Curriculum  /  Math  /  5th Grade  /  Unit 7: Patterns and the Coordinate Plane  /  Lesson 13

Patterns and the Coordinate Plane

Lesson 13

Math

Unit 7

5th Grade

Lesson 13 of 14

Objective

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

Common Core Standards

Core Standards

  • 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. Generate two numerical patterns given their rules. 
  2. Understand that a term is a number in a pattern and corresponding terms are numbers in two patterns that show up in the same place in each pattern (e.g., the second term of each pattern are corresponding terms).
  3. Form coordinate pairs consisting of corresponding terms from the two patterns. 
  4. Graph the ordered pairs on a coordinate plane. 
  5. Look for and express repeated reasoning to identify relationships between corresponding terms (MP.8). 
  6. Explain why those relationships between corresponding terms exist (MP.3).

Tips for Teachers

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

Melissa and Joe want to start saving money. They don’t have anything saved right now. Melissa saves $2 each week and Joe saves $4. 

a.   Complete the table below to see how much money Melissa and Joe will have saved each week.

  A B C D E F
Amount of money Melissa has 0 2        
Amount of money Joe has 0 4        

b.   Which table column represents the point on the coordinate grid below? Label the point with the appropriate letter.

c.   Plot and label the rest of the points on the coordinate grid above.

d.   What do you notice about the amount of money Melissa and Joe will save? What do you wonder?

Guiding Questions

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Student Response

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Problem 2

Xavier is making two different patterns. Pattern P has a starting number of 0 and he adds 8 each time. Pattern Q also has a starting number of 0, but he adds 2 each time. 

a.   Generate the first 5 terms, or numbers in the pattern, of Pattern P and Pattern Q.

b.   Plot and label the points from the corresponding terms in Patterns P and Q on a coordinate plane.

c.   If the patterns continue, what number will be in Pattern Q when Pattern P has 96?

d.   If the patterns continue, what number will be in Pattern P when Pattern Q has 34?

e.   What relationships do you notice between the numbers in Pattern P and the numbers in Pattern Q? Why does this relationship between Pattern P and Q exist?

Guiding Questions

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Student Response

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Problem 3

The points on the graph, starting in the bottom left and moving up and to the right, represent how Han and Mai counted. 

a.   How much is Han adding each time in his count? Explain how you know.

b.   How much is Mai adding each time in her count? Explain how you know.

c.   Name and locate 3 more points on the graph.

d.   What relationships do you notice between the corresponding terms of Han’s and Mai’s counts?

Guiding Questions

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Student Response

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References

Illustrative Mathematics IM Grade 5 Unit 7 Practice Problems Section C — #3

IM Grade 5 Unit 7 Practice Problems Section C #3, accessed on Sept. 21, 2023, 12:01 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.

Modified by Fishtank Learning, Inc.

Problem Set

15-20 minutes

Discussion of Problem Set

  • What is the relationship between the x- and y-coordinates on the coordinate plane in #3? How do you see that pattern in the coordinate grid? How would you see it in a table? 
  • What relationships did you notice in the coordinate pairs in #4(e)? Why did these relationships exist?
  • How did the relationship between corresponding terms in #2 differ from the relationship between corresponding terms in #4?

Target Task

5-10 minutes

Ellen and Mundi each want to write a pattern that is 10 numbers long. 

Ellen writes 0 as her first number and adds 2 each time to get her next number. 

Mundi writes 0 as his first number and adds 6 each time to get his next number. 

Ellen’s pattern:   0  ,   2  ,       ,       ,       ,       ,       ,       ,       ,       

Mundi’s pattern:   0  ,   6  ,       ,       ,       ,       ,       ,       ,       ,       

a.   Complete Ellen and Mundi’s patterns. 

b.   How many times greater is Mundi’s fourth number than Ellen’s fourth number?  What about the seventh numbers? The tenth numbers? 

c.   What pattern do you notice in Part (b)?  Why do you think that pattern exists?

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 more complex relationships between corresponding terms.

Lesson 14
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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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