Place Value with Decimals

Lesson 1

Math

Unit 1

5th Grade

Lesson 1 of 13

Objective


Build whole numbers to 1 million by multiplying 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.NBT.A.2

Criteria for Success


  1. Make a model to represent the magnitude of 1 million.
  2. Understand the magnitude of 1 million in a variety of ways, including:
    1. as some number of ones, tens, hundreds, etc. (e.g., 1 million is 1,000,000 ones, 100,000 tens, 10,000 hundreds, etc.)
    2. as 10 × 10 × 10 × 10 × 10 × 10.
  3. Write repeated multiplication sentences to represent various powers of ten written in standard form (e.g., 10,000 = 10 × 10 × 10 × 10).
  4. Explain patterns in the number of zeros when multiplying 10 by itself repeatedly.

Tips for Teachers


  • Today’s lesson is mostly a review of Grade 4 content. Anchor Task #2 may take a fairly long time, however, so you may choose to build this lesson out over two days, especially if you’re spending time in the first days of school on building culture and routines. Another option would be to move Anchor Task #3 to Lesson 2. In that case, the Problem Set should only include #1.
  • One fun exercise aligned to the objective that goes beyond the regular block is to start a class collection of something with the goal of reaching a specific quantity, like 1,000 soda cans, 10,000 popsicle sticks, etc. Be wary of aiming for 1 million or 100,000, as this can take a LONG time.
  • Today's Problem Set is very short so that more time can be spent on the Anchor Tasks and establishing math routines for the beginning of the year. 
  • There is no Homework today to allow teachers to build in math routines throughout the first week of school.

Lesson Materials

  • Tape (1 or more per class) — Either tape or a stapler can be used here.
  • Hundreds flats (At least 100 per class period) — See Anchor Task 2 for how to prepare this material before the lesson.
  • Millions Place Value Chart (1 per student) — Students might need more or less depending on their reliance on this tool.
  • Stapler (1 or more per class) — Either tape or a stapler can be used here.
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Anchor Tasks


Problem 1

How much is a million?

Guiding Questions

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Problem 2

Make a model to represent the size of 1,000,000.

Guiding Questions

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References

John A. Van de Walle Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 3-5 (Volume II)Activities 10.15, 10.16, and 10.18

Van de Walle, John A. Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 3-5 (Volume II). Pearson, 2nd edition, 2013.

Modified by Fishtank Learning, Inc.

Problem 3

a.   Use a place value chart to model the size of 1,000,000, building it from bundles of 10 starting with the ones place. 

b.   Use your work in Part (a) to solve each of the following:

  1. 10 $$\times$$ 10 = ______________
  2. 10 $$\times$$ 10 $$\times$$ 10 $$\times$$ 10 = ______________
  3. 10 $$\times$$ 10 $$\times$$ 10 $$\times$$ 10 $$\times$$ 10 $$\times$$ 10 = ______________

c.   Use your work in Part (a) to write each of the following as a product of tens: 

  1. 1,000 = ____________________________
  2. 100,000 = ____________________________
  3. 100,000,000 = ____________________________

Guiding Questions

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Problem Set


Answer Keys

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Discussion of Problem Set

  • Look at #1. Did anyone change their answer or add to it? What changed your mind?
  • Look at #2 & #3. What do you notice about the number of times 10 was multiplied together and the number of zeros in the solution? Why does that relationship exist? 
  • Look at #4. Do you agree or disagree with Jose? Why or why not? (You can use this question as a way to focus on error analysis and what makes a good explanation.) 

Target Task


There is no Target Task today to allow teachers to build in math routines throughout the first few days of school.

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

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Lesson 2

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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