Recently, I surveyed more than 20,000 teachers about their biggest challenge in math instruction. One of the most overwhelming responses was that their students don’t know their math facts. I have to agree that a lack of math fact understanding and memorization is an area of concern for me as well. This issue is a not a new trend. Math facts, especially multiplication facts, have been a hot topic since I was in elementary school. I still remember taking “mad minute” tests as a child where we had to solve a certain number of problems in one minute.
We now know that teaching strategies through games and hands-on activities are more beneficial that repetitive drill. But it’s essential that the games and activities you use are intentional and follow a specific framework. To help me stay focused and intentional, I’ve created a series of systematic lessons and activities students can use to memorize and understand multiplication fact practice. You can find those lessons here.
The first step for students is to SEE the different representations of the math facts. For example in multiplication, students sort arrays, repeated addition, and equations. This allows students to begin understanding what the multiplication number sentence means.
After students sort multiplication representations, they should then progress to leveled flashcards. At this point, students aren’t ready for traditional abstract flashcard practice. Instead, students should begin with the set of Build-It flashcards. In this set, students will actually build each multiplication problem. They could use counters or snap cubes for this activity. After students have concrete experience, they can then use pictorial models of each multiplication problem as a flashcard. This pictorial model helps bridge concrete and abstract. Then, in the third set of flashcards, students can try to answer the multiplication problem using an abstract strategy.
Multiplication Strategies Booklet
Students should also have the opportunity to WRITE about the strategies they use to solve each set of multiplication problems. This allows students to internalize their learning. For each set of facts, students describe a strategy they could use to solve a multiplication problem. If I have a student who has already worked their way to automaticity in that set of problems, I ask students to explain to a friend how to use a strategy. Students also represent problems using arrays, repeated addition, grouping models, and a number line.
It’s so important to teach in context, so for each set of facts that students work though, be sure to have them solve AND write multiplication word problems, which is another reason it’s so important to have students write about the strategies they use. For example, if students are working on their four facts they will solve two problems where four is a factor and write two problems where four is a factor.
While I do believe that timed tests can be misused, they can also play a positive role in the classroom. Rather than giving students a certain amount of problems to solve in a set amount of time, I have students solve the entire set of multiplication problems and time how long it took to complete all of the problems. This alleviates the extra stress that comes with a timed test. I also have students graph how long it took to complete the test to encourage metacognition. I staple multiple versions of the set of facts to the timed test graphing sheet to give students four different opportunities to take the test.
To help keep my students organized with each of these activities, I give them color coded bookmarks. The bookmarks show what is expected from students each week. The activities are listed in the order in which they should be completed. As students complete an activity, they check it off on the day it was completed. You can see these activities here!
I did add a few extras at the bottom of each bookmark, because these are things we do weekly, if not daily. I send home a Weekly Multiplication Game with students every Monday. These games only require dice or a set of playing cards, which I provide if students don’t have at home. This isn’t an assignment to be graded. Instead, it’s an opportunity for fun practice.
I also give students who need additional support a Multiplication Fact Booklet that will take them through each multiplication problem for that set of multiplication facts. This gives students the extra support they may need and it solidifies understanding.
Xtra Math is another great practice tool. However, it’s important to keep in mind that it is a tool. Nothing replaces the conceptual activities where students actually work with multiplication facts.