What is the CRA Math Method?


Preparing for a new math unit doesn't stress me out. I start by looking at the standards, move to the assessment and from there I think CRA and the rest of the pieces fall into place. 

What is the CRA Math Method? 

CRA refers to the three levels of support or modes of communicating math ideas to students. You begin with concrete (hands-on & tangible materials), move to representational (drawings & visual models) and finish with the abstract (numbers & equations). 

When you introduce a new idea to your students, starting with the concrete allows your students to understand the idea more easily and completely than they would if you began with numbers and equations straight away. 

Starting with the concrete also ensures that more of your students will be able to access and explore the concepts you are teaching. 

How Do I Use the CRA Method?

If I had to name the two most important aspects of the CRA approach I would tend towards the fact that you NEED to link the three levels together and that you need to understand that the three "levels" aren't necessarily linear (more on that below)! 

To use the method to teach, for example, basic addition, I might start with linking cubes (concrete). In order to link the concrete to the representational, I would ask the students to "draw (representational) a picture with circles that matches your blocks".  

In order to link the concrete and the representational levels you will ask questions such as "Show me the part in the picture that matches your 3 blocks" "Can you tell me where the total is in your blocks? And where is that total in your picture?" You are quite literally asking questions that require your students to link their concrete model to their representational drawing. 

When you move ahead to abstract (the addition equation in this case) you will want to ask these linking questions again. 

The CRA Method is NOT Necessarily Linear

A powerful math activity will link the concrete, representational and abstract together. Moving back to the basic addition example, this would look like an activity where students choose two numeral cards and add them together by build linking cubes to match the numbers on their cards, drawing with circles on a whiteboard to match their cubes and to write a matching equation. 

If your students aren't ready for an activity with that many steps just yet there is no reason why you couldn't have your students build with blocks and write a matching equation (concrete & abstract) one day, have them build with blocks and draw a related picture (concrete and representational) another day and come back on a third occasion to ask students to add numbers using pictures and an equation (representational and abstract). 

While there is an order in terms of concrete being most supportive and abstract being least supportive, you don't (and shouldn't!) have to move strictly in a "one-at-a-time" linear fashion through the three levels. 

Anything Else I Need To Know? 

Yes! As you are asking your students to use a variety of hands-on materials and representations, remember that they aren't all created equally! Some concrete materials are more supportive than others and it is not at all wrong to use two or three different concrete materials to illuminate a concept. You can read more about how different hands-on materials lend different levels of support when teaching place value here

What Topics Can I Teach Using the CRA Math Method? 

So many! I will link a few blog posts here so you can see how the CRA method can be used to teach specific topics: