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

Patterns and the Coordinate Plane

Lesson 5

Math

Unit 7

5th Grade

Lesson 5 of 14

Objective

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

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.

Criteria for Success

  1. Draw horizontal and vertical lines in the coordinate plane. 
  2. Understand that horizontal lines are parallel to the x-axis and perpendicular to the y-axis and vertical lines are perpendicular to the x-axis and parallel to the y-axis.
  3. Discern the pattern that horizontal lines all have the same y-value and vertical lines all have the same x-value. 
  4. Name the coordinates of a point that lies on a horizontal or vertical line, including without needing or being able to plot that point.

Tips for Teachers

Lesson Materials

  • Graph Paper (2 sheets per student)
  • Optional: Quarter inch graph paper (2 per student) — This is optional in case you don't have graph paper.
Fishtank Plus

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

Anchor Tasks

25-30 minutes

Problem 1

Amiyah and Brian were playing Battleship. Brian guessed the coordinate pair (5, 8) and got a hit. What coordinates would you recommend Brian give for his next guess? Explain your reasoning.

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.

Problem 2

a.   Draw a line that passes through points $$Y$$ and $$Z$$.

b.   Plot one other point on the same line as $$\overleftrightarrow{YZ}$$ and label it $$X$$.

c.   List the coordinates of $$X$$, $$Y$$, and $$Z$$ in the following table.

Point Coordinates
X  
Y  
Z  

d.   What do you notice about the coordinates of points $$X$$, $$Y$$, and $$Z$$? What do you wonder?

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

Achievement First Grade 5, Unit 9, Lesson 3 (2017-2018) — "Think About It!"

Grade 5, Unit 9, Lesson 3 (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, 3:30 p.m..

Modified by Fishtank Learning, Inc.

Problem 3

Use the table below to answer the following questions.

Point Coordinates
H (4, 2.5)
I (10, 2.5)
J (8, 2.5)

a.   Before plotting the points, what do you notice about their coordinates? What do you wonder?

b.   Plot the points on a coordinate grid. Then connect the points by drawing a line through all of them.

c.   Determine the coordinates of another point that would lie on this line.

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 A > Lesson 5 — Concept Development

Grade 5 Mathematics > Module 6 > Topic A > Lesson 5 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, what’s the relationship of line e to the x-axis and y-axis?
  • What do all of the points of line e have in common in #1f? 
  • In #2, how did you know that the points given in parts (a) and (c) were on a line that was not parallel to the x-axis? For the lines that were parallel to the x-axis, what was the distance of every point on those lines from the x-axis?
  • In #3, how did you know that the points given in parts (a) and (b) were on a line that was not parallel to the y-axis? 
  • In #4, what’s the relationship of line h to the x-axis and y-axis?
  • What pattern occurs in the coordinate pairs that let you know that line h is vertical in #4d?

Target Task

5-10 minutes

Use the following grid to answer Parts (a)-(f).

 

a.   Use a straightedge to draw a line that goes through points E and F.

b.   Which axis is parallel to the line you drew?

c.   Which axis is perpendicular to the line you drew?

d.   Plot two more points on the line you drew.  Name them G and H.

e.   Give the coordinates of each point below.

E:  ___________ F:  ___________

G:  ___________ H:  ___________

f.   Give the coordinates of another point that falls on the line you drew that isn’t shown in the coordinate plane drawn above. 

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 parallel lines on a coordinate plane (optional).

Lesson 6
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