Multi-Digit Division

Lesson 15

Math

Unit 3

4th Grade

Lesson 15 of 16

Objective


 Identify and extend growing shape patterns.

Common Core Standards


Core Standards

  • 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.

Foundational Standards

  • 3.OA.D.9

Criteria for Success


  1. Make sense of a three-act task and persevere in solving it (MP.1).
  2. Identify the rule of a growing shape pattern (MP.7, MP.8).
  3. Use the rule of a growing shape pattern to extend it to subsequent terms (MP.8). 
  4. Use the rule of a growing shape pattern to find its $${n^{\mathrm{th}}}$$ term (MP.8).
  5. Determine whether the pattern will contain a term with certain features (e.g., will there be a certain shape in the pattern made up of $$x$$ number of squares?) (MP.7, MP.8)

Tips for Teachers


  • This problem set only has two problems. Two additional problems we recommend for this Problem Set are the Performance Assessment Task “Piles of Oranges” found on Inside Mathematics and the Performance Assessment Task “Squares and Circles” found on CCSSMathActivities.com. We are unable to reproduce the content here, but you can find and print the tasks at the links provided.
  • An additional problem we recommend for today's homework is the Performance Assessment Task "Buttons" found on Inside Mathematics. We are unable to reproduce the content here, but you can find the task at the link provided.

Lesson Materials

  • Optional: Square inch tiles (30 per student or small group) — Students might not need these depending on their reliance on concrete materials. This could be counters instead.
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Anchor Tasks


Problem 1

Act 1: Watch the video, Stage 5 Series: C.

a.   What do you notice? What do you wonder?

b.   What will Stage 4 and Stage 5 look like? Make a prediction. 

Guiding Questions

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References

Questioning My Metacognition Stage 5 Series

Stage 5 Series by Graham Fletcher is made available on Questioning My Metacognition under the CC BY-SA 4.0 license. Accessed Jan. 24, 2018, 12:42 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

Act 2: Use the following information to determine what Stages 4 and 5 will look like - 

Guiding Questions

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References

Questioning My Metacognition Stage 5 Series

Stage 5 Series by Graham Fletcher is made available on Questioning My Metacognition under the CC BY-SA 4.0 license. Accessed Jan. 24, 2018, 12:42 p.m..

Modified by Fishtank Learning, Inc.

Problem 3

Act 3: Using the image of the solution below - 

a.   Show or describe how you saw the pattern.

b.   Find a partner who saw the pattern differently than you did. Compare and discuss your different approaches to the problem.

Guiding Questions

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

References

Questioning My Metacognition Stage 5 Series

Stage 5 Series by Graham Fletcher is made available on Questioning My Metacognition under the CC BY-SA 4.0 license. Accessed Jan. 24, 2018, 12:42 p.m..

Modified by Fishtank Learning, Inc.

Problem 4

Act 4 (the sequel): Watch the video, "Stage 5 Series: E" -

What will Stage 4 and Stage 5 look like?

Guiding Questions

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

References

Questioning My Metacognition Stage 5 Series

Stage 5 Series by Graham Fletcher is made available on Questioning My Metacognition under the CC BY-SA 4.0 license. Accessed Jan. 24, 2018, 12:42 p.m..

Modified by Fishtank Learning, Inc.

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

  • Look at #1d. How did you figure out whether there would be a shape in the pattern made up of 423 triangles? 
  • Look at #2. How did you determine how many squares would be needed for the 20th shape in the pattern?
  • Optional: Look at Piles of Oranges #4. How did you know Mrs. Chang was wrong? 
  • Optional: Look at Squares and Circles #5. How did you figure out how many squares would be needed for 40 circles? 

Target Task


Claudia shades squares to create the pattern of X shapes below. 

Claudia shaded 5 squares to make the first X. She then shaded 4 more squares each time she makes a new X in her pattern. 

a.   Shade squares on the grid below to make the fourth X in the pattern.

b.   How many squares will Claudia shade to make the seventh X in her pattern? Show or explain how you know. 

c.   Will there be any X in Claudia’s pattern that has exactly 40 shaded squares? Show or explain how you know. 

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

Answer Keys

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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.

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Lesson 14

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Lesson 16

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Understanding and Interpreting Remainders

Topic B: Division of up to Four-Digit Whole Numbers by One-Digit Whole Numbers

Topic C: Multi-Step Word Problems and Patterns

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