The transition from additive thinking to multiplicative thinking is very difficult and abstract for some kiddos. Think about it, for as long as they’ve been working with numbers, the number 2 has represented two *things*. Two ducks, two cookies, two linking cubes, etc. Now, with multiplication, 2 x 8 means 2 *groups of* 8. That’s huge. So, of course, it’s important that students get LOTS of concrete practice with the concept of multiplication–building 2 *groups of* 8. And then they should represent that same idea __by drawing it__ (The representational stage of __CRA__).

Once students have a strong understanding of the meaning of multiplication, we can extend that understanding by bringing in place value concepts and using multiples of 10. This is an essential understanding that must be in place *prior* to moving to multi-digit multiplication.

A great way to start this journey is with a version of Count Around the Circle from the book __Number Sense Routines__, by Jessica Shumway. Students sit or stand in a large circle. Start out skip-counting by a single digit number, for example 2. Go around the circle, and each student says the next multiple of 2–2, 4, 6, 8, 10, etc. Next, do the same routine with students counting by 20s instead. You want them to see that it’s the same pattern. Feel like a challenge? Try 200s. Make this a regular routine in your classroom. It’s a great way to practice multiplication facts and to stretch students to think about larger numbers.

Next it’s time to bring all of your CRA stages together. I created a little work mat with number cards that you can use for small group instruction.

Here I turned the factors around and had the student build (and draw) 20 x 8. Once the student has built the model with units, encourage him to group them into tens for easier counting. |

This photo shows the representations of 8 x 20 and 20 x 8. |

Here’s a shortcut way to draw representations of larger numbers. |

Ooh, what a great class challenge. Let students work in pairs to come up with as many solutions as possible! |

Ready to try it? Download the work mat and number cards __here__.

Anonymous says

Thank you for the multi mat & number cards… You have tons of fab ideas!

Donna Boucher says

Thanks so much!

Collaboration Cuties says

Wow, this is so great!!! I’ve been involved in a staff development already this summer that is all about concrete -> representational -> abstract and this is great to add to what I’ve been learning! I am going to have to check more of this out! Thank you for all of the links!

Amanda

Collaboration CutiesDonna Boucher says

CRA is so important, Amanda! Glad to hear it’s been included in your staff development.

A Classroom of Flowers says

Thank you very much for sharing your creativity! I’ll be using this activity in my Math Centre next year!

Donna Boucher says

My pleasure!

T Bell says

As a homeschooling Mum, I LOVE your explanations and products. Thanks so much for taking the time and effort to create such great blog posts, freebies and products; it is very much appreciated.

Donna Boucher says

So glad that you find my blog useful! Thanks so much for your sweet comment. 🙂

MK says

This is amazing! I just linked to this resource in my Pins of the Week post.

Thanks for sharing your great ideas!

Mary Kate

Windy City Learning

Anonymous says

Any suggestions for a student that always counts one extra when adding, subtracting,and even multiplying? We’ve tried to model “keep or in your heart” then count up but to no evail.