Multiplying Decimals

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SWBAT multiply multi-digit decimal numbers greater than 1 by numbers greater than 1.

Big Idea

Since decimals are an extension of the base-ten number system, the same algorithms for calculating with whole numbers apply to decimals.

Think About It

7 minutes

Students work in pairs to complete today's Think About It problem. I expect that my students will be pretty good at using estimation to determine where to place the decimal points. After 3-4 minutes of work time, I will ask students share out where and how they decided to place the decimal points.

After listening to several explanation, I will inform students that today we're going to discover a general rule that we can use to multiply decimal numbers. 

Intro to New Material

15 minutes

To begin the Intro to New Material portion of the lesson, I plan to have students synthesize what they noticed as they completed and discussed the Think About It problem.  I expect that my students will get us to, or close to, a generalization. When we reach this point I will let students know that they have just discovered a rule that will help them to multiply decimals.   

I will then have students fill in Key Idea #1 on the Guided Notes:

The total number of decimal places in the factors is the same as the number of decimal places in the product.  We can check the resulting quantity by estimating.

For the next three problems on the INM, I want students thinking about the key point above, and consider the number of decimal places in the factors as a guide to their calculation. After they complete these problems, I will have them share out where to place the decimal in the products.

We then fill in Key Idea #2:

Since we know where to place the decimal point, we can multiply the decimals like they are whole numbers and place the decimal point in after we multiply.

Together, we then complete the final two examples.

Partner Practice

15 minutes

Students work in pairs to complete the Partner Practice problem set.  As students are working, I circulate around the room and check in with each pair.  I am looking for:

  • Are students explaining their thinking to their partners?
  • Are students annotating the problems?
  • Are students using estimation to check their work?
  • Are students placing the decimal point in the correct place in their products?
  • Are students answering in full sentence answers, where needed?

I'm asking:

  • Explain how you determined this product.
  • How do you know your answer is reasonable?
  • Why did you use estimation to check your answer?
  • When did you use estimation?

After 10 minutes of partner practice time, I have the class come back together for a conversation. I ask a student to pick one of the first problems, and present how (s)he knew where to place the decimal point.

Students then complete the Check for Understanding problem independently.

Independent Practice

15 minutes

Students work on the Independent Practice problem set.  As they're working, I circulate around the room and ask students about the work they are completing.  I insist that students are annotating and making estimates for the word problems (not just in this lesson, but as a general rule).  

Closing and Exit Ticket

8 minutes

After independent work time, I have students look at Problem_3 from the Independent Practice section, about Rick's car.  I have students guide me through the annotation and sense-making of the problem, and we make an estimate together.  I then write the multiplication in two ways on my paper under the doc camera:  

29.7 x 10.45 and 10.45 x 29.7

I ask students which one is correct.  I'm looking for students to name that either is correct. Multiplication is commutative, so we can write the factors in any order.  I then ask students which way is easier to work with.  I want my students to write the longer factor on top, as it makes organization of their work space much easier.

Students then independently complete the Exit Ticket to close the lesson.  A sample is provided.