I will give Max, Kristina, and Dima a shape- there are two squares, and one circle. If Dima and Kristina have the same shape, who has which shape?
All of them figured out right away, but I think it was a good warm-up. I also asked them to explain why they thought that their answer was correct, to get them involved- it was the beginning of the class, and they were still playing around a bit, and haven’t gotten into “concentrating mode” yet.
Now, I will give Katya, Matthew, and Sasha a colored pencil-there are two red pencils, and one green pencil. If Matthew and Sasha have different colored pencils, what color pencil does Katya have?
They also answered this one right away, and had no problem explaining their answer.
This time, I will give Katya, Kristina, Max, and Dima a poker chip. There are three blue poker chips, and one white chip. Katya and Dima have the same colored chip, but Dima and Max have different colored chips. Who has the white chip?
They though a little bit on this one (don’t give them hints until they thought for some time), and soon figured out the answer. I think that these problems were a perfect warm-up for the class, and the kids started to pay more attention after this. This warm-up wasn’t too hard, but wasn’t extremely easy, either, so, without having to struggle, the kids started to get more involved and interested in the lesson.
Dima, Kristina, Matthew, and Katya have different pets. Each of them has a turtle, a cat, a dog, or a bird. Who has which pet?
Matthew has a fluffy and fuzzy pet.
Katya has a pet that has feathers.
Kristina has a pet with shining green eyes.
Dima got his pet from the aquarium.
I used this problem, first of all, to get all of them thinking, but more importantly, to show them how to make a basic table. I asked them what we could use to mark down who has which pet, and who doesn’t have a certain pet, and they said a table, so that is what I did. I wanted them to answer, “a chart”, or “a table”, but I wasn’t actually expecting them to figure that out- I was going to tell them myself. The problem itself wasn’t very hard for the kids, but, with multiple clues, it took a little while to complete the table and to figure out who had which pet in the end.
The children saw that the table was useful in this case, but they need more exposure to these types of problems to fully appreciate this type of information organization.
A mouse, a fox, a zebra, and a dinosaur want to see how they compare in height, but they are not allowed to see each other. They are given these clues:
The mouse is taller than the dinosaur.
The fox is taller than the mouse.
The zebra is taller than the dinosaur, but shorter than the mouse.
List them in order from tallest to shortest, or vice versa.
The kids burst out laughing when hearing that a mouse is taller than a dinosaur, a zebra is shorter than a mouse, etc. They thought that the problem was very silly, and they still seemed to be a bit confused with the sizes while solving the problem. I asked the kids how I could represent that one of the animals is taller than another, and they said to write the names of the animals from top to bottom (taller animals on the top, shorter animals at the bottom) - a wonderful solution. After righting down the heights of the animals compared to each other (using their strategy), they figured out the answer very easily- all they had to do was look at the “diagram”.
Let’s pretend that Peter is a cook. The first day, he makes three chocolates. The next day, he makes two cakes, and four cookies. The next week, he makes two different types of soup, seven pancakes, and nine meatballs. What is the name of that cook?
About a second after I asked the question, they answered- correctly. Also, if the problem is being addressed to only one child, instead of saying that Peter is the cook, they should be told that they are the cook. It’s more interesting that way.
A teacher told a group of kids that zebras had stripes. Later that day, the kids went to the zoo, and they saw an animal with stripes. A child said that it was surely a zebra, because it had stripes. Was the child’s thinking correct?
The kids thought that the child was perfectly correct, until I hinted to them about there being other animals with stripes as well, not only a zebra. After that, they realized that the child was wrong. Without the hint, they didn’t seem to be able to figure it out.
Let’s say, that every time Dima eats a chocolate, he is happy. I just came out of my room, and I saw that Dima was happy. Can I now say that he just ate a chocolate?
Dima really liked the fact that the problem was about the fact that he was eating chocolate, and being happy after it. They again responded the same way as in the previous problem, but this time I didn’t give them a hint (since this was just a variation of the previous problem, they should be able to figure it out now). They thought for a while, and then decided that Dima is sometimes happy without having to eat a chocolate before it.J
A string has three cuts made in it. How many pieces of string did that form? What about with four cuts? Try it with a piece of paper.
When there were three cuts made, they though there would be three pieces, so I started with two cuts. The same thing happened with two cuts. Then I asked them about zero cuts, they said, “Zero pieces!” two seconds later… “Oops! There will be one piece!” Then I asked them, “What about one cut?” Without hesitating, they yelled, “One piece!” “Really?” I replied. “Let’s check”. We checked by cutting the string once. It made two pieces. They finally understood. Later, I asked them to come up to the whiteboard and “cut” the string in various numbers of cuts.
How many corners does a table have? Four! If one of the corners was cut off, how many corners would be left? Try it with a piece of paper.
“Three!” the kids shouted. It is understandable that people expect the numbers to go down when you subtract/cut something. “OK. Let’s check.” I showed them with a piece of paper, and said, “Look! I cut off a corner, and got MORE corners!” The kids were startled, and excited. I did it again, and kept getting more corners. A few kids said that it was impossible, and some others argued that I did it, so it must be possible.
Teach the kids how to play 20 questions.
It’s way too hard for them. They just starting guessing- “Is it a table? Is it a couch? Is it our planet?” The kids are too young to play twenty questions, but they can play pretty well if the game is played only within a specific category. For example, if I am only allowed to think of something in the category of food. That would be a lot easier for the kids, because at this age they do not yet understand the concept of first asking more general questions, and slowly narrowing down to more detail. They just guess randomly, and think that eventually they will get it right. I would suggest gradually introducing categorizing and generalizing skills while playing this game.