Weekly Questions #1

Here's a feature that I'll run each week where you can work together with your child to solve a math problem. If you find it's too easy or that it goes too quickly, find a different way to come up with an answer. And another. And another! Sometimes it's easy to solve a problem, but you can extend your understanding by forcing yourself to think outside the box and into a space that might be a little less comfortable. Good luck and have fun!

Primary (1-3)

Tim, Craig, and Kinnon made 114 snowballs, but they dropped 15 of them on the way back to the fort. They used 55 in the great battle. How many snowballs did they have at the end?

Junior (4-6)

Is it better to receive $300 a week or to be paid hourly at a rate of $7.50 per hour. What factors could affect your decision?

Intermediate (7-8)

Cheryl has three pairs of shorts and five coordinating shirts. How many days can Cheryl wear a different combination of shirts and shorts?

Multiplication Methods

Before we start, do this question (at least go through the motions in your head):

45 x 23

Did you line them up first so the four was above the two and the five was above the three? Then did 3 x 5, then 3 x 4, then dropped to the next line and wrote a 0, then continued to multiply the rest then added 135 to 900 to get your answer, right? That's how most adults today learned to multiply a two-digit number by another two-digit number. Easy. Now... can you explain the mathematics involved in doing that? What happened to make that work?

Think of it another way.

You know that that 45 can be shown as tens and ones: 40 and 5. 23 can be shown as 20 and 3.

If we divide them up first into their tens and ones, we can multiply them separately, then add them back up later. Often as adults we attack things in bits at a time instead of doing it all at once, so let's do that now.

40 x 20 =  800
40 x 3 = 120
5 x 20 =  100
5 x 3 = 15

If we add 800 + 120 + 100 + 15, we get 1035, which is the same answer we got above.

Does it make more sense to look at it this way? Think of it in terms of groups of items if it doesn't. Think about 40 chocolates or 40 marbles.

If your child is having trouble with multiplication, try to show them this method of multiplication. Same results, different way of getting to the answer.

Math Mindset

One thing that I have always found interesting is the hesitancy many people have to get involved with math, but many people do have "math anxiety"! If you (as an adult) think back to grade school, I'll bet that there's quite a few that would agree with feeling uncomfortable with math as well.

Some students are incredibly hesitant and frustrated with math. They can be fine with language, fine with social studies, etc., but math can be terrifying for a good percentage of kids. I want to put forward that part of the reason could be that they are sometimes used to following the steps to solving a problem without actually understanding what is going on mathematically.

There's a big difference between "doing arithmetic" and "doing mathematics". Compare them as "going through the motions" vs. "understanding what you're doing". When I was in school (and likely you had the same experience), we were taught one way, and repetition and rote memorization of math facts were the way to go. It worked, and I think this way still has a place, but by deepening students' understanding it stays with them, because it makes more sense.

For example, which of these two sets of questions promotes a deeper understanding?


Set 1



Set 2

23 + __ + 1 = 25

__ + 3 + __ = 1

12 + 2 + 2 + 2 + 2 + 2 =


For Set 1, even if you don't 'get' the process of adding up ones and tens, you can line them up and do it because you've seen it done.

For Set 2 however, the learner is given the opportunity to explore different options. If they want to line up the numbers and add, they can do so. If they want to use mental math, they can do that. They can work backwards and find answers through subtraction and they can look for patterns to help them solve the problem. In having those options available to them, students can look at the relationships between the numbers in the sentence to use those skills (addition, subtraction, patterning, etc.) and understand that doing simple addition doesn't exist in a vacuum

Students need to understand what they’re doing. I'll show more examples in posts to come.

Blog Start!

Something that has come up again and again in my own reflection in teaching practice is how little time we take to share the great things we're doing with other people, whether it be other teachers or parents. As an educator, I am always looking for new and interesting ways to effectively pass on information to students, but it's tough to stop and talk sometimes when there's always so much going on at school.

This blog will be primarily for parents, but with any luck it'll be useful for teachers as well. My hope is to show the difference between "old math and new math", giving authentic examples and solutions from classes at Lawfield Elementary in Hamilton, Ontario. I'll also make sure to share math puzzles and problems on the site that parents can share with their children. Post the answers you come up with together!

I hope you find it interesting and can use the information to help guide your kids towards math thinking at home, and I hope that I can share some ideas with other educators. Talk about what you see with your colleagues! Discussion amongst teachers is what puts true value to a strategy.

Don't be afraid to think about math in new ways, and if you have anything to share, please post to comments.

You're going to see a rush of new posts and information as I get things started around here!

Thanks for reading!