Saturday, May 4, 2013

Lesson 15- Math Mix

Heads and Legs:

 In a garden, there are five horses. On each of the first three horses, sits a rooster. On each of the last two horses, sits a fish. How many heads and legs are there all together?

“Fish and chickens ride on horses? Haha!” The kids solved the problem by making a little diagram with little circles representing heads, and lines from those circles representing the number of legs that animal has (the animals who sat on top of the horses were drawn above the horses, and the kids thought that doing that really mattered to solve the problem).  I offered the kids to draw the animals sitting on the horses in columns, with the animals under the horses, but the kids refused to do that, since it was “not following the rules of the problem”. It is good that they pay attention to the directions of the problem, but I think that I should spend some more time discussing the importance of various parts of a problem.

Fill in the blanks:
*sorry, the image was not inserted correctly. It will be posted later.

The kids figured out what had to be in each row, and then solved the problem easily. Give everybody a chance to share what they think. This didn’t seem to be too hard for the kids, but it was a good warm-up type of problem. It is good for the kids to recognize and figure out what figures and inner figures had to be in each row, column, and diagonal- don’t tell them those things! Let them think! It might not seem like it, but it is the most important part of the problem!


Is it possible to put 5 checkers in such a way that each checker touches 2 others? 3 others?  

I gave each child some poker chips (that is what we used instead of checkers), and they played around a bit. Most of them solved it after a little while, others were stuck, and were explained how to do it by the children that already figured it out, and NOT by me. We only had time to make the 5 checkers touch 2 others. Later we will try making each of the checkers touch three others.

Elevator Problem:

I know one tall building in Antarctica. Only one person lives on the first floor, 2 people live on the second floor, 3 people live on the third floor, and 4 people live on the fourth floor. There is an elevator in the building.  On what floor does the elevator stop most often?

At first, they all thought that the elevator visits the fourth floor the most often, which is the most obvious response. I let the kids think for a couple of minutes, and everybody still stuck to their answer. I gave them a hint; “is there any place in the building that all the people need to go to, that the elevator would take them to?” Soon after this, they figured out that everybody in the building needs to get to the exit (the door) at some point, and that is on the first floor. “Or they can jump out the window!” said one of the kids. I said, “Do you normally see people jumping out the window from the fourth floor?” “Fine…”

Flower colors:

Once, Sasha drew a flower. He had blue, red and white colors.  “It is not white” – said Max. “It is blue or red” – said Kristina. “It is red” – said Dima. It is known that at least one of the kids guessed wrong, and at least one guessed right.  What color is the flower?

We checked the combinations possible for who was lying and who was telling the truth, and we were in the middle of solving the problem, when the kids started to fool around, so I stopped, and moved on to the next activity. I will re-state this problem and try it again next time.

Passing Trains:

A train is going from the US to Canada, at 60 mph. Another train is heading in the opposite direction- from Canada to the US, and it is moving at the speed of 40 mph. When the two trains pass each other (meet), which one will be closer to Canada?

The kids didn’t seem to understand what the point of the problem was- “Wait… won’t they be in the same place when they meet?” OK… I guess I didn’t succeed in tricking these children… J


Boiling Eggs:

If it takes 2 minutes to boil one egg, how long will it take to boil three eggs?

“Will the eggs boil in the same pot or in different pots?” “What about you decide?”, I answered. The kids were moving in the right direction. “Um… usually eggs are boiled in the same pot, so… let’s have them boil in the same pot.” The kids were getting really close. “Wait, if they’re in the same pot, it’s not like first one will boil and then the other! They will boil at the same time, so it will also take only 2 minutes!” These kids are smart!

Play Pentagrams. Try building solid rectangles out of them.

The kids were surprisingly good at this! They built small rectangles, and a lot of them got really close to making a rectangle using all the pieces. I gave each of the kids a set of pentagrams, so they would be able to work on their own if they wanted to. Which they did.







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