Having concrete and representational experiences are essential if students are to build a deep understanding of the four operations. For example, 3 + 4 looks completely different than 3 x 4. The shift from additive thinking to multiplicative thinking can be difficult for kiddos. Common Core makes the transition in 2nd grade as students use addition to find the total number of objects arranged in an array. In 3rd grade, students are expected to find whole-number products.
So, how can we help our kiddos develop strong mental images of addition and multiplication? Always present the concepts in the context of word problems, have students use manipulatives to act out the situations (concrete), and give them plenty of practice drawing models of the addition and multiplication situations (representational). Remember, models aren’t fancy art pictures…they’re simple models that focus on the math. Circles and squares can represent anything!
My I Have/Who Has game uses representations of both addition and multiplication. You can see it combines expressions (abstract) with models (representational). It’s a great whole class game, but you can also throw it in a workstation and just let the kids sequence the cards. The easiest way is to lay all the cards out face up (in an array…ha ha). Players start with any card, find the card that follows it, and the next one, etc. Make sure they are reading the cards out loud to bring in the communication component. If they do it right, they should end up with the card they started with.