Structure Spotlight

Intro to the Size Model:
Exploring Number Relationships

The Size Model is a bar model that has equal-sized cells in each row. Each horizontal row represents the same total quantity. So in the model above, the sum of all the cells in row C is the same for the cells in row B and row A.

The Size model always has equal-sized groups. That is, each row will have the same number in each cell.

If you’re starting out with using the size model with students, here’s a couple of tips for getting started.

Whole-half model: Start with physical materials.

Whole-Half-Quarter Size Model

Start by allowing students to spend time with tiles or interlocking cubes that you will later use to create 3-D models.

After playing for a bit, ask students to make a train with their cubes or tiles. The total number is not as important but it should be an even whole number (for now) and a quantity that students can handle easily in front of them.

Create equal groups; connect to a story

Invite students to make two equal groups from just their cubes.

You can add in a story context here to assist with connection to the activity, such as needing to divide students up into two equal sports teams. They have to have the exact same number of people on each team! How can we make sure we have two equal teams?

Again, the specific numbers are irrelevant right now. We’re working on the idea of 2 equal groups of whole numbers.

Allow students to share their two groups and let them prove that the two sets are equal.

Moving on: 3-D to 2-D transition

You may decide that this exploration was enough for now and they can continue with other quantities another time.

When you decide to move on, you can represent their 3-D cube relationship in a 2-D form.

Use gridded chart paper so that you can represent the exact number of total cubes.

If you’re representing a child’s work that had 12 total cubes, outline a 1 x 12 rectangle.

Alternatively, you can trace around the cubes on a piece of paper, making sure to show the individual units as well.

Ask the student to show you how they made two equal groups, or halves, of their quantity.

It’s not important to label the number of cubes right now.

Equal Groups

Represent their two equal parts on the row under the total. The width will be the same but now you can show a big division between the two groups.

Spend time talking about the model and hearing what students notice. Ensure that they know that each row represents the same total quantity.

Spend time creating whole-half size models with other students’ quantities as well.

Ask: “What is the same and what is different about these models?”

So much of math is noticing what stays the same and what changes...