Multiplication and Division Fact Families

My third graders have been working on multiplication and division for months!  First, we focused on understanding what multiplication is.  After the conceptual understanding was in place, we began to memorize our facts so that we can use them with fluency.  (For my blog post about this, click HERE.)  

We have now moved on to division in our lessons, but will continue to do timed tests and memorization for a few more weeks.  About a third of the class has completed their ice cream sundaes (See the picture below; they have memorized their facts through the twelves), and moved on to division timed tests. 

Yesterday, one of my students came to me before the timed test and said, "I don't know how to do the division threes."  She had just passed the ones and twos, but was completely convinced that she did not know the answer to the threes.  (Remember, she had learned ALL of her multiplication facts through the twelves!)  

We were in our first week back from Christmas vacation, during which each student completed review homework that looked like this (including a page for each set of fact families from the ones through the twelves):

We went to check her homework, and she had completed the whole thing.  Perfectly.  All twelve pages.  We talked about the idea that if you know your multiplication facts, you know your division facts, also.  This is because they are in the same fact family.  I could not get her to believe me until I showed her the division sentences that she had written!  Her "light bulb moment" was a joy to see.  Her smile lit up the room when she realized that she already knew every answer.

Sometimes I assume that students understand the big picture behind something, because they are able to do the specific task that I assign.  But how do I know for sure?  I guess I actually have to talk to them.  Individually.  If she hadn't approached me to let me know her dilemma, I would not have known there was a problem.  It's also possible that they might forget what something means.  After all, I forget things all the time!!  (Where did I put my keys?)

I'm a little embarrassed to admit all of this... sometimes I focus so much on the students who are obviously struggling that I don't see what's happening with my "on grade level" kids.  When I pull a small group to work with, these kids are usually not part of it.  So here's a resolution for the new year: I will try to meet with each student individually, once per week, to talk about where they are in their math journey.  (It seems much easier to do this for language arts, between reading with students and doing fluency testing, etc.) 

This week, I plan to show each student their completed fact family practice book and ask for an explanation of how it works.  It should be interesting!

If you are interested in my Multiplication and Division Fact Family Practice Pack, you can find it in my TpT store.

Happy Teaching with Fact Families,