Multiplying Decimals Card Sort

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SWBAT multiply decimals.

Big Idea

How can we use fractions to multiply decimals?

Do Now

10 minutes

This lesson follows our work with Adding and Subtracting fractions. We'll begin with some review problems to assess their understanding of this topic:

Do Now: Use your ideas about place value and adding and subtracting decimals to find the sums and differences below.

  1. 27.9 + 103.2
  2. 0.45 + 1.2
  3. 2.011 + 1.99
  4. 34.023 – 1.23
  5. 4.32 – 1.746
  6. 0.982 – 0.2

After 5 - 8 minutes I will randomly call students to the board to show their work on the Do Now problems. Once the answers are posted I will ask students to review them. If students disagree with the work, we will discuss the problem further. The most common mistake occurs on Problem #5: Students sometimes forget to add a zero as a place holder before subtracting.

Card Sort Activity

15 minutes

In a previous lesson my students have worked on an activity that is similar to the main activity in this lesson. This enables to launch to go smoothly, since they are familiar with the procedure. I will explain to my students that in this activity, they will use equivalent fraction and decimal representation of numbers to think about how to deal with place value when multiplying decimals. Students will also use their understanding of improper fractions and mixed numbers in this activity. 

After we complete our discussion of the Do Now, I will give each group of students a set of Multiplying Decimals Card Sort cards. (It will save time if you pre-cut the cards for students.) This resource comes from the CMP3 Curriculum which we use in my school. 

Directions for Students

  1. Spread the cards out on your table so everyone in the group can see them.
  2. Sort the cards into groups with equivalent expressions.  For example, 728/100 and 7.28 are equivalent, so they can be grouped together.  Are there any other cards in this group?  What other groups can you form?
  3. Communicating with your group is very important for this activity, so be sure to work together.

I plan to give my students about 20 minutes to work through the activity. As they work, I will circulate throughout the classroom to assess their understanding.  Groups may struggle with some of the cards, but it's important to let them work together to complete the activity. 

Activity Review

10 minutes

Like in our earlier Card Sort lesson, we'll review the activity with a class discussion.  I will ask some leading questions that will allow for different groups to share their thoughts and strategies for the card sort.

  • How many groups do you have?  

Students may respond with different answers, which will lead to the following question.

  • Name the cards in one of your groups?  

It's best to start with one group of students and have them share a set of cards that they matched, while other students see if they've matched the same cards.

  • Why did you group them together?   How do you know which decimal answer matches your fraction answer?

Students should explain their thought processes and strategies.  I will call on several groups to answer this question, because it is helpful for students to hear different strategies.

  • Does anyone disagree with this group?

If there are groups that disagree, it is important to see why they differ.  It could be that they didn't correctly change a fraction to a decimal or they didn't multiply the fractions correctly.

Based on a previous discussion and activity, I expect that my students will have used the denominator of the fractions to determine the last place value of the decimal.  

  • Based on the card sort activity, what is one strategy for multiplying decimals?  What patterns do you see that will help you multiply decimals?

Students should realize that they can convert the decimals to fractions and use their prior knowledge of multiplying fractions. We will begin to discuss the patterns they may find when changing their answers back into decimals.  The discussion will continue in the next lesson where students develop an algorithm for multiplying decimals.

Exit Ticket

5 minutes

Students will complete an Exit Ticket that will serve as an assessment of their understanding of the lesson.  This will be used to plan future lessons, separate students into groups, and differentiate activities.

Exit Ticket

Complete the following problem using a fractions strategy.

0.08 x 0.21

After about 5 minutes, I will collect students' work.