Teacher calls out numbers consecutively, starting at 0.
When a student hears their number being called they immediately raise a hand. When the teacher tags the hand, they stand up.
If more than one hand was raised, those students lose. They become your helpers, tagging raised hands.
If only one hand was raised, that child wins the round.
“Each game takes about 45 seconds,” Hamilton says. “This is part of the key to its success. Children who have not learned the art of losing are quickly thrown into another game before they have a chance to get sad.”
The experience of mathematics should be profound and beautiful. Too much of the regular K-12 mathematics experience is trite and true. Children deserve tough, beautiful puzzles.
What are the best numbers to pick? Patrick Vennebush hosted on online version of the game at his Math Jokes 4 Mathy Folks blog a few years back, though we didn’t have to bend over into rocks—which is a good thing for some of us older folks.
Interrupt your regular math programming to try this fantastic math doodling investigation, and you might even win a prize!
Anna Weltman wrote a math/art book, and Dan Meyer is offering a classroom-size set of them to the winner of his fall contest (deadline Tuesday, October 6, and homeschoolers are welcome, too).
Even if you don’t want to enter Dan’s contest, spirolateral math doodles—or “loop-de-loops”—make a great mathematical exploration.
How to Get Started
To make a spirolateral, you first pick a short series of numbers (1, 2, 3 is a traditional first set) and an angle (90° for beginners). On graph paper, draw a straight line the length of your first number. Turn through your chosen angle, and draw the next line. Repeat turning and drawing lines, and when you get to the end of your number series, start again at the first number.
Math Concepts: division as equal sharing, naming fractions, adding fractions, infinitesimals, iteration, limits Prerequisite: able to identify fractions as part of a whole
This is how I tell the story:
We have a cake to share, just the two of us. It’s not TOO big a cake, ‘cuz we don’t want to get sick. A 8 × 8 or 16 × 16 square on the graph paper should be just right. Can you cut the cake so we each get a fair share? Color in your part.
How big is your piece compared to the whole, original cake?
But you know, I’m on a diet, and I just don’t think I can eat my whole piece. Half the cake is too much for me. Is it okay if I share my piece with you? How can we divide it evenly, so we each get a fair share? How big is your piece?
How much of the whole, original cake do you have now? How can you tell?
I keep thinking of my diet, and I really don’t want all my piece of cake. It looks good, but it’s still just a bit too big for me. Will you take half of it? How big is that piece?
Now how much of the whole, original cake do you have? How could we figure it out?
[Teaching tip: Don’t make kids do the calculation on paper. In the early stages, they can visualize and count up the fourths or maybe the eighths. As the pieces get smaller, the easiest way to find the sum is what Cohen does in the video below—identify how much of the cake is left out.]
Even for being on a diet, I still don’t feel very hungry…
In the land of Fantasia, where people communicate by crystal ball, Wizard Mathys has been placed in charge of keeping the crystal connections clean and clear. He decides to figure out how many different ways people might talk to each other, assuming there’s no such thing as a crystal conference call.
Mathys sketches a diagram of four Fantasian friends and their crystal balls. At the top, you can see all the possible connections, but no one is talking to anyone else because it’s naptime. Fantasians take their siesta very seriously. That’s one possible state of the 4-crystal system.
On the second line of the diagram, Joe (in the middle) wakes up from siesta and calls each of his friends in turn. Then the friends take turns calling each other, bringing the total number of possible connection-states up to seven.
Finally, Wizard Mathys imagines what would happen if one friend calls Joe at the same time as the other two are talking to each other. That’s the last line of the diagram: three more possible states. Therefore, the total number of conceivable communication configurations for a 4-crystal system is 10.
For some reason Mathys can’t figure out, mathematicians call the numbers that describe the connection pattern states in his crystal ball communication system Telephone numbers.
Can you help Wizard Mathys figure out the Telephone numbers for different numbers of people?
T(0) = ?
T(1) = ?
T(2) = ?
T(3) = ?
T(4) = 10 connection patterns (as above)
T(5) = ?
T(6) = ?
and so on.
Hint: Don’t forget to count the state of the system when no one is on the phone crystal ball.