Place Value with Decimals

Lesson 6

Math

Unit 1

5th Grade

Lesson 6 of 13

Objective


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

Common Core Standards


Core Standards

  • 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. Divide whole numbers by powers of 10 expressed in standard form (e.g., $$5,000\div 100$$).
  2. Divide whole numbers by powers of 10 expressed in exponential form (e.g., $$432,000 \div 10^3$$).
  3. Multiply whole numbers by powers of 10 less than 1 expressed in fractional or decimal form (e.g., $$5,000 \times \frac{1}{100} $$ and $$432,000 \times 0.001$$) and see that this is equivalent to dividing those whole numbers by the reciprocal. (Note: students do not need to know and are not introduced to the term reciprocal.) 
  4. Generalize the pattern that dividing a whole number by a power of 10 results in the digits in the number shifting one place to the right for each power of 10 (MP.8). 

Tips for Teachers


Students will only divide in cases where the quotient is a whole number. Students will divide by 10 with decimal quotients in Topic B. 

Lesson Materials

  • Millions Place Value Chart (3 per student) — Students might need more or less depending on their reliance on this tool.
  • Base ten blocks (3 thousands, 30 hundreds, 30 tens, 30 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. $$3,000 \div 10=$$ ___________
  2. $$3,000 \div 100=$$ ___________
  3. $$3,000 \div 1,000=$$ ___________

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

c.   Use your conclusions in Part (b) to find the solutions below. 

  1. $$60,000\div 100=$$ ___________
  2. $$700,000\div 100,000 =$$ ___________
  3. $$2,400,000 \div 10,000 =$$ ___________

Guiding Questions

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Student Response

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Problem 2

a.    Solve. 

  1. $${107,000 \div 10}=$$ ___________
  2. $${107,000 \div 10}^2=$$ ___________
  3. $${107,000 \div 10}^3=$$ ___________

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

c.   Use your conclusions from Part (b) to find the solutions below. 

  1. $$390,000 \div 10^4 =$$ ___________
  2. $$1,050,000 \div 10^2 =$$ ___________
  3. $$806,000,000 \div 10^5=$$ ___________

Guiding Questions

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Student Response

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Problem 3

a.   Solve. 

  1. $$4,000 \div 100$$
  2. $$4,000 \times\frac{1}{100}$$
  3. $$4,000 \times 0.01$$

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

c.    Use your conclusion from Part (b) to find the values below. 

  1. $$30,070,000 \div 1,000$$
  2. $$8,900,000 \times 0.01$$
  3. $$50,000,000 \times \frac{1}{10,000}$$

Guiding Questions

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Student Response

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Problem Set

15-20 minutes


Discussion of Problem Set

  • What do you notice about the number of zeros in your products when dividing by 10, 100, and 1,000 relative to the number of places the digits shift? What patterns do you notice? 
  • Look at #2. What does your picture look like? 
  • Look at #3e and #3f. What was similar about these problems? What was different? 
  • Look at #3g. How did you solve for the missing value? What would the solution be if it were a division equation rather than a multiplication one? 
  • Look at #6. How many zeros does each product have? Why?

Target Task

5-10 minutes


Problem 1

Solve.

a.   $$128,000 \div 100 =$$ _________________

b.   $$67,000 \div 10^3 =$$ _________________

Student Response

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Problem 2

Explain the pattern in the number of places the digits shift in each of the quotients above and relate it to the numbers on the left side of the equations. 

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

Build decimal numbers to thousandths by dividing by 10 repeatedly.

Lesson 7
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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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