I recently visited a 3rd grade class to share with the teacher ideas for teaching multiplication facts. She was particularly frustrated that her students were struggling with the larger facts – the sixes, sevens, eights, and nines. It was clear that while students had experience connecting multiplication with the idea of equal groups, students did not have many strategies for deriving the product of an unfamiliar number fact. Essentially, students only skip counted every time.

It seemed like I needed to share some additional strategies for deriving the product.

I began with the distributive property and the idea of breaking a “big” unknown multiplication fact into smaller known facts.

We started by remembering that multiplication means equal groups.

This meaning of multiplication leads to repeated addition, which leads us to the distributive property…

Here is the same image with color coding…

Eventually, students were able to imagine the repeated addition in their head and go straight to writing the fact with the distributive property.

A SECOND STRATEGY

We then moved to the second strategy: area model.

While the model is different, the conversation ended up being very similar. Students saw the distributive property lurking inside the rectangle.

FRAYER MODEL

As an ongoing routine, I shared with the teacher the Frayer model. Students folded a piece of paper into the “diamond paper”.

Then we placed a multiplication fact in the middle. Let’s say it is 7 x 6. Each quadrant serves a purpose…

Students had some SERIOUS trouble writing a story problem for 7 x 6. For 7×6, we would expect something along the lines of “There are seven girls in line. Each girl has 6 dollars. How much money do they have in all?”. Instead, students were writing addition questions like “I have 7 toys…and then Joe shows up with 6 more toys. How many toys do we have in all?” This really hit home that students spent their year trying to memorize multiplication facts rather than understanding what multiplication MEANS.

I suggest 3rd grade teachers begin Day 1 of school with the Frayer model to represent multiplication facts. Start with something small like 2 x 3. As various representations of multiplication are taught, the teacher should expect to see those representations show up in the Frayer models students are creating. Over time, students will REMEMBER all their facts…not memorize them.