This site is called Everywhere Math, because we love finding and doing math, truly, everywhere! These days, we see a lot of math in the place closest to us: home. Home is where the children in our family — like the children in so many families right now — are doing school every day.
I’ve been challenged while working with my fourth grader, even when he’s been assigned work from the math curriculum I played an instrumental role in creating! This past week, the fourth graders were working on different strategies for adding and subtracting multi-digit numbers, including the standard algorithm (i.e., carrying for addition or borrowing for subtraction). Computation-focused work can be valuable, but my son struggled to stick with it, and he much prefers to compute mentally than to show his work, much to my chagrin!
So I came up with some ways to pare down the number of problems he did each day, while also stretching his number sense and increasing the level of challenge at the same time. Let’s call this approach "making more with less" … "lemons out of lemonade" … pick your turn of phrase. Basically, I know I have at most 10 good minutes of work time with my child, and I need to make every one of those minutes count.
Below are some of the questions I asked this week to focus his attention in a mathematically powerful way and elicit the evidence I know his teacher needs, while she gets to know her students from a distance.
"From the remaining problems, select only those that have a sum (total) less than 1,500. How can you know for sure before solving them that the sum of each one will definitely be less than 1,500? … Awesome! Now, find the exact sum."
"Choose one problem to solve with the standard algorithm. Why is the algorithm a reasonable strategy for the problem you chose?"
"Find a problem that will not require any regrouping (e.g., carrying). How do you know? Now find the sum."
"... OK, now write a problem that will definitely require regrouping. Use the standard algorithm to solve it so your teacher can see that you know how to do it that way."
"Hmmm, in just looking at the ones places in your answers, I can see a sum right away that cannot be correct. Can you find it? How can you correct it? Can you tell why you got an incorrect sum the first time?"
The mathematics educator in me loves these questions because
a) they’re much more interesting than “What’s the sum?”,
b) they push students to exercise number sense and estimate,
c) they invite generalizations (“If the sum of the digits I’m adding is greater than 10, I’ll need to regroup … if it’s less than 10, I won’t!”), and
d) they require students to think about their own thinking (i.e., they have a metacognitive element).
The parent in me loves these questions because, well, they’re fun. My child cares about and is interested in them. They add a spirit of puzzling — and even of mystery — to the mathematical work. This is much more engaging for students and for those of us (parents, teachers, siblings, grandparents, friends) who are working with them: now we have something really interesting to talk about! This spirit of mystery, puzzling, and friendly challenge is also what those of us who love mathematics enjoy about the subject: I want students, including those who are also my children, to experience mathematics in this way.