When I was a child, math was my favorite subject and as a parent now I'm always looking for ways to share my love for math with my kids. While my daughter loves to read and play games that spurred her imagination, I found it harder to engage her with math problems.
She loves spending time singing "Let it Go," dressing up like Queen Elsa, and hearing made up stories about Elsa, Anna and their adventures. I wondered if I could make math just as imaginative, exciting, and creative as the things she already loves to do.
One day, my daughter asked me how she can have ice powers. Somewhere, a light bulb went off. "Aha!" I said, "that takes a lot of time, and you have to practice a lot to get these powers -- and you first need math powers to make ice." We pulled up Google images and searched for ice crystals. I showed her how ice is made of crystals that have special shapes. In order to get the right shapes into the crystals, she needs math powers.
It has been a few months now, and she is on the quest to get math powers so that one day she will be able to make ice out of vapor. We came up with a few games to play, and one of the rules we established was that she can't guess the answer. If she tries to guess, sometimes we will decide that maybe we aren't in the mood to play this game and move on to something else.
Here are the five games we made up to easily do mental math while in the car, at home, or while going for a walk.
1. Series: What comes next?
Starting with the basic counting (1,2,3,4,5..), I will make up different series and ask her what comes next. E.g., I'd skip a number (2,4,6,8,10,..) or count backwards, or skip multiple numbers (e.g., 4,8,12,16,..). She's starting to warm up to these, and I can see her recognizing patterns and figuring out the right answers. I expect this game to lead into multiplication tables eventually, but right now it's a little too early. What I find more interesting is that she is recognizing patterns in numbers and matching them.
If she gets a little overwhelmed, I'll weave in a story about the characters from Frozen -- e.g., when Elsa was young, she could only make snowflakes that had 2, 4 or 6 branches, because she didn't know what came after 6 in that series. And I'll ask my daughter if she can help Elsa figure it out? Suddenly, she'll engage and will want to figure out the solution by herself.
2. Arithmetic with twists
We do arithmetic questions all the time -- addition, subtraction, and even fractions at times. Our games are almost always verbal, and she uses her fingers as the visual aid. Starting out, she didn't know what "plus" or "minus" meant, so we always talked in terms of concrete examples (e.g., if you have 2 snowflakes, and I gave you 5 more, how many will you have?). I'd often relate it to "plus" or "minus" so that she starts to get the more abstract concept of these operations. ("See, that's 2 + 5, which is 7").
As she started being more comfortable with small additions and using operators, I started to ask her questions where one of the operands was a larger number, e.g., 22 + 3. If I asked her 2 + 3, she would often count to 2 and then count 3 more to get the number. But because 22 was a bit daunting to count to, she quickly started "conserving" numbers and just started with 22 and counted from it. So, she will start at 22, and count upwards from it.
3. If (a+b)=c then what is ...
One aspect I love exploring with my daughter is to see if there are concepts that are obvious to me but may not be obvious to her. It can reveal how tough it might be for them to pick up on mental math. For example, I asked my daughter one day: if 3 + 4 is 7, how much is 4 + 3? As I was asking her this question, I realized she may not find it as obvious as I do. And she didn't. But it led to a fun conversation about numbers and how it doesn't matter in what order you add them. And I am looking forward to have the same conversation about the minus operator -- and how it doesn't work the same way!
Another similar exercise we play is to help her think about breaking down harder problems into easier ones. A common question I ask her is, if 5 + 6 is 11, how much is 5 + 7? Sometimes I have to help her and explain what I did, and we keep going and build it up to as much as 9 + 9. In the process, I can see her suddenly burst out with joy when she realizes that she can figure out the answer to 9 + 8 in the context of 9 + 7 being available to her, so it really isn't that hard after all!
4. Odd one out -- and using it for numbers
This remains a favorite game of ours. This helps her classify things and find the one that doesn't fit -- and we can play this for 10-15 minutes on end without getting tired. I recently started using it in the context of numbers and other math concepts. E.g., I would ask her to pick the odd one out from 1,2,3,5,7, or 10,20,30,40,15. It often leads to fun conversations about numbers. And because it's number powers that will one day help her make ice, she's fully engaged!
One time, we brought up the odd one out between square, rectangle, triangle and circle. She could figure out that it was a circle that's different, but she couldn't articulate why. So we took a piece of paper and started drawing them, and I showed her how when two straight lines cross, they make angles. And circle doesn't have sides or angles but the others do. And guess what, snowflakes and ice crystals have shapes with angles too!
To my delight, it stuck with her, and when we talked about angles a few weeks later, she remembered what angles were and talked about shapes in reference to angles (e.g., a triangle has three angles).
5. Clue: If x and y, then...
This is a game we started playing recently and challenges her analytical reasoning. I'd ask her, for example, if Queen Elsa is older than Prince Hans, and Hans is older than Princess Anna, who is the oldest of them? We use age, items, and other attributes but always keeping it to the question of using two inputs to infer a bigger truth. At times when I'd use her friends' names, the conversation can get quite amusing -- she'll reason why she thinks Alice is older even if it is contrary to my statements.
In all of our questions, though we celebrate figuring out the right answer, I am more keen to engage her and have her think. Even if the answer is wrong, if she is trying to figure it out, I feel rewarded. And if that means I invoke Queen Elsa's ice powers, then so be it!