# Using a MathPlay Approach for 3rd Grade Multiplication

During my elementary school years in Colombia, I vividly remember memorizing the multiplication tables while constantly being tested on them by my father. My dad kept emphasizing that I needed to memorize them for the upcoming topics and grade levels. As a kid, I felt there was a sense of urgency in knowing the multiplication tables by heart. My father would have me write pages after pages of each table, then he would ask me each one at a time in order and then out of order. Finally, he would do a rapid fire of questions expecting an “almost” immediate response. I believe that’s how my dad learned, and although it was stressful, his method was effective, and I did in fact memorize the multiplication tables.

Last year in 2023, my older daughter started third grade. I was so excited about “officially” exploring multiplication with her. As her father and an educator, I want her to learn her multiplication tables without making it a stressful experience. Personally, I found value in all the drills and repetition as it helped me build endurance and a sense of accomplishment. At the same time, I want my daughter to enjoy learning and not be afraid to make mistakes. So, what do we do? Do we use a traditional approach? Or a more student-centered approach? To be honest, we ended up using a combination of both. My daughter still writes out the multiplication tables, as I believe it does help her convert it to memory. Once she’s done with that, it’s time to do the rapid questions. However, we take turns asking the questions. She usually quizzes me first while looking at the times tables to make sure I don’t make any mistakes (sometimes I do, with purpose). Then, I ask her the questions and we repeat this process a few times.

My rationale to take turns is to make it a more user-friendly experience and to take off some of the pressure. In all honesty, she does not seem to be overly stressed while we practice and study, which makes the learning process fun and inviting. In addition to the drills and rapid questioning, we also implemented three MathPlay components to our multiplication review sessions: visualizing, playing, and making connections.

#### Visual Multiplication

When I ask my daughter, “What is multiplication?” She quickly recalls the definition she was given in school, “It’s repeated addition dad.”If I then ask her to give me an example, she is comfortable using something like 4 x 5, or “four groups of five which equals twenty.” I believe she understands what multiplication is, but I wanted to make the concept more concrete and relatable for my nine-year-old mathematician.

While we were practicing in our basement (a.k.a. MathPlay headquarters), we started playing with shapes. In my experience, using manipulatives can have a positive impact on how students understand mathematical ideas regardless of age/grade level. We started with a basic question like, “How many sides/corners are in a triangle?” Then we expanded the question while adding more triangles. She quickly noticed it was like the multiplication table for three and the idea of repeated addition became a more tangible idea.

I believe our approach of using shapes really helped her visualize multiplication and it also made it a more concrete and enjoyable experience. Below is one of the later questions she tried involving hexagons.

#### MathPlay Activities

The idea of MathPlay for me started with my daughter before she officially started school. Over the years, it has continued to grow and develop to the point that now she expects a MathPlay activity on whatever topic she’s learning in school. During the December winter break, we found ourselves reviewing for an upcoming test on the multiplication tables from 1 to 6. It was a fantastic opportunity for a multiplication dice game. Once again, using our little whiteboards we drew two big circles placing a multiplication symbol right in between them. Mariana used the red die while I used the green one. We then both rolled within our circle, and she then had to write the product of the two numbers.

It was a simple game, but we were both very engaged. I also enjoyed that the numbers were truly generated randomly. When I ask her a question (during our rapid fire), I tend to ask the question(s) I consider more difficult many more times. The dice game was a great way to boost her confidence with the times tables up to six.

#### Making Mathematical Connections

As my daughter became more and more comfortable with the times tables up to 6, I felt it was time to make deeper connections. Using counters, we started building “perfect squares.” Then we counted the total number of counters we used: 1 x 1, 2 x 2, 3 x 3, 4 x 4, 5 x 5, and 6 x 6. We noticed how 1, 4, 9, 16, 25, and 36 created perfect squares. It was such a natural and organic progression of ideas.

We then started looking for manipulatives in our basement that we could use to represent these perfect squares. After exploring together and having some meaningful conversations, this is the pattern of perfect squares we came up with:

I really hope you find these ideas helpful and can use them with your students or children in the future. I would love to learn what other math play ideas you are using for multiplication. What was your experience like? How did your students respond? What was the level of engagement like?

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