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One of the best ways to illustrate the differences in multiplication and division is to use children’s literature or introduce a math happening that occurs in our everyday life. In Suh’s article (2007) Tying It Altogether, she discusses the important five strands of mathematics proficiency (seen in Figure 1.1 on page 3) and shares a classroom practice called “math happenings.” This routine was a way to bring in real-life problems, which students found relevant, that became the centerpiece for their problemsolving activity. Each Monday, the teacher came to school and told the students that she had a math happening.

The students were genuinely interested because most students love stories their teachers tell about their lives. She would find an interesting math happening that occurred over the weekend, for example, a measurement conundrum she faced when installing a playground in her backyard when having to abide by the building restrictions, space constraints, and the esthetics of the yard. Students needed to figure out if the configuration would fit in different arrangements in their small, fenced backyard. This math happening became part of their math routines and so on; students started bringing in their own math happenings. Having the personal mathematics connections made the process of problem solving and reasoning worthwhile for her students, and they communicated their solutions in a convincing manner so that they could help their teacher or friend solve a math happening.

Using a math happening or literature connection where one poses different contexts for remainders can help students make sense of division. Here are a few different scenarios to consider: How does each different context make one think differently about the remainders? [1]

  • 2. A pet storeowner has 14 birds and some cages. She will put 3 birds in each cage. How many cages will she need?
  • 3. A father has 17 cookies. He wants to give them to his 3 children so that each child has the same number of cookies. How many cookies will each child get?
  • (Problems from Otto, Caldwell, Lubinski & Hancock (2012) Putting Essential

Understanding to Practice Grades 3-5)

What would you do with the remainders in these three scenarios? The three different contexts allow for one to consider different ways to “treat” the remainder. In the case of the balloons, there are 2 remaining balloons that you cannot really share equally among 3 kids. In the case of the pet store, you can fill 4 full cages but 2 birds will be without a cage. The reality is that you cannot just keep the birds loose so you may want to get an extra cage. Finally, the last example with the cookies, one would be left with 2 extra cookies and if one wanted to share them by dividing them into fraction, that would solve that problem.

There is much to talk about with remainders. Take another example,

Mom had $25 and wanted to give her 4 kids money to spend at the carnival. How much could she give each child?

Each child can get $6 each, but mom would have $1 remaining. This problem begs the student to consider taking the remainder and changing it to a decimal $0.25 so that each child can get $6.25.

Think about it!

How docs providing a variety of contexts for multiplication, division and scenarios with remainders deepen students' understanding of the operations? Create your own scenarios with different interpretations for multiplication and division?

  • [1] I had 20 balloons. I wanted to give them to my 3 children so that each child wouldhave the same number of balloons. How many balloons did each get?
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