Post date: Feb 27, 2017 8:4:45 PM
What we did: Discussed binary numbers and in particular how to count to 1023 on your fingers.
We motivated this by solving the problem of how to weigh items of wright 1kg, 2kg, 3kg, ..., 15kg on a balance scale using the minimum number of weights. The weights are only allowed to be placed on one site of the scale. The answer is to use weights of 1kg, 2kg, 4kg and 8kg.
Labeling the fingers on one hand with values 1, 2, 4, 8, 16, we found we can count to 31 on one hand. On two hands we can count to 1023.
We played briefly with the magic trick here. The kids all got copies of the cards to take home. http://www.mathmaniacs.org/lessons/01-binary/Magic_Trick/
Things to try at home:
Modify the scale problem above where you can now put the weights on either side of the scales. What is the minimum number of weights needed so you can weigh items from 1kg to 40kg. This is really the famous weighing problem of the French mathematician Claude Gaspard Bachet de Meziriac (1581-1638). "A merchant had a forty-pound measuring weight that broke into four pieces as the result of a fall. When the pieces were subsequently weighed, it was found that the weight of each piece was a whole number of pounds and that the four pieces could be used to weigh every integral weight between 1 and 40 pounds. What were the weights of the pieces?"
What is the highest number you can count to using your fingers and toes?
Understand how the magic trick works.
Binary numbers game. A good mental arithmetic workout! http://games.penjee.com/binary-numbers-game/
Links:
Introduction to binary numbers from Khan Academy. https://www.youtube.com/watch?v=ry1hpm1GXVI
Counting to 1023 on your fingers with binary. https://www.youtube.com/watch?v=1SMmc9gQmHQ