# How to Use Models to Solve Math Problems

Instructor: Lynne Hampson

Lynne Hampson has a Masters in Instr. Design & Bach. in Elem./Spec. Educ. She taught 8 years in Elem. Core, Science, Coding, Microsoft, Internet Safety, and Life Skills.

In this lesson, we will discuss using models to solve math problems. We will look at two examples together, modeling and measuring the area of a quadrilateral and the volume of a cube.

## Models for Math Problems

Models are either a drawn or created representation of an object. They are used as a visual to aid in understanding a concept. We use models in many facets of everyday life. Architects draw scale models of large buildings before they build the actual building. Students use modeling in math by using ones blocks, tens blocks, and hundreds blocks. They also draw shapes to show the length, width, and height of a three-dimensional object.

There are many different types of models that can be used because there are many types of shapes to measure. For example, the formula and model will look different for a circle, cylinder, or sphere. In this lesson, we will be explaining how to use the area model for quadrilaterals and the volume model for cubes.

An area model is a drawn depiction of a two-dimensional quadrilateral that is used to visualize the area formula.

A volume model for a cube is similar to the area model in that it is a visual representation, but instead of a two-dimensional shape, it is a three-dimensional object.

## Using Models for Math Problems

Math can seem abstract or hard to visualize when merely using an area or volume formula to solve a problem. Is it possible to use a model to help visualize the answer? Yes, it is possible, and by drawing a model you may be able to transfer this knowledge from pencil and paper into a real world skill. Models take the formula and make sense of it with a visual representation of WHY we need the formula to complete the task.

When measuring the area of a quadrilateral, there are two measurements to account for, length and width. This is because two-dimensional objects do not pop out at you like three-dimensional figures. For example, let's say you are buying new carpet and need to know the area of your room in order to purchase enough carpeting for the floor.

The floor is not three-dimensional, it is flat, so you measure the length and the width, and multiply them together to find the square feet of carpet necessary. We call it square feet because that is what you are really measuring. Have you ever seen those one-foot by one-foot carpet squares? A lot of commercial retailers have them. They are a great example for measuring square feet because you can actually see the feet in squares. If you count how many you use in your room, you can tell how many square feet it is without even using the formula.

Back to using the area model to measure your room for new carpet. First, draw a picture that looks like the shape of your floor. Some rooms will look like a square, some are other quadrilateral shapes. It doesn't have to be exact, it is just a visual model. Next, you will measure the length of the room. Write down the length next to the length side of the object you drew. Now, do the same with the width. Then, multiply length times the width to find out how many square feet you need. The model will serve as a guide to show how many square feet of carpet you must buy. If your room shape does not conform to a standard quadrilateral shape you may need to break it down into smaller simple quadrilaterals and then add up the smaller areas to get the total area.

For a room that is 9 feet by 9 feet:

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