# Hundred Face Challenge

A couple years ago Malke Rosenfeld, author of Socks are Like Pants, Cats are Like Dogs,  used Cuisenaire Rods with some students to create the Hundred Face Challenge. The gist of the challenge is that the student must create a face with the sum of the face equal to 100. She extended the activity by adding additional constraints, you can see her original challenge here. This exercise has caught on and now it’s a “thing”. You know an internet “thing”. Not like the ice-bucket challenge or bullet-proof coffee, but we’ll get there. Math isn’t quite that cool yet. But I get ever more hopeful every day.

First go around was with my 5-year-old: while he is advanced in many areas of mathematics, addition is not one of them. Asking him to add to 100 was going to be a bit like torture, so we hatched a plan. We call each orange rod 10, based on the white units, and 10 orange rods became his “starting out” blocks. We know he needed ten because everyone knows 10 x 10 = 100.  At any point, he could exchange one or all of the rods for other rods. I served as the banker, which meant I got to keep strict control of all blocks coming in and going out. If he wanted blocks he had to prove to me that what he asked for was the same as what he was giving back. This process is a bit slow and cumbersome but worth it.

What we learned from the Hundred Face Challenge:

1. Mental addition would make things go much quicker.
2. It is easier to make round objects with smaller blocks.
3. Patience and attention to detail make building faces easier.
4. There are a lot of combinations for 10. More than we can count.
5. Any number can be broken into a combination of smaller numbers except 1.
6. Having limitations makes you think harder and be more creative.
7. When you run out of blocks of one color, you have to improvise. Pouting doesn’t change reality.
8. P, age 5, needed an idea. The general instruction to “build a face” was overwhelming. He needed to build a thing. We built King Alfred, a ninja turtle, and a scary cat.
9. A, age 4, loves the possibility of doing whatever she wants with a face, and changes plans multiple times before she is done.
10. Blocks can be traded multiple times until you get the exact combination you desire. Which leads to the idea that numbers can be grouped in all kinds of ways within a number, but it is still the same number.
11. All blocks of the same color behave in predictable ways which make them more or less desirable for building certain body parts.
12. Sharing blocks means the desirable pieces get used first. It is better to have a plan going in.
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Given how much fun we have, and how much we learn from this activity, it is going to remain part of my bag of tricks for some time. If you want to participate in the hundred face challenge, you can send your images to me at sonya at arithmophobianomore.com. I will post them on my FB page. and submit them here. Or tweet them out using #hundredface or #hundredfaces and mention me @nomathfears.

• What a great list of “What we learned”!

I found too that even some of my more confident mathematicians made slips with the counting. Most of the time careful calculating isn’t my main thing, but this exercise seems like the right place for it – it is all about a hundred after all, and it’s great that there are so many ways through with the calculation! Mostly I use the rods, like you for more algebraic/conceptual thinking rather than for calculating, so it’s also a change and not burdensome.

I like the idea of being more prescriptive about the faces – a scary cat – a mutant ninja turtle – I might try that too!

• Sonya Post says:

We have done this exercise for several days now. It gets better each time. P. gets overwhelmed easily so I had to narrow his choices down. We tried a several versions of a Pharaoh and couldn’t make it happen. This might be a challenge for your group!

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