the coordinate grid below at (2, 6).

b. Alex says that the ordered pair (2, 6) is 2 units from the x-axis and 6 units from the y-axis. Do you agree or disagree?

Guiding Questions

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References

Achievement First Grade 5, Unit 9, Lesson 2 (2017-2018) — "Think About It!"

Grade 5, Unit 9, Lesson 2 (2017-2018) is made available by Achievement First as a part of their Open Source web portal under a CC BY 4.0 license. Copyright © 1999-2017 Achievement First. Accessed May 25, 2018, 3:09 p.m..

Modified by Fishtank Learning, Inc.

Problem 3

a. Plot the following points on the coordinate grid below:

Point A: (3, 8)
Point B: (7, 2)
Point C: (6, 0)
Point D: (0, 4)
Point E: 3 units to the left and 4 units up from point B
Point F: 5 units to the right and 2 units down from point D

b. What are the coordinates of point E? Of point F?

Guiding Questions

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Problem Set

Problem Set

Answer Keys

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Discussion of Problem Set

Look at #2(b). Which shape is 2 units from the y-axis? Does this correspond with the x-coordinate or the y-coordinate?
If point A lies at a distance of 3 units from the x-axis, which coordinate do you know?
Where did Amy stop in #5? If someone chose point A, what error might they have made? What about point C? Point D?
Graph paper is sometimes used when working on the coordinate plane. How is graph paper helpful in working on the coordinate plane?

Target Task

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

Coordinates for points are shown in the table.

Point	Coordinate
W	(2, 3)
X	(4, 0)
Y	(5, 2)
Z	(0, 1)

Graph all the points from the table in the coordinate grid. Label them with their corresponding letters.

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 1

Lesson 3

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

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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