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.

## 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.

## Let’s See The Strategy In Action

Have you visited The Math Spot Strategy Library? It’s full of specific instructional sequences that support your students in understanding a wide variety of math skills!

Let’s take a look at the progression for 10 more and 10 less in the strategy library. Can you see the math strategy of “Working Backward to Progress Forward” in play on day 5?