What is Division

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Objective

The students will relate division to multiplication by solving for an unknown factor.

Big Idea

The students will listen to the story, "The Doorbell Rang" by Pat Hutchins. While interacting with this wonderful story, students will begin to realize when to solve for an unknown factor using division.

When the Doorbell Rings

20 minutes

Introduce the story, "When the Doorbell Rang" to the students. Many of them have most likely heard it already.  I remind students that they should listen with a "math ear".  You may want to consider displaying the illustrations in some way as you read the story.  I use my document camera. I also have twelve circles cut out to represent the cookies.  My white board is magnetic, so we will be able to put the "cookies" on the board with magnets.  

Mathematicians, will you please gather at our community area for a story?  Thank you for joining me so quickly.  We have been working on counting by equal groups of numbers and realized what we were really doing was multiplication.  Today I want to share a fun story about some children trying to share cookies.  You may have heard this story before, but remember we are listening as mathematicians and looking for the patterns or rules. 

As I read, we will act out the story with these circles. They will represent the cookies. I will call students up as we go.  But before we start, how can we arrange the cookies on the cookie sheet to make it easier to count them?  Great idea, we could use an array.  I know when I make cookies I always place them on the tray using an array.  Can someone come up and arrange them?

These 3 clips show students working on organizing using arrays.  In the first, the sound is not on, but shows a student organizing into equal groups, but then using my prompts to create an array. Next, a classmate reorganized into another possible array.  The third student obviously needs some help with his understanding of arrays in general.  This activity showed me three different levels of concept understanding.

 

Allow a few students to do this, naming their array. This is a good review of the past few lessons and the children are able to see arrays in a real world use. 

As I read, I have students come up, draw circles for their plates and then put in their cookies. Every now and then, I will ask students why one child can't have more than the other. This helps them remember it must be fair.  I explain in math we use the term equal to mean each person, side, group, has the same number as the others.  As the students work out each problem, write up representations in number form.  Or, talk about the number sentences and list them afterwards.  That depends on your pacing of the story reading.

Watch this video to see how I read in an interactive way and work with the students to define the term division using the story.

Students will be taking from one plate to fill others.  Have conversations about how they are systematically taking from one plate to fill another.  What have they noticed? 

Sharing the Loot

20 minutes

Following the whole group work, I send partners off to work with a different number of "cookies".  Each partnership is given 18 bingo chips to represent the cookies.  Their job is to determine the equal shares of 18 and write the appropriate equation for that division in their math journals, along with a drawing to show the manipulative work.

Ok, boys and girls.  Let's pretend that Grandma makes you some cookies!  She will bring over 18 cookies for you.  What I would like you and your partner to do is divide the cookies into as many equal shares as you can. Then draw the representation of those equal shares and label them with the correct equation, just like we did on the board with Grandma's 12 cookies.  

In order to pair up the students, I ask them to arrange themselves in a human 2 by 9 array.  I have 18 students in my math class and one person was absent, so we discuss the "remainder" when our array isn't working.  I am surprised and pleased when a student suggests an uneven group of 3.  After they are arranged, while they work I listen in and add suggestions.  

When you try this, use the observation information to guide your next lesson.  It is obvious which students are beginning to understand the idea of equal shares. With these students, you can begin to use multiplication to guide their division work.

These students are using a trial and error strategy and working on what to do with a remainder.

Closing

10 minutes

After the students have time to explore and create equal groups, I gather them at the community area and have them share their thinking and product.  This is an important time for students to hear several ways of attempting to solve the problem and to compare their work to others. Remind students to use our classroom talking moves correctly when commenting, and to think about differences and similarities in strategies and outcomes.