Multiply or Divide? Exploring Word Problems that Compare.

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SWBAT solve word problems that use multiplicative comparison.

Big Idea

Students learn to figure out what vocabulary in word problems tell them to multiply or divide and understand how to use the multiplicative comparison.

Warm up: Counting by Twelves

10 minutes

My students are afraid of twelves!

We opened up the lesson today with this odd little video about Little Twelve Toes from Multiplication Rock.  This little video opened up some interesting talk about number systems and base 12. It was an interesting mix of comments in the room about this, as they couldn't get beyond the idea of having 12 toes or 12 fingers. I didn't pursue the conversation too much farther because I wanted them to say their 12 times tables and count by 12. That was my real purpose behind showing this very creative video. It really got them talking about how different life would be if we had twelve toes and a different base system. 

After we orally recited our twelves, I switched the video to Counting By Twelves because I wanted them to count more. It is a little more energetic! It appealed to one of my students who is generally very shy. I think kids who struggle with multiplication feel more apt to try if the drilling is fun and light.

It got us moving on a cold snowy Monday! I use these little videos to get them excited about their math lessons and we would be dividing more today. It switched it up a little.

Reviewing the Box Method of Dividing

15 minutes

I had written a simple two digit by one digit division problem on the board, 79 ÷ 3 = n.  I asked for a volunteer to come up and explain, using proper math terms, how to divide it out.

One girl volunteered and finished up the problem beautifully using the boxes logically and carefully. I asked for a volunteer to check her work using the inverse. This boy in this video took a few minutes to remember what he needed to do, but as he talked, we can see that the concept is really registering in his brain as he checks the work.Checking 2 divided by 1. He continues on and finished up with everyone watching.Checking 2 ÷ 1 digit continued. This type of peer support models Math Practice Standards 1, 3, and 6. He is communicating both in writing and in his words about adding in the remainder, but does it with the support of the class. In this next movie, another boy does a wonderful job of explaining using place value words, structure and attention to precision as he demonstrates the standard using the rectangular sections to find his quotient. Dividing 3 by 1 starting .mov As he continues to finish, he reasons his work really well.Dividing 3 by 1 continued. This proved supportive help to a person who was struggling. Notebook Division...She Get's It!.


Multiply or Divide? How do we know?

20 minutes

 I brought up Learnzillion lesson 3017, by Amy Ordonez to help students see a visual as we look at division and multiplication in word problems as comparing. This reinforces understanding visually before we really look at the words in the SB file. Multiply or Divide SB File

When we were done, I brought out the SB file and began by comparing two different word problems. We examined what we know, what we want to know and discussed thoughts about how we would develop equations. We looked at the final questions and compared the language as we solved them together. This discussion proved to be very insightful and helped students understand the differences in the language. This is our SB notes as taken in class:Multiply or Divide Class Notes.

I had to go back and forth between pages to continue to compare the language. I explained that word problems are sometimes mixed up in assignments and that identifying the language, visualizing the situation in the problem and developing the equation using variables would help them solve correctly. 

I took this opportunity to introduce what a unit fraction is because word problems often will ask us to find a fractional part of a whole. We talked about the meaning of the reciprocal of the unit fraction in relationship to the whole. 1/4 of 4 would be the same as dividing 4 by 4. I used my fractional pieces on the smart board to demonstrate that 1/4 times 4 would create 1 whole.The Meaning of Reciprocal I explained that  dividing by four was the same thing as multiplying by 1/4 because 1/4 represented a whole being divided by 4. So, in a word problem that asks us to find a unit fraction of the whole, we would divide by the reciprocal or multiply by the fraction.

This concept is really difficult, and does not need to be mastered at this point. But, I indulged them in the idea and hoped they would understand that 1/4 of a number meant that they needed to divide 4 to find the answer and it was the same as multiplying by 1/4. I think it is important to challenge them by exposing them to deeper concepts in small doses. I think this is good teaching, and if done lightly, I have noticed it stirs up their curiosity about math.

Homework Assignment

15 minutes

To close the lesson, I assigned this worksheet. It includes some social studies and real life connections. I wanted to make sure that students felt secure about their work and so we read each one aloud. We discussed and talked about equations. Would we divide or multiply? Because homework is practice in my classroom and I want the concept really mastered well, I set them up with coaching their reasoning about each problem ahead of time. I gave them about 10 minutes to get a start on their work. Multiply or Divide Multiplicative Comparison Assignment 2 Division