Math Chat: Sense and Math-Ability
As the school bell rings and my students pack their bags, I often think about the ways that math education has changed since I was in their shoes. I remember struggling with word problems, just to figure out that Susan bought 432 watermelons at the store. When I would ask why she did this—was she pursuing a career in importing and exporting watermelons?—I was told, “it’s only a word problem. Just trust the math.” We were taught not to question it, so we didn’t.
Even now, when absurd questions like this are largely gone from our curricula, I still see students blindly trusting the math above all else and ignoring their innate reasoning. This relationship between “the math” and our reasoning is called number sense.
If you’ve read my previous articles, you know that I see huge disparities in my students’ math knowledge and confidence. They get so wrapped up in assigning personal identity—thinking that they can only be “good” or “bad” at math— that they forget all the math they do every day. This isn’t limited to teenagers, either. It’s a societal problem that affects adults too.
Take my friend prepping for math portion of the GRE. One word problem asked about the weight of bricks. She threw up her hands dejectedly and said, “I wish this used real measurements. I know a brick weighs five pounds, so why isn’t that correct?” I checked the answer key. Turns out, the answer was five pounds! By using more realistic numbers, we as teachers try to build a trust in your innate number sense. You can help your kid build that skill in tandem with their time in math class. And like any skill, practice makes progress.
The most obvious example of number sense is guessing how many jellybeans are in that giant glass jar at the library. But it’s often easier (and more fun) to build number sense through real-world instances in your everyday life. When we go shopping tomorrow, how many grapes should we buy? Making a multiple-choice game where some answers are obviously wrong is a good on-ramp. Should we buy 1 grape, 30 grapes, or 400 grapes? Like we discussed last week, we can add modifiers to change the outcome. What if these are grapes for giants, and just one will feed us for a month?
Playing the estimation game allows for so many possibilities, because you can ask kids to estimate just about anything. How many bread slices do we need for our PB&Js?
How many sand shovels will we need for our camping trip?
And how many more minutes do we think Papa will be in the bathroom?
How high do you think you can jump? Try it!
How long will it take to clean up the toys? I’ll time you!
How many toy cars do you think we have? (The answer to that last one is clearly infinite. I believe the couch is making them continuously.)
Yes, it can be silly, but also this is where that spatial reasoning and number sense come into play! As your kid grows, you can start introducing more practical real-world examples: You have $57, and you spend $18 on lunch. Will you have enough money left over to get ice cream for $8?
Soon, they’ll be able to ask the questions we grapple with as adults: Will I be over my monthly budget if I buy this IKEA couch? Will it fit in my car, or do I need to rent a truck? Or is it worth my time and energy to try to find a used one instead? Don’t wonder in your own mind, ask out loud! Your kids might get in on these questions, too, but in their own way (“what if we got a bouncy castle instead?”)
Sure, we can calculate. But more importantly, can we estimate?
By treating estimation and number sense like a fun game, you’re building math skills for the future. So start small with a few easy estimations, and know that someday you’ll have a math whiz ready to estimate the jellybeans in the giant jar or deciding where the couch will fit. Remember, being close to right is better than accidentally becoming a watermelon exporter.
Happy guesstimating!
