Place Value with Decimals

Lesson 11

Math

Unit 1

5th Grade

Lesson 11 of 13

Objective


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

Common Core Standards


Core Standards

  • 5.NBT.A.3.B — Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

Foundational Standards

  • 4.NBT.A.2

Criteria for Success


  1. Compare decimals by making use of the structure of the place value system (MP.7), namely that one of any unit is greater than any amount of a smaller unit. Thus, the largest place value in each number contains the most relevant information when comparing numbers. If both numbers have the same number of largest units, the next largest place value should be attended to next, iteratively, until one digit is greater than another in the same unit. 
  2. Record the result of comparisons using >, <, or =.
  3. Compare numbers written in various forms, including standard, word, and expanded form. 
  4. List numbers in ascending or descending order. 

Tips for Teachers


  • There are lots of common misconceptions that come up in the context of comparing decimals. These include:
    • Thinking that a longer decimal is a greater decimal (e.g., 0.493 is greater than 0.8)
    • Thinking that a shorter decimal is a greater decimal (e.g., 0.48 is greater than 0.493)
    • Getting tripped up by an internal zero (e.g., in the number 0.07)
    • Thinking decimals between 0 and 1 are less than zero (e.g., thinking 0.48 is less than 0)
    • Reciprocal thinking (e.g., thinking 0.5 is greater than 0.8 because $$\frac{1}{5}$$ is greater than $$\frac{1}{8}$$)
    • Not seeing the equivalence of decimals with zeros at the end (e.g., thinking that 0.48 is not close to 0.493 because they don’t know 0.48 = 0.480)

Keep an eye out for these and other misunderstandings. 

  • Before the Problem Set, you could have students play an adapted version of the game “Corn Shucks” from Building Conceptual Understanding and Fluency Through Games by the Public Schools of North Carolina. (Adapt it so that students are writing decimal numbers - perhaps having them using 6 digits to write a number from the hundreds to the thousandths place.)

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 (Various quantities per student or small group) — Students will need various quantities depending on how they assign the value of each base ten block, or they may not need these at all 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


Problem 1

Would you rather have Option A or Option B? Explain.

Option A:

1 hundredth

2 thousandths

Option B:

4 thousandths

 

Guiding Questions

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Problem 2

Compare each of the following, recording the result of your comparison using <, >, or =. Show or explain your thinking.

a.   0.045 and 0.318

b.   0.705 and 0.7

c.   15.406 and 15.43

d.   0.560 and 0.56

Guiding Questions

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Problem 3

List the following numbers in order from least to greatest: 

0.48 0.5 0.493 0.07 0 1.0 0.8

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)p. 268, Formative Assessment Note

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 4

Compare two hundred seven thousandths and $$\left(2\times\frac{1}{10}\right)+\left(6\times\frac{1}{100}\right)$$. Record the result of your comparison using <, >, or =.

Guiding Questions

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Problem Set


Answer Keys

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Discussion of Problem Set

  • Look at #1e. What did you get? Explain your reasoning. 
  • Look at #3. What did you get? Explain your reasoning. 
  • How did you solve #4? If you had to estimate the value of K, what would you say it is? 
  • Look at #5f. What did you get? Explain your reasoning. 
  • How did you strategize which numbers to assign to each letter in #8? Was it easier to start with a certain comparison? Why? 
  • Look at #9. Is this always, sometimes, or never true? Explain your reasoning. 

Target Task


Problem 1

Determine if each comparison is true or false. Record your answer with an X in the table below.

  True False
$$3.87 < (3\times1)+\left(9\times\frac{1}{10}\right)$$    
94.13 < 94.130    
2.567 > two and fifty-eight hundredths    

Problem 2

Four people competed in a high jump competition. The table below shows each person’s best height.

High Jump Competition

Student Height (in meters)
Andre 3.09
Julia 2.007
Max 2.4
Reina 3.005

List the heights in order from the least to greatest. 

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 10

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Lesson 12

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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