1. Lesson 3-13 Comparing Decimals
Overview: Students compare decimals using <, >, and =.

3. Math Message
Write a number sentence using the symbols >, =, or < to show which decimal is larger: 0.95 or Be prepared to explain how you know.

4. Math Message Follow-Up
How did you know which one was larger?
Possible Responses

5. Possible Responses

7. Follow-Up Question
Caitlin agreed that 0.95 > She said this is true because 95 > 3. Do you agree with her reasoning? If not, can you give an example in which her strategy will not work?
Sample answer: No. For example, 0.23 < 0.9 even though 23 is greater than 9. Looking at the numbers to the right of the decimal point and comparing them like you compare whole numbers does not work.

8. Here is another number story to go along with the decimals 0. 3 and 0
A can of soup weighs about 0.3 kilogram. A centimeter block weighs a little more than 0.95 gram. Which weighs more-the can of soup or the centimeter block? OR

9. In the context of the number story, can you still say 0. 3 < 0. 95
In the context of the number story, can you still say 0.3 < 0.95? Why or why not?
No. The decimals do not refer to the same whole. The number story includes kilograms and grams. Comparisons are only valid when two decimals refer to the same whole. OR

10. Which weighs more, the can of soup or the centimeter block
Which weighs more, the can of soup or the centimeter block? About how many times more?
Sample answer: The can of soup weighs more than the centimeter block. 1 kilogram = 1,000 grams; 0.1 kg = 100 grams; 0.3 kg = 300 grams. The can of soup weighs about 300 times as much as the centimeter block.

11. In this lesson, you will compare two decimals to the hundredths place by reasoning about their size. You will recognize that comparisons are valid only when the two decimals refer to the same whole. You will record the results of your comparisons with the symbols >, =, or <, and justify your conclusions by using visual models.

12. Just as with fractions, it is important to look at the whole when comparing decimals. If the whole is different, the comparisons will not be valid.
Write a number model using the symbols >, =, or < to record the result of the comparison. Be ready to justify your conclusion.
A box of dental floss contains 50 meters of floss. Samantha used 0.4 meter to floss her teeth. Her brother Eli used 0.56 meter to floss his teeth. Who used more dental floss?
Eli; 0.56 > 0.4 or 0.4 < 0.56

13. Possible Strategies

14. Possible Strategies

16. In the 2012 Summer Olympics, American swimmer Missy Franklin won the 100-meter backstroke. The times of the top two swimmers were and seconds. Which was the winning time?
58.33 seconds; < 58.68

18. Possible Strategies:

19. Possible Strategies:

20. Math Journal page 102. (5 min independent) (8 min with a partner)

21. Summary and Exit Problem
Vanna said, “0.10 meter is more than 0.2 meter because 0.10 meter is 10 longs, but 0.2 meter is only 2 longs.” How can you help Vanna see her mistake? What incorrect reasoning do you think Vanna used to get her answer?
Sample answer: 0.10 represents 1 tenth and 0 hundredths, or 1 long represents 2 tenths and 0 hundredths, or 2 longs. So 0.2 is more than 0.10.
Sample answer: Vanna might have thought of the numbers to the right of the decimal point as a whole numbers 10 and 2. She knows that 10 > 2, so she incorrectly reasoned that 0.10 must be greater than 0.2.