Multiplying Decimals by Decimals

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Objective

SWBAT multiply decimals by decimals

Big Idea

Multiplication with decimals is a life skill used when making purchases and measuring

DO NOW

15 minutes

The students will be completing 3 multiplication problems involving decimals and whole numbers.  Students should work these problems out independently.  Instruct students to do a HUSUPU to find a partner. Once with a partner, tell the students that they are to go over the problems using the steps they took to get to their answer.  As students are doing this, walk around a listen for them to use the steps. “First, I stacked them up to make a multiplication problem, next I multiplied like normal, then I counted decimal places in my problem to put that many in my solution.  I know my answer is reasonable because it matches my estimate”.  Students will benefit from having to explain their thinking and it helps drive home the “how” to do the problem.   (SMP 1,2, 3, 6)

Multiplying Decimals by Decimals (Teacher Directed)

20 minutes

I will be modeling for students how to multiply decimals by decimals.  For each problem, I will estimate my answer first, then I will solve.  My modeling will include thinking out loud and then having the student write down what I’m doing.  As students are doing this, they will be instructed to pay attention to the steps so they can come up with their own rule for multiplying decimals by decimals.

Common misconceptions:  students do not realize that there are several ways to represent multiplication problems.  I will be addressing this as I go along.  Each example represents a way they may see a multiplication problem in the future. 

Multiplying Decimals by Decimals (Students Try)

20 minutes

Tell students that the class will be completing each problem together.  Students will need to estimate their answer first (this helps with placement of the decimal), set up and then solve.  When students have completed their problem, they can write it on the white board, and as a group have them reveal their answers.  Ask students how they came up with their solution.  Students should be able to tell you how they did the problem and this will help when they write the steps in their notes.

As you walk around, watch to see that students are modeling the problem as directed.  It is not necessary to complete all practice problems.  Do as many as you feel your group of students needs.  When the students are ready, have them write down the steps to multiplying decimals by decimals (SMP 8).  Students can do a think-pair-share to help facilitate this process.   Once students have put their thoughts down, go over the steps with them to make sure they have it. 

Word Problems

20 minutes

Students will be applying what they know about multiplying decimals by decimals to the real world word problems.  Before letting them work independently, tell them they will need to explain in words what they did and why they did for each problem. As they finish each problem, they will do a HUSUPU to go over that problem with a problem, using the “what” and “why” to facilitate conversation. (SMP 1,2,3,6)

Directions:

  1.  Circle key words that tell you it is a multiplication problem.
  2. Estimate your answer
  3. Find a solution
  4. Explain in words “what” you did and “why” you did it.
  5. Prove that your answer is correct.

After each problem, find a partner to share your reasoning and solution.

To make the HUSUPU move easier, have the students put the number of the problem they are working with on their finger.  This way they can partner up with someone who is working on the same problem.   Students should return to their seats when they are done sharing and start working on the next problem. 

Closure + Homework

10 minutes

Students will be working on a problem called the Domino worksheet.  This is a nice activity to do because it is self checking. They start in box one and find the answer.  The answer follows the arrow into the small box which then becomes the new number in the second big box.  Now they have a new problem.  They find the solution and the solution becomes the new number in the next box.  Make sure students are following the arrows correctly.  When the worksheet is complete, the students should have the answer in the circle at the end.

Remind students that they can still estimate their solution to help with decimal placement.

Students can work on this at home because they are able to tell if they are correct or not.

Tools:  Domino worksheet 1 and 2