Lesson 12 | Place Value with Decimals | 5th Grade Mathematics

Objective

Use place value understanding to round decimals to the nearest whole.

Common Core Standards

Core Standards

The core standards covered in this lesson

5.NBT.A.4 — Use place value understanding to round decimals to any place.

Number and Operations in Base Ten

5.NBT.A.4 — Use place value understanding to round decimals to any place.

Foundational Standards

The foundational standards covered in this lesson

3.NBT.A.1

Number and Operations in Base Ten

3.NBT.A.1 — Use place value understanding to round whole numbers to the nearest 10 or 100.
4.NBT.A.3

Number and Operations in Base Ten

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

Criteria for Success

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

Round decimals to the nearest ten, hundred, thousand, etc., using a number line.
Round decimals to the nearest whole using a number line.
Understand that, by convention, numbers at the midpoint between two benchmarks are rounded to the greater of the two benchmarks.
Use the $${\approx }$$ symbol to record estimations.
Understand the advantages and disadvantages of rounding to various places (e.g., rounding to a larger place makes it easier to operate with that number, rounding to a smaller place is closer to the actual value, etc.) depending on the situation.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

While students haven’t rounded decimals to the nearest ten hundred, thousand, etc., they have rounded whole numbers to those places. Thus, Criteria for Success #1 is essentially spiral content, which students should be able to access easily.
You’ll want to avoid using terms like “round up” and “round down,” since these terms can be confusing for students. “Rounding up” a number results in a change in the value of the place to which you’re rounding, where “rounding down” does not. Often students will change the value mistakenly as a result.

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Anchor Tasks

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

Problem 1

Is 7.6 closer to 7 or closer to 8? Plot 7 and 8 on the two outermost spots on the number line below. Then plot 7.6 to prove your answer.

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 2

Round each of the following numbers to the nearest hundred, ten, and whole. Record your answer with the “$$\approx$$” symbol

a. 99.248

b. 314.5

c. 24.93

Guiding Questions

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Problem Set

Problem Set

Answer Keys

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Discussion of Problem Set

Look at #1. Which value is closest to the original number? Is that the case for #1b and #1c, too? Why or why not?
Look at #2. What is your list? How did you come up with it?
Look at #3a. If you were to take the rounded whole value and round that number to the nearest ten, what would you get? Why would you get a different value than when you rounded the original number to the nearest ten?
Look at #4. To what was 4.97 rounded? Why shouldn’t the number have been rounded?

Target Task

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

Problem 1

Round each of the following to the nearest whole.

a. 8.546 $${{\approx}}$$ ___________

b. 11.499 $${{\approx}}$$ ___________

Student Response

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Problem 2

Round the following to the nearest hundred, ten, and one.

149.075

Student Response

An example response to the Target Task at the level of detail expected of the students.

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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

Extra Practice Problems

Answer Keys

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Word Problems and Fluency Activities

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

Lesson 11

Lesson 13

Lesson Map

Topic A: Place Value with Whole Numbers

Build whole numbers to 1 million by multiplying by 10 repeatedly.

5.NBT.A.1 5.NBT.A.2

Use whole numbers to denote powers of 10. Explain patterns in the number of zeros when multiplying any powers of 10 by any other powers of 10.

5.NBT.A.2

Explain patterns in the number of zeros of the product when multiplying a whole number by 10. Recognize that in a multi-digit whole number, a digit in any place represents 10 times as much as it represents in the place to its right.

5.NBT.A.1 5.NBT.A.2

Explain patterns in the number of zeros of the product when multiplying a whole number by powers of 10.

5.NBT.A.2

Explain patterns in the number of zeros of the quotient when dividing a whole number by 10. Recognize that in a multi-digit whole number, a digit in any place represents $${\frac{1}{10}}$$ as much as it represents in the place to its left.

5.NBT.A.1 5.NBT.A.2

Explain patterns in the number of zeros of the quotient when dividing a whole number by powers of 10.

5.NBT.A.2

Topic B: Place Value with Decimals

Build decimal numbers to thousandths by dividing by 10 repeatedly.

5.NBT.A.1 5.NBT.A.2

Explain patterns in the placement of the decimal point when a decimal is multiplied by any power of 10. Recognize that in a multi-digit decimal, a digit in any place represents 10 times as much as it represents in the place to its right.

5.NBT.A.1 5.NBT.A.2

Explain patterns in the placement of the decimal point when a decimal is divided by a power of 10. Recognize that in a multi-digit decimal, a digit in any place represents $${\frac{1}{10}}$$ as much as it represents in the place to its left.

5.NBT.A.1 5.NBT.A.2

Topic C: Reading, Writing, Comparing, and Rounding Decimals

Read and write decimals to thousandths using base-ten numerals, number names, and expanded form.

5.NBT.A.3.A

Compare multi-digit decimals to the thousandths based on meanings of the digits using $${>}$$, $${<}$$, or $$=$$ to record the comparison.

5.NBT.A.3.B

Use place value understanding to round decimals to the nearest whole.

5.NBT.A.4

Use place value understanding to round decimals to any place.

5.NBT.A.4

Place Value with Decimals

Objective

Common Core Standards

Core Standards

Number and Operations in Base Ten

Foundational Standards

Number and Operations in Base Ten

Number and Operations in Base Ten

Criteria for Success

Tips for Teachers

Anchor Tasks

Problem 1

Guiding Questions

References

Problem 2

Guiding Questions

Problem Set

Discussion of Problem Set

Target Task

Problem 1

Student Response

Problem 2

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

Lesson Map

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