Multiplication is a wondrous thing, unless you’re the child who only gets through the first row of problems on your time-test while your classmates finish the whole sheet.

In my class this child was Andrew. I knew he was learning, but it didn’t show on the timed-tests. I was confused, looking for answers, and wanted Andrew to succeed. As I searched the research I found out something startling. I hadn’t been teaching multiplication. I had been testing it. That’s went I set out to make multiplication meaningful in my classroom.

Somehow within the American education system time-tests have become the overwhelmingly favorite teaching method for multiplication facts. This is is how I learned them and I wouldn’t be surprised if you learned them this way too. Unfortunately, time-TESTS are assessments, not teaching strategies and they often do more harm than good. The key to introducing students to meaningful multiplication is to practice through experiences.

Find the magic in meaningful multiplication by following these 4 steps:

  1. Create a meaningful scenario
  2. Let your students grapple with it
  3. Have a discussion
  4. Introduce the “groups of” strategy

Think about the instances in your life when you need multiplication. Usually we need multiplication when we are considering groups of items. For instance, if you have three iPads in your classroom, a teacher on your team has three in her classroom, and another teacher on your team has three, how many iPads do you have access to? (Assuming you are on a friendly teaching team and they agree to share).

How did you think about this scenario? Did you add 3 + 3+ 3? Did you multiply 3 X 3? Did you skip count 3, 6, 9? Did you visualize the iPads in each room and count 9? There are many ways to come to correct solution. Teaching students to multiply means leading them to the strategy of multiplying 3 x 3, because in most cases it is the most efficient. This is much different than beginning to have students memorize their multiplication facts because, “they’ll need them in fourth grade.”

1. Create a Meaningful Scenario

The first step to introducing students to multiplication is giving them a meaningful scenario (like the iPads). When we multiply we are simply looking at “groups of” items in different quantities. The scenarios are endless. Here is an example:

This fall Jill, Kole, and Liv went on a nature walk to collect interesting leaves. When they got back to Jill’s house they dumped out their bags and compared their finds. Jill discovered that she had 5 red leave. Kole looked at his and also had 5 red leaves. When Liv looked at her leaves she also had 5. They decided this was because they had visited the same areas and gotten similar types of leaves. How many read leaves did they get all together?

2. Let students grapple with the scenario.

Some students will have the answer right away and some will need a minute to think. This will depend on the strategy they choose in order to solve the problem. Give students a minute to think. Then prompt them to think about the strategy they used to get their answer. After waiting a sufficient amount of time give the students the correct answer. This takes the pressure off of those who choose to share. They can’t get the wrong answer and the discussion can more easily center on the strategies instead of answer-finding.

3. Have a discussion.

At this point, ask students to turn to a partner and share their strategy. If this is the first time you’ve tried this be prepared for students to have very short conversations or to use this time to talk about everything but their strategies. As long as you monitor this sharing step, it makes each student accountable to think and begin to talk about mathematics. After students have shared with a partner I ask, “Who has a strategy of their own, or a strategy their partner shared, that they would like to share with the class?” This gives those who couldn’t verbalize a strategy (or hadn’t thought of one) a chance to share along with those who came up with a great strategy themselves. As students share strategies record them on the board and revoice them… “Oh, so you’re saying that you added Jill’s leaves, to Kole’s leave, to Liv’s leaves to come up with 15? That will work! Would that look like this? 5 + 5 + 5.” Acknowledge all of the strategies that do work and question/discuss those that don’t.

4. Introduce the “groups of” strategy.

You’re bound to have a student who says, “I saw that there were three 5s and I added them up.” This is your ticket to teaching the “groups of” strategy! To this you reply, “Oh. So you saw that there were 3 groups of 5? What did you do with those groups?” At this point students usually bring up that you can add all the 5s together or that you can skip count by 5s. Hooray! At this point you can introduce the notation. I would write these lines on the board.

3 X 5

3 “groups of” 5

I tell my students that the “x” stands for “groups of.” Mathematicians use this notation because it is the most efficient (the fastest and most accurate way) of writing “3 groups of 5.” We then all write  3 X 5 = 15. I usually then ask, so what would happen if I only had 2 groups of 5? We discuss and end up with the notation 2 X 5 = 10.

From here the discussion can circle back around to step 1 of this introductory process. Students need many, many, many opportunities to work their way through scenarios like this, to think about their strategies, and to come up with the efficient notation. A great way to get this practice in is to have a multiplication mania day (or week). See our next blog post for details about this meaningful multiplication activity.

There are also many modules dedicated to multiplication within the Elementary Mathematics Teachers Academy. Come select the modules you are interested in and we’ll package these into a custom course and give you Master’s credit for completing it.