Curriculum  /  Math  /  5th Grade  /  Unit 7: Patterns and the Coordinate Plane  /  Lesson 12

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.

Lesson Materials

  • Graph Paper (1 sheet 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

25-30 minutes

Problem 1

a.   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)
   
   
   
   
   

b.   Plot length and width of each rectangle on the coordinate grid below.

c.   If Jada drew a square, how long and wide was it?

d.   If Jada’s rectangle was 2.5 cm long, how wide was it? Plot this point on the coordinate grid.

e.   If Jada’s rectangle was 3.25 cm long, how wide was it? Plot this point on the coordinate grid.

Guiding Questions

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Student Response

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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. 

a.   Construct a graph to show how many total pages Jessica will have read at the end of each day for the first week of August.

b.   What ordered pair corresponds with how many pages Jessica has read at the beginning of August?

c.   What does the ordered pair (2, 27) represent in the context of this problem?

d.   Jessica reads for 4 days. How many pages into her book is she?

e.   How many days will it be before Jessica has read 45 pages?

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

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

5-10 minutes

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

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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.

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

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

Lesson 13
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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

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