The Multiplication and Division Connection

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SWBAT develop fluency in solving multiplication and division problems.

Big Idea

Students can solve multiplication and division problems quickly by recognizing the relationship between the two operations.


10 minutes

Sometimes when I multiply, I find that when I think of a song it makes it easier to remember! I want to teach you a new song for multiplying that may help you remember some of those tricky doubles! 

My students love to sing and I hear them use songs like this when they come across the problems and so I try to give them as many tools as possible.

I need 3 students to help me, who can come up here? Now here I have 3 students. I write 3 students on the board.

Each student has 2 eyes (write it on the board).

How many eyes do all 3 students have together?

Who can tell me how they figured that out? I'm expecting a wide range of responses from students -  multiplied, repeatedly added 3 up, skip counted by 2, etc. (MP7, MP8)

What if I told you that I have 6 eyes, and they are shared equally between 3 people.  I write this on the board. How many eyes does each person have?

On the board I now have both equations written. I start prompting them with questions to think about similarities and differences between the equations and what they represent (MP1, MP2). Common Core standard 3.OA.B.5 requires students to apply properties of operations as strategies to multiply and divide (ex: If 6 x 4 = 24 is known, then 4 x 6 = 24 is also known).

Who can tell me which problems are division problems? And which are multiplication problems?

Now who can tell me what looks the same about these? And different? 

Guided Practice

10 minutes

I’m going to hand each pair of you two foam dice, and I want you each to roll 1 of them. I will show you what I mean with Kayla.

Model each rolling a rolling a foam dice, and writing those numbers on a piece of paper.

We have a 6 and a 4. I’m going to use these numbers to set up my first multiplication problem, which is 6 x 4 = _____ .

Who knows the product of these numbers? With that knowledge, and all that you know about multiplication and division, what else do we know about this relationship between these numbers?

Here I expect students to tell me that by understanding the commutative property of multiplication they know that 4 x 6 = 24 (MP6). And when they know the total number of objects in the equal groups they can also divide these objects equally into groups (3.OA.C.7, 3.OA.B.5).  As we make these discoveries, I write all four equations on the board. Students may also reference place value strategies and properties of operations (3.NBT.A.2) to solve.

Kayla and I will choose 1 of the problem from these four equations and write a word problem for it. 

Independent Practice

35 minutes

When each of you return to your seats you and your partner will each roll 1 of the dice and then you will solve all 4 equations in the family. Choose 1 of the equations and together write a word problem that matches.

It is important here that students have time to practice these strategies in order to build fluency in multiplying and dividing (3.OA.C.7). Students must have time to explore the relationships between the operations to create a deeper meaning (MP7). There will naturally be some students who don't grasp this concept quickly and require additional guidance. I always intentionally create my groups, although it may appear random as I partner them off. I place struggling students with higher performing students so that they can help their classmates. I monitor all of the groups asking questions and looking for misconceptions. When I see students who particularly struggle I stop and help those groups with additional guidance. 

Asking students to write their own word problems allows them to really think about what it means to multiply or divide and how that can be communicated in words (MP1, MP6) . They must think critically about what it means to create or divide groups and what types of objects they can use to represent this. Today I walk around with my iPad and film students reading me the problems they wrote. I will use this today and tomorrow for a quick check for understanding. 

Close- Check for Understanding

5 minutes

Now turn your eyes to the screen and get a fresh sheet of paper. We are all going to solve one of the problems your classmates created!

Here I show a video of a group reading their problem. Students solve the problem on a note card and hand it in to me as a check for understanding. I do a quick spot check, and any students who got it wrong will be pulled tomorrow in a small group.