I'm guessing this was about five years ago. I was at an all-day workshop when a high school math teacher sitting next to me asked about the Problem of the Week (PoW) from mathforum.org that I had assigned to my students. I happened to have an extra copy in my backpack and handed it to her.
Dad's Cookies [Problem #2959]
Dad bakes some cookies. He eats one hot out of the oven and leaves the rest on the counter to cool. He goes outside to read.
Dave comes into the kitchen and finds the cookies. Since he is hungry, he eats half a dozen of them.
Then Kate wanders by, feeling rather hungry as well. She eats half as many as Dave did.
Jim and Eileen walk through next; each of them eats one third of the remaining cookies.
Hollis comes into the kitchen and eats half of the cookies that are left on the counter.
Last of all, Mom eats just one cookie.
Dad comes back inside, ready to pig out. “Hey!” he exclaims, “There is only one cookie left!”
How many cookies did Dad bake in all?
Maybe you'd like to work on this problem before reading on.
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The teacher started solving the problem right away. She was really into it—so much so that I think she completely tuned out whatever the presenter was talking about at the time. She ran out of paper and grabbed more. At one point, she looked up from her pile of notes and said something I interpreted as: I know this problem can’t be that hard, but what the actual hell.
It was now morning break.
She kept working on it.
By lunchtime, she turned to me and asked, “Okay, how do you solve this?” I reread the problem, drew a few boxes on top of her paper (inside the green).
She understood the drawings right away and knew I had solved the problem with a few simple sketches. I just really appreciated her perseverance.
I share this story because a few nights ago I was at our local Math Teachers’ Circle, where Joshua Zucker led us through some fantastic activities using Zome models. We were asked to compare the volume of different polyhedrons. Our group completely struggled with one of the shapes. We tried formulas. We tried equations. And we got completely befuddled. Our paper ended up looking exactly like the teacher’s pile from years ago.
Over the years, I’ve had students tell me, “Mrs. Nguyen, my uncle is an engineer, and he couldn’t help me with the PoW.” (Substitute “uncle” with any other grown-up family member, and “engineer” with any profession, including math teacher.) I even received a note from a student’s tutor letting me know I shouldn’t be assigning problems to 6th graders that he himself couldn’t solve. (The student’s parent fired him after that.)
I like to think my love of problem-solving will rub off on my kids. I hope they grow to love the power of drawing rectangles as much as I do.