Drawing Equal Group Models

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Objective

Students will be able to solve simple division word problems using an equal groups model.

Big Idea

The equal groups model used in multiplication can be used to solve division problems as well!

Opener

3 minutes

One of the great things about teaching division to 3rd grade students is their strong sense of "fairness". When it comes to dividing "things" (such as a treat), students are acutely aware of how much each person is getting. So the idea of "equal groups" is pretty well established, it's just up to the teacher to make the connection.

I start this lesson by asking the students about a time they have needed to divide something into equal groups, or a situation in which they have witnessed this occur.  After they think for 30 seconds, I have them share their thinking with a partner.

Today, I tell students, we will be using the equal groups model to solve problems in which a group of something (called the dividend) is being divided into a certain number of groups (divisor). They will be trying to find the unknown quotient, in this case, how many in each group.  

"Where have you seen equal groups before?" (Multiplication).  

"How do you think using equal groups for multiplication is related to using equal groups for division? For this second questions, I want students to "think in their heads", rather than share out. 

Direct Instruction

5 minutes

First I go over this example of a simple division problem word problem and the steps that can be taken in order to solve it.  

Then I model the following problems for the students with cubes, children (placing them in groups) or by drawing an equal groups model on the board.

16 divided by 4 =

15 divided by 5 =

8  divided by 2 =

Try to encourage them not to shout out the answers, which most of them should know because of their work with multiplication!  The focus is on learning the process, so we are using simpler numbers when we are learning a procedure because it makes it easier for us to recognize how the steps work.

Guided Practice

20 minutes

Have the students work with you as you model the following examples:

24 Black-tailed Jackrabbits are hiding in the desert scrub. It is twilight and they want to go search for plants to eat. They are going to go to the hillside, the edge of the road, the canyon, and the wash (a dry riverbed).  If they are going to travel in equal groups, how many jackrabbits will be in each group?

27 Gila Monsters are walking down a wash.  (This would never happen, as they are extremely rare).  They make a plan to split into the following groups:  one group will hunt for eggs, another will search for a puddle in which to moisten themselves, and the final group will lay in wait for baby lizards.  How many Gila Monsters will be in each group?

18 Downy Woodpeckers are going into the forest to hunt for delicious insects.  Some will go to Eastern White Pine trees and some will fly to Hemlock trees.  If they are going to split into equal groups, how many Downy Woodpeckers will be in each group?

16 Merriam's Kangaroo Rats are hopping around looking for seeds.  An equal number of them find seeds in the dirt, near some rocks, under a Palo Verde tree and next to a Saguaro cactus.  How many of them went to each place?

If there is time, I invite students to make up a story for the following equations.  Unless they have been researching animals, don't hold them to scientific accuracy at this time, as the emphasis is on division.  Later they will use real information to create division word stories!

28 divided into 4 equal groups =

32 divided into 8 equal groups =

42 divided into 7 equal groups = 

Monitor and adjust.  Watch their work to make sure that the models are neat enough to read. Also encourage students not to make super detailed pictures at this time, as the point of the picture is to solve the math problem. Later, when they come up with their master examples, they will be able to take more time on the art. 

Independent Practice

25 minutes

As the students work through these word problems independently or with a partner, pay careful attention to how they are drawing their models.  Again, don't let them become over absorbed in creating detailed pictures and, on the other hand, don't let them make such a sloppy model that it's impossible for them to count the items with accuracy.  Suggest tally marks!  

Two of the problems have an unknown dividend.  I kept notes so that I could remember which students were flexible enough in their thinking to recognize this without prompting.

Wrap-up

5 minutes

To close, we review the names for the parts of a division equation (dividend, divisor, and quotient).    I ask the students to describe to a partner, how the equal groups model can look different from an array. This is a review question, as this should already be familiar to them from multiplication.  

Ask for volunteers to share something they feel more confident about or an area in which they would like further practice.