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:
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!
Checkers:
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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