Patterns and the Coordinate Plane

Lesson 12

Math

Unit 7

5th Grade

Lesson 12 of 14

Objective


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.

Common Core Standards


Core Standards

  • 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.
  • 5.OA.B.3 — Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule "Add 3" and the starting number 0, and given the rule "Add 6" and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

Foundational Standards

  • 4.OA.C.5

Criteria for Success


  1. Graph points represented in a description of a situation on a coordinate plane.
  2. Contextualize and decontextualize a coordinate pair based on the situation, e.g., the point (2, 27) in Anchor Task #1 represents how much money Jessica has ($27) after a certain amount of time babysitting (2 hours) (MP.2). 
  3. Solve real-world problems regarding information represented on a coordinate plane (MP.4).

Tips for Teachers


This lesson connects the work of graphing points on the coordinate place to solve real-world and mathematical problems (5.G.A) with analyzing relationships (5.OA.B), connecting content across domains.

Fishtank Plus

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

Anchor Tasks


Problem 1

  1. Jada drew a rectangle with a perimeter of 12 centimeters. What could the length and width of Jada’s rectangle be? Use the table below to record your answer. 
Length (cm) Width (cm)
   
   
   
   
   
  1. Plot length and width of each rectangle on the coordinate grid below.

  1. If Jada drew a square, how long and wide was it? 
  2. If Jada’s rectangle was 2.5 cm long, how wide was it? Plot this point on the coordinate grid. 
  3. If Jada’s rectangle was 3.25 cm long, how wide was it? Plot this point on the coordinate grid. 

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

Illustrative Mathematics IM Grade 5 Unit 7 Lesson 13 Activity 1

IM Grade 5 Unit 7 Lesson 13 Activity 1, accessed on Sept. 25, 2023, 2:24 p.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.

Problem 2

Jessica has already read 15 pages in her book. For the month of August, she reads 6 pages every day. 

  1. Construct a graph to show how many total pages Jessica will have read at the end of each day. 
  2. What ordered pair corresponds with how many pages Jessica has read at the beginning of August? 
  3. What does the ordered pair (2, 27) represent in the context of this problem? 
  4. Jessica reads for 4 days. How many pages into her book is she? 
  5. How many days will it be before Jessica has read 45 pages?

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

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

  • How did you determine where else to plot points in #1(b)?
  • How did you determine how many cookies you could buy with $16 in #2(c)? How can you use the table or graph to help you solve?
  • How did you termine how much 15 cookies would cost? How can you use the table or graph to help you solve?
  • How did you solve #3? How did the graph make it easier to solve? What was difficult about the way the graph was set up, though?
  • What coordinate pair represents how much money Dan will have saved after 3 weeks? How much will he have saved?
  • How long would it take Dean to read 20 books in #5? How do you know? How many books could he read in 12 days? How do you know?

Target Task


Akash has $5 in his bank account. He earns $10 a month in allowance for doing his chores, which he puts in his bank account. He uses the graph below to record the amount of money he has in the bank each month after putting in his allowance. 

a.   Which ordered pair represents the amount of money Akash has in the bank before receiving any month’s allowance?

  1. a.   (0, 5)

  2. b.   (0, 10)

  3. c.   (10,0)

  4. d.   (5,0)

b.   Which ordered pair represents the amount of money Akash has after 2 months of receiving allowance?

  1. a.   (2, 20)

  2. b.   (2, 25)

  3. c.   (20, 2)

  4. d.   (25, 2)

c.   After how many months does Akash have $45 in his bank account? Show or explain your work.

Student Response

Create a free account or sign in to view Student 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.

Extra Practice Problems

Answer Keys

Answer keys for Problem Sets and Extra Practice Problems are available with a Fishtank Plus subscription.

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.

icon/arrow/right/large copy

Lesson 11

icon/arrow/right/large

Lesson 13

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?

Effective Instruction Made Easy

Effective Instruction Made Easy

Access rigorous, relevant, and adaptable math lesson plans for free