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Spirocakes

by Laura Overdeck

Pancakes taste great in any shape, even a plain old circle. But they’re even yummier when they have crazy designs. The folks at 10MinuteMath made a tool that spins out pancake batter the same way as one of our favorite toys, Spirograph. In Spirograph, you stick your pencil into a hole in a flat wheel with teeth (a “gear”); as you turn the gear inside a bigger ring, your pencil draws really cool, spirally shapes. If the gear doesn’t come back to its exact starting spot, it has to go around again and again, making new layers of loops. The “Pangraph” pancake gadget has a gear that goes around the inside of a ring, pouring the batter in the same loopy lines…and then you get to eat your art!

Wee ones: If you’ve poured 4 loops of batter, then squirt 1 more, how many loops have you made?

Little kids: If your spirocake has 2 overlapping circles, what’s the biggest number of places the lines can cross?  Bonus: If you put chocolate chips on each “petal” of your 8-petal spirocake, and you’re on the 5th one, which petal will you land on if you add 5 more chips?

Big kids: If an 8-toothed gear rolls around inside a 40-toothed ring, how many times will it spin to come back to its starting point?  Bonus: What if the ring has 44 teeth? How many times will the little wheel spin to end up at the beginning?

 

 

 

 

 

 

 

 

 

 

Answers:
Wee ones: 5 loops of batter.

Little kids: In 2 places.  Bonus: You’ll be back on the 2nd petal, since the first 3 chips will land on 6, 7 and 8, then the 4th will land on petal 1.

Big kids: 5 times — it will make a 5-petal flower.  Bonus: 11 turns. The gear will spin 5 times and fall 4 teeth short of its starting point. When it rolls around the ring a second time, it will spin another 5 times and fall 8 teeth short — perfect. That lets it do 1 more spin to end up at the start! (Note: This is all relative to the ring’s edge, not to the room at large: The gear will fall short a little of its original orientation on each spin, so it will spin only 4 times and 10 times relative to the room.)

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