Partial Product Strategy for Multiplying Decimals
Lesson 6 of 10
Objective: SWBAT apply the Distributive Property to the multiplication of decimals.
During the previous lesson, we worked to develop an algorithms for multiplying decimals. Today's_Do_Now problems were selected to assess their understanding of the algorithms. (These problems will appear again later in this lesson.)
Calculate each product
1) 300 x 12.6
2) 400 x 53.14
When we first work on these two problems, I expect some of my students will struggle to determine the placement of the decimal point in the product. Since each expression contains a whole number and a mixed number, they should be able to estimate. But, this may not occur to them immediately. As students work I will walk around to assist students and informally assess the progress of the group.
After allowing students five minutes to work on the Do Now problems, I will have students share out their work and answers with their group. If there is a lot of disagreement among the groups, we will discuss the problems as a class.
Next, I will teach students how to calculate the products for the Do Now problems using an alternative method, Multiplicating Decimals using Partial Products.
Example 1: Using partial products and the Distributive Property to calculate the product of 300 x 12.6
My students are familiar with the Distributive Property from our work earlier in the course, but I like to begin this demonstration with a review of the Property. I will ask the following questions:
- What is the distributive property?
- How can we apply the distributive property to decimals?
I want to make sure that my students remember that the property is a combination of multiplication and addition. I will remind them that we have used it in the past both to simplify expressions, and, to perform mental math (i.e., to break a number into a sum, find both products, then add to find the desired product). Thus, the strategy that I am teaching them is not new. I am teaching them to apply it to real numbers, rather than simply integers.
I will not be surprised if some of my students suggest that we "break" 12.6 into 10 and 2.6. Such a sum would build directly on our prior work with mental math. Although that is one possibility, I am hoping that we will be able to work with 12 and 0.6 today, to isolate the decimal portion of the quanitity.
Here is the algorithm that I will introduce today:
Step 1 - Separate 12.6 into an addition expression with two addends.
300 x (12 + 0.6)
I like to ask my students, "What number should be distributed?" Once my students answer this question, we move on to Step 2.
Step 2 - Distribute the factor outside the parentheses.
300(12) + 300(0.6)
I want the process to feel intuitive to my students. Since I know that they know what to do at this point. I ask, "What's the next step?" My students will say "solve" or "simplify the expression". Then I will ask, "Would you be able to do this mentally?"
Step 3 - Simplify the expression
I like to encourage students to try to solve the problem mentally, or at least to make an estimate. Estimation is an important strategy in problem solving. And, if students are able to calculate the correct answer mentally, they will better understand why the partial product strategy can be helpful.
Example 2: Use partial products and the distributive property to find the area of a rectangular playground with the dimensions of 400 meters by 53.14 meters
Example 2 adds a layer of context to the problem. I will have several students guide the class through the solution to this problem as I scribe on the board.
After the Mini-Lesson I want to give my students the chance to practice, while at the same time getting up and moving around so that they maintain focus and energy. To accomplish these goals, students will participate in a Station Activity. The preparation is simple.
- I will have the problem for each station written on an index card and placed at the station.
- Students travel from station to station in groups.
- At the start, each group receives an index card with the starting position on the back.
Before setting them off on their tour of the stations, I will encourage students to use partial products to solve the problems, suggesting that they can use other strategies to check their work. As they tour the stations, students record each problem, their process, and their answer in the space provided on the Partial Product Stations handout. I always remind students to record each station in the correct place! If you start at Station 5, you record the solution in the location on the worksheet for Station 5.
I plan for students to spend about 5 minutes at each station. They will rotate from the first station using a process that I will explain at the end of the first rotation. After 3-4 stations, I will conclude the station work and we will review the answers. I will randomly select students to share their answers with the class. If there is any confusion, I will have students explain their work. This way, students get to practice with some of the problems and to listen to solutions to problems that they have not yet attempted. Look for MP1.
Up to this point in the lesson, students have worked with the class or the group on problems. The Exit Ticket is an individual assessment so that I get some indication of how well students are able to work independently.
Students will receive an index card and will complete the problem below, which I will write on the board.
Complete the problem using partial products.
600 × 19.6
After 5 minutes, I will collect the cards. The results will be used to design future lessons and determine the placement of students in groups.