Keira googled herself and found Dad’s blog. She said I should write more often. To be more precise, she said I should write more often about her.

I have to reach waaay back to late August/early September.


One day, she came home from Michael’s with several new bottles of paint.

“They were two for a buck fifty, so I got twelve. Twelve!”

I asked her how much she paid.

“Twelve bucks.”

I shot her a look. No poker face.

“Okay, okay,” she said and began to figure it out, spreading out the bottles in pairs on the lawn.

Then, she joined two pairs. “Two dollars and… three.”

She made two groups of four from the remaining four groups of two.

“Three, six, nine. Nine dollars!”

I’ve tagged this post “#tmwyk” (“talking math with your kids”). That’s generous, I know. I took “less helpful” to heart. Bordering on no help at all. But hey, it was summer. “I’m off the clock, kid.”

As a result, Keira developed a strategy. It’s hers. In joining two pairs of bottles of paint, she dealt with dollars before considering cents; she started with the part of the quantity that’s more important–the larger part. After joining two pairs, she knew that $3 was easier to work with than $1.50. Friendlier. She can skip-count by threes. If I got a do-over? More paint. Would Keira have skip-counted to $12 (16 bottles) or would she have doubled $6 (8 bottles)? In about five years, she’ll be expected to set up a proportion–and set aside her intuition!–or calculate a unit price to practice similar textbook exercises.

At the time of this conversation, I was also reading up on proportional reasoning. I noticed that Keira was “attending to and coordinating two quantities”: the number of bottles of paint and the amount of money.

Previously, I shared my thinking about planning a proportional reasoning unit using the KDU model. In that post, I came up with some elaborations to flesh out the MoE’s open/vague content standards. I missed the “attending to and coordinating two quantities” thing. Later in the year, I attempted Dan Meyer‘s Nana’s Paint Mixup math task in a Mathematics 8 classroom. It flopped. For several reasons. For one, I had taken for granted that students had understood that the problem involved two quantities. Paint was being added willy-nilly. I could have asked “What quantities can be counted/measured?” I didn’t.

Fast-forward one week…


This surprised me. I mean, here she is days before proudly wearing a t-shirt that she picked out for back to school.


Keira identifies as a mathematician. And author, and artist, and athlete, and engineer. When I created the Which One Doesn’t Belong? sets here, Keira was my go-to. She loved the challenge of identifying (at least) one reason why each image in a set didn’t belong. It didn’t matter that the content came from high school.


(John Stevens tells a similar story in his new book, Table Talk Math. Highly recommended!)

“I’m nervous about new Grade (Math)” didn’t add up, so I asked Keira about it. “You have to add and subtract big numbers,” she said. This is a kid who wrote several stories over the summer, such as The Magical adventures of the Fruitimals and the Food Fight, in which the plot could be summarized as strings of two-digit subtraction problems. For fun.


Sometimes, there can be a disconnect between mathematics at school and mathematics at home. This is not one of those times. Keira described schoolmath in terms of calculations. Her description of homemath–at least here–wouldn’t be markedly different. We’re talking about arithmetic, not ideas about infinity.

For the record, I don’t believe that Keira was nervous about Grade 3 math. Rather, she has picked up on peoples’ perceptions of mathematics: math is something that is okay to be nervous about.

[TMWYKS] Rainbow Loom

Christopher Danielson brought you #tmwyk, or talking math with your kids. I bring you #tmwyks, or talking math with your kid sister.

It happens to every parent, I think: the kid says something and nobody has to ask “Where’d she hear that?” Maybe it’s the kid’s choice of words. Or maybe it’s the tone, pitch, or rhythm that gives you away. Rare is it for me that these are proud parenting moments.

A recent exception:

Gwyneth (9 years old): What patterns do you see?

Rainbow Loom

Keira (6 years old): Red, white, yellow, red, white, yellow, red, white, yellow.

Gwyneth: Great! Can you find another pattern?

[TMWYK] Aero Bubble Bar

Recently, Nestlé launched the new AERO bubble bar throughout Canada and the UK.

For the benefit of the American readership:



From the press release:

As well as offering a unique bar design, guaranteed to stand out from the crowd, AERO’s innovation isn’t just for show. The new design sees the bar divided into ten easily snappable ‘bubbles’, making it less messy to eat and more portionable. What’s more, each of the ten ‘bubbles’ are designed to melt more easily in the mouth, maximising the taste of AERO’s signature bubbly chocolate.

I brought one home a couple weeks ago. I put the bar’s portionability to the test.

ow2adI snapped off two bubbles each for Keira (5), Gwyneth (8), and Marnie (N/A). Plus, two for me. (Missed math teacher opportunity, I know.) Two pieces were left over. “How much more should we each get?” I asked.

“Half,” Keira answered. She told me to make two cuts: two becomes four, or n(Keira’s family). For shits and giggles, we played with different cuts. What I learned from Keira:

the halves and the halve nots

“Or two-quarters,” Gwyneth piped up.

“Huh?” I returned, caught off-guard. “Tell me more,” I recovered. Gwyneth told me to cut each of the two bubbles into four quarters, giving us eight quarters. Eight pieces can be shared equally between four people. Each of us should get two pieces, or two-quarters.

Gwyneth’s strategy–divide each piece into fourths rather than make four pieces in all like her sister–surprised me. It’s a strategy that makes sense to her: dividing each piece into fourths means she’ll be able to form four equal groups. It’s a strategy that’s flexible: I don’t think she’ll be fazed by a curveball, like an additional bubble or family member.

Symbolically, we have:


The result is trivial; her thinking is not.

For more math talk with kids, please follow Christopher Danielson’s new blog.