Division by Sharing Vs. Grouping (Day 2)

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Objective

Students will be able to share objects equally to find quotients, or use known quotients to find missing factors.

Big Idea

Children need to understand that there are two different contexts for division. This 3 day lesson path will engage them in activities that act out the different types.

Mini-Lesson

10 minutes

When the students arrive at the community area, I ask them to form a circle.  I then ask a student to be my partner to help me act out some stories about cookie orders for our Production Company (yesterday's lesson). This modeling strategy is called Fishbowl and works well when you are using manipulatives.

I have cubes and cups to represent our cookies and packages. I have a chart on the board already with 3 columns: Total, Cookies Per Package, Number of Packages.  I ordered the columns in this way to model a division equation, but I am not using the symbol yet.

If you use this mini lesson, tell different stories to the students and ask them to help you fill in the chart with your known information and then act out what needs to be done to find the missing factor or the missing quotient.  Possible stories may be:

We have 27 cookies baked.  We can put 3 cookies into each package.  How many packages can we fill?

We have 27 cookies baked.  We have 7 packages to fill. How many cookies can we put in each?

Active Engagement

25 minutes

When you are ready to send the students off to work on their own, you may want to consider having them work with partners.  The conversations and teamwork is always helpful in concept development.  It also helps me assess understanding when I can eavesdrop!

When I have the students move into the active phase of the lesson, I hand them baggies with cubes and cups. I also fill in different parts of our chart on the board and ask them to copy it into their math journals. These will be the situations they work to solve.  I usually have all work done in the journals, instead of a worksheet, as it acts as a glossary for the students as we go through the year.

As the students work, I typically stand by and listen in.  Many times I ask them to explain what they are doing, why they are doing it, or prompt them to dig deeper.  This is a perfect time to do some one-on-one or small group work as well.

These boys did not have a strategy when they began.  I prompt them to consider the chart more and talk with me about what "per" means.  Then the lightbulb lit!

This group is also working on a grouping task and were not in agreement of the outcome.

In this clip, the student explains that they "passed out" the cubes in to the nine packages.

Share

10 minutes

To close each of these two sessions, I have students come up and share how they solve the problems on our chart.  As each partnership completes explaining, I ask if anyone did it differently. This is a great time to stretch your students' thinking. You never know what the responses will be here, but the debates and different ways of thinking are always valuable. Don't skip this part.