# Place Value, Rounding, Addition, and Subtraction

## Objective

Round multi-digit numbers to any place value.

## Common Core Standards

### Core Standards

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• 4.NBT.A.3 — Use place value understanding to round multi-digit whole numbers to any place.

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• 3.NBT.A.1

## Criteria for Success

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1. Round multi-digit numbers to any place value using a number line to justify reasoning.
2. Know that, by convention, a number at the midpoint between two benchmarks is rounded to the larger of the two benchmarks.
3. Use the $\approx$ symbol to record estimations.
4. Understand the advantages and disadvantages of rounding a value to various place values, including the precision of rounding a number to a smaller place value (MP.6) and ease of working/operating when rounding a number to a larger place value.

## Tips for Teachers

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Before the Problem Set, you could have students play "Becca's Battle" from Building Conceptual Understanding and Fluency Through Games by the Public Schools of North Carolina.

### Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Task 3 (benefits from worked example). Find more guidance on adapting our math curriculum for remote learning here.

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• Problem Set
• Student Handout Editor
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• Vocabulary Package

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### Problem 1

Is 4,125 closer to 4,100 or 4,200? Plot 4,100 and 4,200 on the two outermost spots on the number line below. Then plot 4,125 to prove your answer.

#### Guiding Questions

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### Problem 2

1. The number 96,381 lies between 96,380 and 96,390 on the number line. Label all the other tick marks between 96,380 and 96,390. Is 96,381 closer to 96,380 or 96,390 on the number line?

1. Which hundred is 96,381 closest to on the number line? Plot 96,300 and 96,400 on the two outermost spots on the number line below. Then plot 96,381 to prove your answer.

1. Which thousand is 96,381 closest to on the number line? Plot 96,000 and 97,000 on the two outermost spots on the number line below. Then plot 96,381 to prove your answer.

1. Which ten thousand is 96,381 closest to? Show or explain your thinking.

#### Guiding Questions

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#### References

Illustrative Mathematics Rounding on the Number Line

Rounding on the Number Line, accessed on Sept. 11, 2017, 8:36 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 3

1. Solve.
1. 147,951 rounded to the nearest million is ________________.
2. 147,951 rounded to the nearest hundred thousand is ________________.
3. 147,951 rounded to the nearest ten thousand is ________________.
4. 147,951 rounded to the nearest thousand is ________________.
5. 147,951 rounded to the nearest hundred is ________________.
6. 147,951 rounded to the nearest ten is ________________.
2. What do you notice about the rounded values in Part (a)? What do you wonder?

#### Guiding Questions

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#### References

EngageNY Mathematics Grade 4 Mathematics > Module 1 > Topic C > Lesson 9Concept Development

Grade 4 Mathematics > Module 1 > Topic C > Lesson 9 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

## Problem Set & Homework

• Problem Set Answer Key
• Homework Answer Key

### Discussion of Problem Set

• Look at #3b. How did you round this number to the nearest hundred thousand? What made it more challenging to do so?
• Look at #5a. How did you round this number to the nearest thousand? What made it more challenging to do so?
• Look at #8. What happened when you rounded the same value to various place values? Which estimate is the most precise?
• Tell your partner your steps for rounding a number. Which step is most difficult for you? Why?
• What makes 5 special in rounding?
• How does the number line help you round numbers? Is there another way you prefer? Why?
• What is the purpose of rounding?
• When might we use rounding or estimation?
• What are the advantages and disadvantages of rounding to a large place value? A small place value?

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### Problem 1

Round 765,403 to the given place value:

a.   Thousand __________________

b.   Ten thousand __________________

c.   Hundred thousand __________________

#### References

EngageNY Mathematics Grade 4 Mathematics > Module 1 > Topic C > Lesson 9Exit Ticket, Question #1

Grade 4 Mathematics > Module 1 > Topic C > Lesson 9 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

### Problem 2

There are 16,850 Star coffee shops around the world. Round the number of shops to the nearest thousand and ten thousand. Which answer is more precise? Explain your thinking using pictures, numbers, or words.

#### References

EngageNY Mathematics Grade 4 Mathematics > Module 1 > Topic C > Lesson 9Exit Ticket, Question #2

Grade 4 Mathematics > Module 1 > Topic C > Lesson 9 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..