Curriculum / Math / 5th Grade / Unit 7: Patterns and the Coordinate Plane / Lesson 14

Patterns and the Coordinate Plane

Lesson 14

Math

Unit 7

5th Grade

Lesson 14 of 14

Objective

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

Common Core Standards

Core Standards

The core standards covered in this lesson

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.

Operations and Algebraic Thinking

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

The foundational standards covered in this lesson

4.OA.C.5

Operations and Algebraic Thinking

4.OA.C.5 — Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Generate two numerical patterns given their rules.
Form coordinate pairs consisting of corresponding terms from the two patterns.
Graph the ordered pairs on a coordinate plane.
Look for and express repeated reasoning to identify more complex relationships between corresponding terms, such as fractionally multiplicative relationships (MP.8).

Tips for Teachers

Suggestions for teachers to help them teach this lesson

This lesson closely resembles Lesson 13, but instead of the two patterns being straightforward multiplicative ones in which one of the patterns is a multiple of the other, they are a bit more complex. For example, the relationship might involve addition or subtraction instead, multiplication by a non-unit fraction, or a combination of operations. See Anchor Task 1 for examples of these more complex patterns.

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Anchor Tasks

Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding

25-30 minutes

Problem 1

a. Complete the patterns for each set of rules.

Set A

Rule 1: Start at 0. Keep adding 4.

Rule 2: Start at 2. Keep adding 4.

Set B

Rule 1: Start at 4. Keep adding 3.

Rule 2: Start at 9. Keep adding 6.

Set C

Rule 1: Start at 0. Keep adding 5.

Rule 2: Start at 0. Keep adding 3.

b. What are some relationships between the patterns for each set of rules? Be prepared to explain your thinking.

Guiding Questions

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Student Response

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References

Illustrative Mathematics IM Grade 5 Unit 7 Lesson 10

IM Grade 5 Unit 7 Lesson 10 Activity 1, accessed on Sept. 21, 2023, 1:25 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 2

a. Use the rules to complete the table.

Rule 1: Start with 0. Add 2.
Rule 2: Start with 0. Add 5.

	A	B	C	D	E	F
Rule 1
Rule 2

b. What patterns do you notice between the corresponding terms of the two patterns?

c. Plot and label the points from the table on the coordinate plane below.

d. What does the point C tell you about Rule 1 and Rule 2?

Guiding Questions

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Student Response

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References

Illustrative Mathematics IM Grade 5 Unit 7 Lesson 11 Activity 2

IM Grade 5 Unit 7 Lesson 11 Activity 2, accessed on Sept. 21, 2023, 1:26 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 Set

15-20 minutes

Discussion of Problem Set

What relationships did you notice between the two patterns in #3? Why do these relationships exist?
What relationships did you notice between the two patterns in #4? Why do these relationships exist?
How did the terms in Pattern A in #8 compare to the terms in Pattern B? Why does the difference between terms increase?
How did you solve #9?

Target Task

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

5-10 minutes

Problem 1

Sree wrote rules for two patterns.

Pattern for x-values	Pattern for y-values
Starting number = 0	Starting number = 1
Rule: Add 3	Rule: Multiply by 3

Sree the wrote ordered pairs (x, y) using the patterns above. Which ordered pair is one Sree wrote?

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Student Response

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Problem 2

Plot the first three points of Sree’s patterns on the coordinate grid below.

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.

Extra Practice Problems

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Lesson Map

Topic A: Introduction to the Coordinate Plane

Lesson

Define a coordinate plane and identify the coordinates of given points.

Standards

5.G.A.1

Lesson

Construct a coordinate plane and plot points given their coordinates.

Standards

5.G.A.1

Lesson

Construct a coordinate plane with non-unit intervals and use it to plot and identify points.

Standards

5.G.A.1

Lesson

Determine the interval needed to plot various points and practice plotting and identifying points on coordinate grids with various axes.

Standards

5.G.A.1

Topic B: Drawing Figures and Shapes in the Coordinate Plane

Lesson

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

Standards

5.G.A.15.G.A.2

Lesson

Draw parallel lines on a coordinate plane (optional).

Standards

5.G.A.15.G.A.2

Lesson

Draw perpendicular lines on a coordinate plane (optional).

Standards

5.G.A.15.G.A.2

Lesson

Draw shapes on a coordinate plane.

Standards

5.G.A.15.G.A.2

Lesson

Draw symmetric figures on a coordinate plane.

Standards

5.G.A.15.G.A.2

Topic C: Real-World Problems and Patterns on the Coordinate Plane

Lesson

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.

Standards

5.G.A.2

Lesson

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.

Standards

5.G.A.2

Lesson

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.

Standards

5.G.A.25.OA.B.3

Lesson

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

Standards

5.OA.B.3

Lesson

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

Standards

5.OA.B.3

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Patterns and the Coordinate Plane

Objective

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Common Core Standards

Core Standards

Operations and Algebraic Thinking

Foundational Standards

Operations and Algebraic Thinking

Criteria for Success

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Tips for Teachers

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Anchor Tasks

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Problem 1

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Guiding Questions

Student Response

References

Problem 2

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Guiding Questions

Student Response

References

Problem Set

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Discussion of Problem Set

Target Task

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Problem 1

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Student Response

Problem 2

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Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

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