Mathemagic: Tricks For Teachers
Author: terhubung // Category:
Think Of A Number And Variations featuring Jam Jar Algebra
Effect
I ask everyone in the class to write down a number between 1 and 20.
Now double it.
Add fourteen. (Pause and recap)
Now divide your answer by two.
Do I know what your answer is? No? You’re right!
Finally take away your original number.
Put your hand up if your answer is seven!
Method
I write the instructions on the board, and Elise assures me that she can find a number which doesn’t work. I promise her a commendation if she can find one, but being the softie I am she gets one for trying at the end of the lesson anyway. Jordan and Romaine are impressed, so I ask them why it works. This is a bit tricky, so we try a simpler version:
Think of a number.
Add seven.
Take away your original number. The answer’s seven!
Vicky and Michelle are convinced that Sir has lost it big time by now. I offer to make it more complicated:
Think of a number.
Add seven.
Double it.
Divide by 2.
Take away your original number. Even this is too obvious!
I encourage the pupils to make up their own version.
Can they make one that always gives the answer 5?
Jam Jar Algebra
I take two identical jam jars and a pile of Multi-Link cubes for this demonstration.
We work through the original version of TOAN. The class agrees to start with 9.
I put 9 Multi-Link cubes inside one jar so that they can be seen clearly.
When I “double it” I simply produce a second jam jar and put 9 cubes in that too.
Two jars side by side. Fourteen extra cubes are placed on the desk in front of the jars.
Halving it is easy – I just create two piles with a jam jar and seven cubes in each pile. Finally I take the original jam jar away: 7 cubes left.
We try again with four in the jar, and the result is the same.
“Can you see why it always works?”
Elise, perhaps you would like to explain it to the class!
Effect
I ask everyone in the class to write down a number between 1 and 20.
Now double it.
Add fourteen. (Pause and recap)
Now divide your answer by two.
Do I know what your answer is? No? You’re right!
Finally take away your original number.
Put your hand up if your answer is seven!
Method
I write the instructions on the board, and Elise assures me that she can find a number which doesn’t work. I promise her a commendation if she can find one, but being the softie I am she gets one for trying at the end of the lesson anyway. Jordan and Romaine are impressed, so I ask them why it works. This is a bit tricky, so we try a simpler version:
Think of a number.
Add seven.
Take away your original number. The answer’s seven!
Vicky and Michelle are convinced that Sir has lost it big time by now. I offer to make it more complicated:
Think of a number.
Add seven.
Double it.
Divide by 2.
Take away your original number. Even this is too obvious!
I encourage the pupils to make up their own version.
Can they make one that always gives the answer 5?
Jam Jar Algebra
I take two identical jam jars and a pile of Multi-Link cubes for this demonstration.
We work through the original version of TOAN. The class agrees to start with 9.
I put 9 Multi-Link cubes inside one jar so that they can be seen clearly.
When I “double it” I simply produce a second jam jar and put 9 cubes in that too.
Two jars side by side. Fourteen extra cubes are placed on the desk in front of the jars.
Halving it is easy – I just create two piles with a jam jar and seven cubes in each pile. Finally I take the original jam jar away: 7 cubes left.
We try again with four in the jar, and the result is the same.
“Can you see why it always works?”
Elise, perhaps you would like to explain it to the class!
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