# Multi-Digit Division

## Objective

Identify and extend growing shape patterns.

## Common Core Standards

### Core Standards

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• 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.

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• 3.OA.D.9

## Criteria for Success

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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

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• The following material is needed for today's lesson: Square tiles
• This problem set only has two problems. Three additional problems we recommend for this Problem Set are the Performance Assessment Task “Piles of Oranges” found on Inside Mathematics, the Performance Assessment Task “Squares and Circles” found on CCSSMathActivities.com, and the Problem of the Week (Week of September 10) found on Brilliant.org. 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.

#### Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Task 4 (can be done independently). Find more guidance on adapting our math curriculum for remote learning here.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

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### Problem 1

Act 1: Show the video, "Stage 5 Series: C" -

What will Stage 4 and Stage 5 look like?

#### 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 The Match Foundation, Inc.

### Problem 2

Act 2: Use the following information to solve -

#### 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 The Match Foundation, Inc.

### Problem 3

Act 3: Reveal the answer -

#### 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 The Match Foundation, Inc.

### Problem 4

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

What will Stage 4 and Stage 5 look like?

#### 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 The Match Foundation, Inc.

## Problem Set & Homework

#### 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?

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Aaron shaded squares to make a pattern of T shapes, as shown below.

Aaron shaded 5 squares to make the first T. Then he shaded 3 more squares each time he made the next T in his pattern. Aaron continued his pattern.

1. Shade squares to make the fourth T in Aaron's pattern.
2. How many squares in all does Aaron need to shade to make the sixth T in his pattern? Show or explain how you got your answer.
3. Will there be any T in Aaron’s pattern that has exactly 30 shaded squares? Show or explain how you got your answer.

#### References

Massachusetts Department of Elementary and Secondary Education Spring 2014 Grade 4 Mathematics TestQuestion #11

Spring 2014 Grade 4 Mathematics Test is made available by the Massachusetts Department of Elementary and Secondary Education. © 2017 Commonwealth of Massachusetts. Accessed Jan. 8, 2018, 1:15 p.m..

Modified by The Match Foundation, Inc.

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