Division Models to Solve Problems

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SWBAT use models to solve division problems by creating equal groups and record solutions using division number sentences and models.

Big Idea

Word problems involving division can be solved using models.


5 minutes

You already know that you can think of division as sharing equally. Today you will be learning how to create a different kind of model that may help you quickly solve division problems. I want you to have as many division tools in your tool box as possible, that way you can pull them out quickly when you need them!

What are some situations in which you have to make equal groups? (Making teams to play a game, planting rows of flowers in a garden).

I write on the board: Li made 12 tacos. She wants to give some friends 2 tacos each. How many friends can get tacos?

Give students a chance to work in pairs, using counters to help if needed. Next, invite them to share their work and solutions. Remember to supports students in questioning one another, as this builds their ability to make sense of problems and construct arguments to defend their reasoning (MP3).

Key questions: What does your model represent? Which problem solving tools did you use?

Together we read the problems on the board.

What does the 12 stand for? (Total number of tacos).

What does the 2 represent? (The number of tacos each friend gets)

What does the 6 stand for? (The number of friends that get tacos).

I label their explanation under each number so that students can refer back to this information if needed.

Guided Practice

10 minutes

I really love tacos. Now let’s see if we can share those same 12 tacos between a few more people. 

12 tacos                                          12 tacos

3 tacos to each friend              4 tacos to each friend

Work with your partner. For each problem find how many friends will get tacos. Then write a division sentence to represent each situation.

Guided practice is an important portion of my math block because students must apply the ideas we are practicing to different situations with less of my guidance. They must look for ways to solve, discuss with their partner and solve the problem (MP1). In this particular problem it was important for me to see whether or not they could create the groups of 3 and the groups of 4 to model the measurement and grouping in division.

I take time to let students explain their work and share solutions. I ensure I have a few examples of how the problem was solved to illustrate on a poster. I keep visual examples of problem solving strategies up in the classroom so that students are able to refer back to them when needed.

Independent Practice

30 minutes

So you’re telling me that if you know your total number of objects, tacos, cookies, pencils… That you can figure out how many people you’re going to divide them between and how many each person will get?

Good! Because I have a lot of ideas about how I need to share some stuff, but I’m not quite sure how many people I can share equally with and how many to give each person. I bet you guys can help me with this.

I have word problem cards that require division at each table.

Examples of problems: 

Kevin has 12 pencils in his pencil box. There are 3 people at his table. How many pencils will each student get if he shares them equally?

Mrs. Maffei has 24 erasers left. If she wants to give each student 2 erasers, how many students will get erasers?

Elena loves making cookies. She made a dozen cookies and would like to share them with her 3 best friends. How many cookies with each friend get if she shares the entire dozen?

In order for students to develop fluency in solving division problems I feel it's essential to give them ample time to develop strategies. The problems use student names and real world situations so that students can easily relate division to real world situations. My students love to help me pass things out, clean up, set up activities etc. so it's an easy connection to make with word problems. Their models and labeling of parts of division problems were very detailed, which helps me see how they are thinking of each problem and what pieces of lessons are really sticking with them. Their models illustrate for me that they are creating representations of the problem and considering the units involved (MP2) to solve. Common Core Standard 3.OA.3 states students must be able to solve division problems within word problems, so I want to ensure students practice applying the skill. 


5 minutes

After all this practice you’re really becoming division experts! Who can remind me what division is used for? Here I expect student responses to relate division to real world examples like sharing food, making teams, handing out cupcakes. 

Students are becoming very detailed in labeling parts of a problem, using models to represent problems and creating a deeper understanding of groups, measurement and sharing. I have a small number of students who struggled to apply what we learned today in their independent practice. They needed tangible objects (like cups and counters) to pass things out and set up groups, which helped them see what they were creating. 

And who can show me what they have learned about solving division problems?