Place Value with Decimals

Lesson 8

Math

Unit 1

5th Grade

Lesson 8 of 13

Objective


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.

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

Criteria for Success


  1. Multiply decimals by powers of 10 (e.g., $$0.5 \times 100$$ or $$10^2$$, $$432 \times 1,000$$ or $$10^3$$).
  2. Generalize the pattern that multiplying a decimal by a power of 10 results in digits in the number shifting one place to the left for each power of 10 (MP.8).
  3. Understand that a digit in one place (including decimal places) represents 10 times what it represents in the place to its right, 100 times what it represents two places to its right, etc. 

Tips for Teachers


  • You might decide to include a Do Now/Warm-Up exercise at the beginning of the lesson that asks students to solve multiplication equations with single decimal units, e.g., $$0.1\times10$$ and $$0.001\times100$$
  • A common misconception when multiplying decimals by 10 is that one just “adds a zero” to the end of the number, which with decimals does not change the value of the number. If you notice this misconception come up, address it directly with the whole class, using various models and arguments to dispute it. The Target Task should give the teacher helpful feedback on whether this misconception persists by the end of the lesson.

Lesson Materials

  • Thousandths place value chart (3 per student) — Students might need more or less depending on their reliance on this tool.
  • Base ten blocks (1 thousand, 10 hundreds, 50 tens, 60 ones per student or small group) — Students might not need these depending on their reliance on concrete materials. You could just use one set for the teacher if materials are limited.
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Anchor Tasks

25-30 minutes


Problem 1

a.   Solve. 

  1. $$0.03 \times 10$$ = ___________
  2. $$0.106 \times 10$$ = ___________
  3. $$54.8 \times 10$$ = ___________

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

Guiding Questions

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Student Response

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Problem 2

a.   Solve. 

  1. $$0.09 \times 10 =$$ ___________
  2. $$0.09 \times 100=$$ ___________
  3. $$0.09 \times 1,000= $$ ___________

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

c.   Solve. 

  1. $$70.6 \times 10=$$ ___________
  2. $$70.6 \times 10^2 =$$ ___________
  3. $$70.6 \times 10^3 =$$ ___________

d.    What do you notice about Part (c)? What do you wonder?

e.   Use your conclusions from Parts (b) and (d) to find the solutions below.

  1. $$23.48 \times 10,000 =$$ ___________
  2. $$6.059 \times 10^3 =$$ ___________

Guiding Questions

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Student Response

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Problem 3

The value of the 8 in 83.16 is how many times the value of the 8 in 7.8?

Guiding Questions

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Student Response

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Problem Set

15-20 minutes


Discussion of Problem Set

  • Look at #1g and #1h. What’s similar about these problems? What’s different? 
  • Look at #3d. How did the value of the 5 change? Why? 
  • Look at #6g and #6h. What’s similar about these problems? What’s different?

Target Task

5-10 minutes


Problem 1

The value of the digit 7 in the number 17.48 is 10 times the value of the digit 7 in which number?

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Student Response

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Problem 2

Sonya is trying to solve for the missing value in the equation 93.6 × _____ = 93,600. Sonya claims that the answer is 100 because there are two zeros at the end of 93,600 and multiplying by ten results in an extra 0 at the end of the number, so multiplying by 100 would results in two zeros at the end of the number.

  • Explain why Sonya’s reasoning is incorrect.
  • Find the correct solution. Show or explain your work.

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.

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.

Next

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.

Lesson 9
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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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