How To Use Math Manipulatives With an Exit Strategy In Mind

A common reason to be hesitant of using math manipulatives is the need to, ultimately, demonstrate math skills without math manipulatives. But we don’t need to throw our math manipulatives out the window to reach this end! Let’s talk about how to use math manipulatives in your classroom knowing that, in the long run, you will want to take those tools away!

Why Use Math Manipulatives?

Math manipulatives allow your students to understand math concepts at a concrete level. Your students are able to touch, feel and “manipulate” concepts in order to gain a greater understanding.

In terms of the CRA (Concrete, Representational, Abstract) continuum, concrete and hands-on experiences come first!

Consider a student learning about addition for the first time. They will understand the concept of putting parts together more clearly by using a set of counting bears than they would simply taking a look at the equation alone.

A student being introduced to fractions will have a more thorough understanding of parts making up a whole if they are allowed to explore combinations of pattern blocks than they would simply by looking at a fraction and listening to the definitions of “numerator” and “denominator”.

Why Take Manipulatives Away?

If manipulatives are so beneficial to our students, why would we want to work towards taking them away?

The next time you are in the grocery store considering the cost of various products, you certainly won’t get out for base ten blocks to compare decimal numbers. You have an abstract level understanding of comparison of decimal numbers. You are able to look at these numbers and reason about them without the support of a hands-on tool or visual model.

This is what we want for our students as well! Unfortunately, this abstract level understanding isn’t always as straightforward as using math manipulatives for a period of time and then taking them away. So let’s talk about how to use math manipulatives in a way that ultimately, renders them unnecessary!

We need to work to help our students draw connections to this abstract level of understanding.

Setting The Stage to Move Away from Math Manipulatives

Before you ever take math manipulatives away, you are setting the stage for that to happen in the future. You can do this by LINKING your work with hands-on tools to representational models AND abstract numbers and equations.

Remember, you are building a web of understanding for your students. These linking experiences strengthen your web!

So, what does it look like to link to manipulatives? It can be simple!

• Build a number with base ten blocks AND THEN draw a place value drawing to match your manipulatives.
• Tell your students a simple put together story problem, ask them to model the problem using counting bears AND THEN write an addition equation to match the bears.
• Ask your students to cover a rectangle with tiles to find the area AND THEN ask your students to show draw a model of the same rectangle on graph paper.

In the future, when you are ready to take manipulatives away, your students already have tools such as place value drawings, equations and graph paper that they can use to solve problems.

How To Use Math Manipulatives With An Exit Strategy In Mind

When you think your students have a strong enough understanding of a math concept to leave math manipulatives behind, try this math activity that comes up often in my grade 1 and grade 2 math intervention units.

I call the activity “Work backward to progress forward”.

Present your students with a math problem. Essentially, your students are working backward relative to the CRA progression. This means we will have our students FIRST beginning with an abstract attempt to solve a given problem. Next, you will ask students to use a representative model such as a drawing or diagram to check their work. Do they agree with their original thinking or has their model caused them to adjust their solution? Finally, your students use math manipulatives to model the problem a final time. Again, they consider whether they agree with their original thinking or whether they might need to adjust their solution.

Why Does This Strategy Work?

It’s a twist on linking concrete, representational, and abstract together! Often we work forward with our students beginning with a concrete or representational model and then writing an equation or statement that matches their model.

This approach considers how to use math manipulatives in a supportive way to teach our students! But when it’s time to take the supports away, working backward forces our students to attempt the work at a higher level while still offering the supports as needed to check their understanding.