# Magic Hexaflexagons (Age 7)

## The Activities

1. Topic: Counting, Place Values: Book: The Blast Off Kid, by Driscoll. Last week I read this to the little kids.  This week the big kids heard it. They also really enjoyed this story, and could do subtraction, like, if you need 10,000 wrappers and you have 6,593, how many more do you need?

2. Topic: Probability: I had a 4-sided die, a 6-sided die, and an 8-sided die. One kid would randomly choose a die, and the roll the die and tell the other three kids what number they rolled.  The three guessers could then guess which die the roller had, or ask the roller to roll again.

The Three Dice

3. Topic: Geometry, Origami: I helped the kids each make a “Hexaflexagon”, which is a really interesting hexagon that can be “flexed” to have 3 sides.  See the excellent Youtube Video by Vi Hart here.  This site has the template and instructions I used to make the hexaflexagons.

 The 3 sides of a hexaflexagon.

4. Topic: Partial Ordering, Logic: I told the kids some facts about animals competing in a race.  The facts did not give enough information to tell which animal finished in which place, but we tried to draw graphs (similar to the building block graphs we made in past circles) to represent the information we did know.

One kid’s partial ordering graph.

## How did it go?

We had 4 kids at circle this week. It was a fun circle, except that my daughter was extremely tired, and kept crying throughout circle. After circle we had a discussion about this, where she said she did not want to leave circle to calm down because then she’d miss something.  But I said she would have to leave if she couldn’t stop disrupting circle because it was preventing other kids from learning.

#### Dice Guessing

The kids immediately realized that if someone ever rolls an ‘8’, then they must have the 8 sided die.  However, the kids were initially willing to guess after just one roll, so if someone rolls a ‘4’, some kids wanted to guess it must be the 4-sided die. After a few rounds of this, my daughter started to assert that we should keep rolling several times before guessing.  By the end, they had the roller roll the 6-sided die about 6 times before deciding it was safe to guess.

#### Hexaflexagons

All the kids loooooved this activity! It was not easy to get the hexaflexagons set up for each kid, though they were pretty patient about waiting while I helped others with the tricky steps.  Once the hexaflexagons were built, I had the kids color both visible sides, each side a different color. The kids were all suitably amazed when I flexed their hexagon, and made a new, white side appear.  Then they colored the white side a third color, and had quite a lot of fun switching the shape around. They all enjoyed showing their parents the trick after circle.  One kid made a special point of telling me how much she loved the hexaflexagon.

#### Partial Ordering Races.

We worked through three races:

1. The Dog beat the Cat. The Cat beat the Bird. The Snake beat the Dog.

2. The Fish beat the Dolphin.  The Fish beat the Duck. The Fish beat the Frog.

3. The Fly beat the Ant.  The Bee beat the Ant.  The Bee beat the Worm. The Spider beat the Fly.

At first, a couple of the kids were confused by the premise, but eventually they all got it, and agreed that the animals finished in this order: snake, dog, cat, bird.

For the second race, at first the kids wanted to say that the order was fish, dolphin, duck, but then I pointed out we couldn’t tell whether the dolphin beat the duck or not. Eventually we ended up with a picture that showed the fish first, and the other three animals in a tie.

For the third race, the kids were starting to understand what was going on, but it was a much harder example. We were moving along pretty well until my daughter pointed out that we didn’t know if the Bee beat the Fly, or even if the Worm beat the Fly.  We all agreed that the Ant, Worm, and Fly could not have won.

This was a more interesting and trickier activity than I expected, and I’d like to do more with it in the future.  Maybe next time I’ll make squares of paper with the animals’ names on it, and we can arrange the squares according to the information. That would make it easier to adjust things as you learn new facts.