Lesson 18- Math

Colors:

Kristina, Katya, and Max are standing in a line. They all are holding either a blue or green bouncy ball. Two people are holding a green bouncy ball, and one is holding a blue bouncy ball. We also know that some of these people always lie and some only tell the truth.  Kristina says, “I have a blue bouncy ball.” Katya says, “I have a blue bouncy ball”. Max says, “I have a green bouncy ball.” Kristina says, “Katya is lying.” Katya says, “Kristina is lying.” Max says, “Katya is telling the truth.” Who is holding which color bouncy ball? Who are the truth tellers, and who are the liars?

For this problem, I drew a diagram on the white board which showed which person was holding which color bouncy ball. Also, the diagram had arrows pointing from one person to the other with Xs and checkmarks at the ends (depending on whether that specific person was saying that the other was a liar or a truth teller). We checked the possibilities for who could’ve been the liar or the truth teller, and the diagram helped a lot. This problem wasn’t too hard, but it wasn’t very easy either, so it was a good warm up.

Handshake Puzzle:

If there are: 1, 2, 3, 4, 5, or 6 people in a room, and every person shakes hands with every other person, how many handshakes will happen? Can you find any patterns?

ACT IT OUT. Ask a few kids to come to the front of the room, and have them shake each other’s hands, and count how many handshakes would happen in all. We recorded our results in a table, and we also recorded how many handshakes

a)      The person that shook everyone’s hands first

b)      The person that shook everyone’s hands second

c)      The person that shook everyone’s hands third, etc.

They found a few different patterns while solving this problem.

Knots:

Dima has a string. He is holding the ends of the string with his hands. How can Dima tie a knot in the string without switching the ends of the string with different hands?

I brought a scarf so that each child would get a chance to try doing this problem. After each child had a turn and nobody figured out yet, I gave them the hint that your hands can be crossed in any way when you start, as long as your hands are holding the ends of the scarf, and that they stay there for the whole time while solving the problem. After about 5-10 minutes of them trying to solve it (with me giving more and more hints every time), I showed them how to do it. Then I let a few kids try repeating what I did to show them that it was actually possible (they thought that I was cheating, because it was obviously impossible).

Toothpick puzzle:

There are 4 squares joined together to make a bigger square (out of toothpicks). How can you move just two toothpicks to make seven squares?

I brought popsicle sticks (toothpicks are too sharp and small) and they solved the problem using them. I let each child try, and they figured out after a few minutes that the popsicle sticks could be crossed over each other.

Try making a magic square (3x3)

I drew a 3x3 square on the white board, and gave them two numbers to start with (in random places in the square). They tried to solve it from there, but many of the times it ended up not working (obviously, since I just placed the numbers in randomly). Then, I let them try and figure out on their own how to start (and finish) the puzzle. This is actually a pretty hard puzzle.