Memorizing multiplication tables is one of those walls in math. Kids either scale it or struggle with it, and if you’re a kid who struggles with it, it will become the thing that holds you back even though you may understand the higher order math processes that you learn later. Some people brush this struggle off thinking that calculators have made knowing multiplication facts obsolete, but that’s a mistake. Automaticity (the ability to quickly retrieve information) is important. In practical terms, you’re simply not always going to have the time or desire to locate your calculator for quick estimations in your daily activities. In critical thinking terms, the ability to manipulate numbers in your head is a skill that supports flexible thinking and overall numeracy. Strategies for manipulating numbers in your head can be taught.
But can it be fun, too? Of course one person’s fun is another person’s homework. In an effort to find a fun way to practice math facts with my 10-year-old tutoring client, I made up a “game” that engaged her and challenged her and encouraged her to notice some strategies for manipulating numbers.
The materials: The only things you need for this activity are a handful of dice, something to write with, and something to write on. I pulled out my trusty whiteboard and some fresh Expo markers because I know that my client loves them. (Never underestimate the importance of your materials. A kid who falls asleep while writing on white-lined paper with a blue pen might just become a great poet when she is given colored gel pens and black paper!)
The rules: Roll the dice. Using any of the operations your child is familiar with (addition, subtraction, multiplication, division…but you could also try exponents and such as your child is exposed to them) to make the largest or smallest number possible.
The tips: Start out with just two dice, then move to three when your child is ready for more challenge. Play the game along with your child to see if you get the same answers. Show your work so that your child can see your thinking. (That is as simple as writing 2 + 3 + 4 = 9 rather than just 9.) If your son decides he’d rather draw pictures with the Expo markers, so be it. If your daughter demonstrates that she’s solid with her addition and multiplication skills, blow her mind a little by exposing her to exponents. (Rather than 2 x 6 = 12, get a bigger number with 2^6 = 64.) But let’s back up from exponents…because you will notice that usually the best way to get the largest number is to multiply rather than add. Your child, however, may struggle with multiplying a series of numbers like 2 x 4 x 6. This is where you can point out some strategies…
- You can multiply in any order you want, so pick the order that is easiest for you. If you can’t easily remember what 8 x 6 is, perhaps you’re more comfortable with 2 x 24.
- If you are stuck with 8 x 6, you can play with those numbers to find an answer. Cut the 8 in half and double the 6 to get 4 x 12. Still stuck? Cut the 4 in half and doublt the 12 to get 2 x 24. Does this make it easier to find 48? Noticing those opportunities is an important part of math.
- If your child is adding numbers and gets stuck at 6 + 6, demonstrate how to “make ten.” I say something like, “I wish I were adding a number to 10 instead of 6 because that is so much easier for me. I’m going to make the first 6 be 10 by taking 4 from the other 6. Great! That gives me 10, but now the other 6 became a 2. Now I’m adding 10 + 2. That is so much easier for me!”
Colorful dice and fresh markers on whiteboard are just lures to draw a kid into enjoying number play. It may work for your kid. It may not. If you are very comfortable with math, feel free to show your child new ideas and invent other ways to play with the dice. Resist the urge, however, to force your child to understand what you understand. Instead, guide and coach a little bit, and pay a lot of attention to the cues you are getting from your kid. (For example, when I first threw out exponents as a possibility, my son did not show any interest in it. He was totally absorbed in some other idea he was thinking about. I didn’t push it. We rolled the dice again, and when I used exponents again, he turned his attention to wondering whether it mattered how I ordered the exponents…2^6 versus 6^2. An interesting question. Something I wouldn’t have focused on if I had been concerned about forcing him to understand exponents before he was interested.)
Mathematically speaking…While this activity could go in a lot of different directions, the primary math goal is to practice mental flexibility with numerical manipulation. These are just fancy words for the act of deciding whether you should add 2 + 4 + 6 or multiply 2 x 4 x 6 to get the largest value. And once you decide to multiply, it’s about figuring out a strategy for getting the actual answer. Do you see the possibility of multiplying 8 x 6 or 2 x 24 or 12 x 4? Do you need to draw something to get the answer? Do you need to count on your fingers? Also, after you’ve rolled the dice for a while, you’ll notice (and your kid will, too) that rolling a 1 changes the decision of whether to add or multiply to get the largest number. Neat-o.