Place Value with Decimals

Lesson 7

Math

Unit 1

5th Grade

Lesson 7 of 13

Objective


Build decimal numbers to thousandths by dividing by 10 repeatedly. 

Common Core Standards


Core Standards

  • 5.NBT.A.1 — Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
  • 5.NBT.A.2 — Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

Foundational Standards

  • 4.NBT.A.1
  • 4.NF.C.5
  • 4.NF.C.6
  • 4.NF.C.7

Criteria for Success


  1. Make use of the structure of the place value system to extend the place value system to various decimal places by repeatedly dividing by 10 (MP.7).
  2. Establish a new decimal place, thousandths
  3. Represent tenths, hundredths, and thousandths with base ten blocks and on place value charts. 
  4. Understand that the same base ten block models can be used to represent different place values by unitizing, or changing the definition of the whole and assigning value based on the relationship to the unit.

Tips for Teachers


As noted in the Progressions, “the power of the base-ten system is in repeated bundling by ten: 10 tens make a unit called a hundred. Repeating this process of creating new units by bundling in groups of ten creates units called thousand, ten thousand, hundred thousand… In learning about decimals, children partition a one into 10 equal-sized smaller units, each of which is a tenth” (NBT Progression, p. 3). While this idea of decimals being an extension of the place value system was explored a bit when decimals were first introduced in Grade 4, it is extended to further place values including thousandths and, optionally, ten thousandths.

Lesson Materials

  • Thousandths place value chart (1 per student) — Students might need more or less depending on their reliance on this tool.
  • Base ten blocks (1 thousand, 1 hundred, 1 ten, 1 one per teacher)
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Anchor Tasks


Problem 1

a.   Solve

  1. $$100 \div 10 =$$ ___________
  2. $$10 \div 10 =$$ ___________
  3. $$1\div10=$$ ___________

b.   What do you notice about Part (a)? What do you wonder?

Guiding Questions

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Problem 2

a.   Here is a rectangle. 

What number does the rectangle represent if each small square represents:

  1. 1
  2. 0.1
  3. 0.01
  4. 0.001

b.   Use the value of the square and rectangle in Part (a-iii) to draw a model that represents 2.36.

c.   Here is a square. 

What number does each small rectangle represent if the square represents:

  1. 100
  2. 1
  3. 0.1
  4. 0.01

d.   Use the value of the square and rectangle in Part (c-iii) to draw a model that represents 0.354. 

Guiding Questions

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References

Open Up Resources Photo: Grade 6 Unit 5 Lesson 2 Teacher VersionActivity #1, "Changing Values"

Grade 6 Unit 5 Lesson 2 Teacher Version is made available by Open Up Resources under the CC BY 4.0 license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed June 1, 2018, 2:08 p.m..

Modified by Fishtank Learning, Inc.

Problem Set


Answer Keys

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Discussion of Problem Set

  • Look at #2. Do you agree or disagree with Giulia? What base ten models could you use to represent each number? What value would each block have for #2d? What about #2f? 
  • Look at #4a and #4c. What do you notice? What do you wonder?
  • Look at #5. Is Netta correct? How do you know? How was Manny thinking about the model? How else could you have thought about the model? 
  • What happened when we multiplied and divided whole numbers by 10 and powers of 10? Do you think that the same rule will hold when we multiply and divide decimals by 10 and powers of 10? Defend your answer. 

Target Task


Problem 1

Which digit is in the thousandths place of 4.5267?

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Problem 2

Owen drew a picture to represent 0.035:

He said, “The small cubes represent tenths and the rods represent hundredths, which makes sense because ten small cubes make one rod, and ten times ten is one hundred.”

a.   Explain why Owen’s reasoning is incorrect.

b.   Determine two numbers that Owen’s model could represent. For each number, be sure to indicate what a small cube represents and what a rod represents. 

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

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Lesson 6

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Lesson 8

Lesson Map

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

Topic A: Place Value with Whole Numbers

Topic B: Place Value with Decimals

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

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