In my previous post (Link), I shared how I’ve recently starting doing math with my daughter to help her get warmed up for the start of 4th grade. In that post I talked about how I’m using the centers from the Illustrative Mathematics K-5 curriculum (Link) to revisit and practice working with multiplication and arrays.
In the six and half years I worked as a district math curriculum coordinator, a common concern I heard from 4th and 5th grade teachers is that their students don’t come in knowing their multiplication facts. I can attest that my daughter learned a lot about multiplication and division in 3rd grade, but I’ll be honest, she hasn’t done a whole lot of multiplying or dividing this summer (not to mention fluency is something that tends to develop over a period of years, not months). It comes as absolutely no surprise to me that she’s rusty, particularly with knowing her multiplication facts. I’m going to go out on a limb and claim that a lot of kids are rusty at the start of a new school year. We need to give them grace, which means not saying things like, “Didn’t your teacher teach this last year?” We also need to intentionally build in opportunities to practice and dust off the mental cobwebs.
Today I’d like to share how my daughter and I have been practicing multiplication facts. What I like about what we’re doing is that (1) it only takes a few minutes a day, (2) it reinforces flexible use of strategies, and (3) it gives her a second chance everyday. I got this idea from a free math intervention called Pirate Math Equation Quest (Link), developed by Dr. Katherine Berry and Dr. Sarah Powell from the Meadows Center (Link) at The University of Texas at Austin. Their intervention includes a component called Math Fact Flaschards that goes like this:
- Student completes two trials of Math Fact Flashcards, each for 1 minute
- Teacher and student count cards after each timing
- Teacher monitors and provides feedback as needed
- After 2 trials, student graphs the higher score
Rather than use traditional flashcards, I created flashcards that show two facts per card, the initial fact and its turnaround. For example, the card with 2 × 5 also shows 5 × 2. I got this idea from the 4th grade Investigations 2nd edition curriculum. It reinforces the idea that every time you know the answer for one fact, you really know the answer for two (with the exception of square numbers).
Before we start a trial, I always remind her that she is going to “just know” some of the facts because she’s so familiar with them, but for the ones she doesn’t “just know” she can use one of the multiplication strategies she’s learned. The following poster is hanging on the wall next to where she’s sitting so she can turn and reference it as needed.
These are the thinking strategies developed by Origo Education (Link). If you’re not familiar with them, check out this YouTube playlist that includes one-minute videos explaining each strategy. (Link) If you want to see how a child uses one of the strategies, here’s a link to a short video of my daughter talking through the Build Down strategy she used to solve 9 × 7. (Link)
Please note, you can’t just throw strategies at your students. They have to be intentionally introduced and practiced, but it is well worth the time! Students who lack a robust toolbox of strategies have to rely solely on memorization (which is a big ask!) or inefficient strategies like skip counting. If you’re interested in learning more about how to teach these strategies, Origo has a great series called The Book of Facts that shares activities and games for teaching a set of fact strategies for each of the four operations. (Link)
During each trial, I present the flashcards one at a time. I put all of the ones she answers correctly in a pile and any she answers incorrectly in another pile. After the minute is over, she counts the number correct, and then we discuss the ones she answered incorrectly. Sometimes her incorrect answers are because of a simple mistake, and I reinforce that it’s fine because she has been able to recognize the error herself. However, sometimes it’s more than a simple error. I was able to pick up very quickly that she’s also rusty with doubling 2-digit numbers that involve bridging a ten. For example, to solve 4 × 7, she can easily double 7 to get 14 and double 14 to get 28. However, to solve 4 × 8, she can easily double 8 to get 16 but she gets stuck doubling 16. Her answer might be 26 or 36.
Based on this observation, I’ve added in practice with doubling 2-digit numbers. This practice is untimed for now, though I might eventually add these cards into the deck of multiplication flashcards.
At the end of the two trials, we graph her higher score for the day. I really love this because if she blows the first trial for whatever reason, she knows she’s going to get a second chance to get a higher score. It really takes the pressure off.
We’ve only been doing it for a week, so there’s not a lot of data to look at, but I’ve already used her graph to talk about how we all have good days and better days. I also reinforce that while some days are lower, her rate of incorrect responses is consistently low. She only ever misses 0, 1, or rarely 2 cards during a trial. She’s also been really good about stopping and thinking of an appropriate strategy whenever she gets stuck, and she is doing a great job of executing her chosen strategy accurately.
For full transparency, her deck of flashcards includes all of the facts including the “easy” ones like 0s and 1s facts, and I’m okay with that. They’re still facts and she needs to know them. The important thing is that I continue to monitor to uncover any issues where I can support her, like with doubling 2-digit numbers. Eventually I might ween the deck down to the ones that need more intensive practice.
I like that this practice doesn’t take a lot of time, only about 3-5 minutes. If you’d like to try this out in your classroom, you might consider doing it in small groups, which is an idea shared in the Pirate Math Equation Quest intervention I mentioned earlier. During the one-minute trial, the teacher goes around the group round robin style, showing one flashcard to each student. All of the flashcards are placed in one pile and the total correct is the group’s score. The goal as a group is to try to get more and more correct each time. I like that this allows for a bit of a tradeoff. The teacher doesn’t have to feel pressured to run this activity individually with every student, but at the same time, she can learn something about each student as she conducts these trials in small groups. I’m doing this with my daughter everyday, but a teacher might be able to make small groups such that she ends up seeing every student every 3-4 days.
As I was reading over the small group directions, I realized they recommend letting the student continue trying until they get the answer correct. If the student answers incorrectly, the teacher intervenes with a suggestion such as a strategy a student might use. I think I might try that with my daughter rather than setting aside incorrect answers. Helping in the moment seems much more powerful than helping at the end. It also does a better job of validating the power of identifying and correcting mistakes. I like forward to seeing how it goes next week!