## Thursday, March 14, 2013

### Lesson 16- Games, Puzzles, and Manipulatives

http://www.artofinquiry.net/bookstore/ Go to “Math Games and Puzzles”

Hanoi Tower

We started with two rings, and then went on to three. At first, I let the kids take turns moving one ring at a time, but that didn’t work; since each of the kids had their own strategy for how to solve the problem, they all started arguing with each other and saying that they were right and everybody else was wrong. Because of this, I let each of the kids take turns solving the whole puzzle, so that they would be able to complete their idea and strategy and so that they would be able to try to solve it on their own. Since there were many kids waiting to solve this puzzle (it took a few minutes for each child to complete it), I had a few children go and do some of the other puzzles (Rush Hour, Hoppers, and IZZI).

Rush Hour

Oops! Big mistake! I meant to let them play Rush Hour Jr., not Rush Hour! They will only be able to actually solve the puzzles in Rush Hour in a couple of years. Since I accidentally brought Rush Hour to the class, they were only able to solve the first few problems (and even those were still hard for them). Rush Hour Jr. should be at their level, though.

Hoppers

The kids liked this game, and they were good! They quickly figured out the solutions to the problems, and on the puzzles that they couldn’t solve right away, they worked together to think of the different possibilities- working together is a very good skill for them to have, and so is continuing to solve a problem after several tries, instead of giving up.

Cathedral

I explained the kids how to play this game, and they seemed to follow along, but I think that they didn’t quite understand what I was saying. Maybe in a few years this game would be good for them, but for now, it’s a bit too complicated.

IZZI

This is best to be played at the end of the class, because the kids are tired by then, and this game really doesn’t use up any energy… It’s very simple, but the kids seem to love it.

Othello- kids against me

This is a nice game to play with the kids; they get to team up and play against the teacher. They liked it, and they took turns adding pieces to the board. They were actually pretty good (especially considering that this was their first time playing).

## Thursday, March 7, 2013

### Logical Fallacies and other Puzzles

Materials: Set (game), Hanoi Tower

Lying or telling the truth?

If I say that there are only girls in this room, am I lying or telling the truth? How do you know? If I say that you are a million years old, am I lying or telling the truth? How do you know?

Kids reply: Lying!

If I say that you are a boy (talk to everybody at once), would I be lying or telling the truth? Wait… how is this possible? How come Kristina is saying that I am lying, and Dima is saying that I am telling the truth? Something can’t be true and false at the same time, can it?

All of the boys say: “It isn’t both true and false; it’s true!” while all of the girls say, “It isn’t both true and false; it’s false!” Huh? Confusion. “Oh… I get it… it’s true for some people but not others”- very good answer.

“I like cats”- am I lying or telling the truth? How do you know? Is this a fact? Or is it an opinion?

The kids all had their own viewpoints;

“It is true, because since you are saying that you like cats, it means that you do like cats.”

“It is true, because a lot of people like cats.”

“It is false, because I don’t like cats that much; I like dogs more.”

“We don’t know if it’s true or false, because we don’t know what you like and don’t like.”

Which of these are facts, and which are opinions?

We are in a house.

We are humans.

I like blue.

Cats are fluffy.

This is a big house.

There are mermaids in the ocean.

Dragons are real.

The kids needed an explanation between a fact and an opinion; they knew that were things called facts and opinions, but they didn’t seem to know the clear difference between them. They went through this activity quickly though, which was what I expected. On the question, “This is a big house”, the kids couldn’t decide whether it was a fact or an opinion. So, we concluded that opinions weren’t really true or false, because they vary from person to person. The kids enjoyed the fact that I thought that dragons were real, and that there were mermaids in the ocean. J

Analogies:

Bird is to nest as spider is to ___________

Teacher is to school as doctor is to _________

Book is to read as movie is to _________

Paw is to claws as foot is to __________

Cat is to “meaw” as dog is to _________

Black is to white as top is to _________

I explained to the kids what an analogy was, and for the first problem I had to hint them a little, because even after the explanation, they still didn’t quite understand what an analogy was. The hint I gave sounded like this: “A bird does what in a nest?” Kids: “Lives!” “A bird lives in a nest; a spider lives in a…”After they understood well what an analogy was, the rest of the problems were relatively easy for them, and the kids seemed to enjoy doing the analogies.

Backwards Simon Says- Play Simon Says except the kids have to do the opposite of whatever Simon says.

The kids were slowly getting tired, so I decided to play a game for a few minutes. Anyways, the kids seemed to love playing this game, and it involved some thought, because every round, I made the game a little harder- I didn’t just want the kids to be sitting around. This game makes the kids think of opposites of things, and that was something that I noticed seemed hard to them during previous lessons.

Generalizations:

True or false?

“I came to my teacher and she got mad at me. My sister came to her teacher and the teacher got mad at her. My friend came to her teacher and the teacher got mad at her.” Conclusion: Teachers always get mad when people come up to them.

Kids: “You don’t get mad at us when we come up to you, so the statement is false.” “Well, let’s not focus on what is actually happening, but what is in the problem.” Kids: “If only a few people came up to the teacher, then how do we know if everybody does? Only if every person in the whole world comes up to the teacher and the teacher yells at them it would be true. And since that didn’t happen, the statement is false.”- very good.

“I used to own a fish, and it fell out of its tank.” Conclusion: All fish fall out of their fish tanks.

“A fish fell out of its tank? Ha-ha-ha! That is so funny!” “Ok, I’m glad that you are having fun, but we still have to solve the problem.” Kids: “Ok. Not all fish fall out of their tanks! If one fish fell out of its tank (how did it fall out, by the way?), that doesn’t mean that all fish fall out of their tanks!”

“I heard that somebody got eaten by a lion.” Conclusion: It is possible to be eaten by a lion.

Kids: “Well, if somebody got eaten by a lion, then the conclusion is true; it is possible to get eaten by a lion. This time the conclusion makes sense; it’s not like it says, “everybody gets eaten by lions”- that would be strange, because I didn’t get eaten by a lion… well, for right now. Maybe I will…does it feel scary when you get eaten by a lion?”

“I know a person from Antarctica, and he was nice.” Conclusion: All people from Antarctica are nice.

“You know somebody from Antarctica?! That’s so cool! Oh, fine, back to the problem. Um… if you knew all the people from Antarctica, and they were all nice, then the statement would be true, but since you only know one person from Antarctica who is nice, the statement is false.”

These are actually some good answers, considering that these are little kids.

Building Tables:

Figure out who likes which sport- there are four sports; tennis, soccer, basketball, and badminton, and there are four kids; Dima, Kristina, Katya, and Max.

Kristina doesn’t like basketball or soccer.

Max used to like basketball and badminton best, but now he changed his mind.

Neither of the boys likes soccer best.

As they always do, the kids loved that they were in the problem. I called them up to the board (make sure to let all of them solve part of the problem), and asked each of them to figure something out and mark it on the table we drew (sports vs. kids comparison). This took some time, and the kids were already tired and started to roll around on the floor and play around. Again, time for a game.

Simplified Set:

Take out a few cards at random, and ask the kids to find the similarities and differences between the cards; this can be done in the form of a game (every child gets one or two cards, and then I put down a card from the pile, and the kids have to put down the cards that they have, but only the ones that are similar in any way to the starting card.)

If the kids don’t listen, have the child who wasn’t following directions sit on a chair in the corner, or something similar to that, because otherwise, all of the kids take the child’s example and stop listening to directions as well. If a child takes the Set cards and don’t give them back, tell them that either they give the cards back or they don’t get to play the game- easy solution; this happened once during the class, but the kids really wanted to play the game, so they gave back the cards.

Simplified Hanoi Tower: Play with two-three pieces; it’s a complex and at the same time interesting activity for the kids.
We only got to do this for a few minutes, because the class ended, and we ran