Year 5 Boys from Tottenham CS
What did you have to find out?
We had to find out the five weights that were used by the stagehands to counter balance the heavy props. Also, we had to find out the minimum and maximum load they could lift. We also had to figure out what weight combinations we would use to lift each multiple of ten.
What materials did you use?
Paper
Pens
Investigation Sheets
Brains
Smart Board
Computer/ Internet
Problem Sheet
How did you think? What strategies did you use? How did you solve this problem?
To solve this problem we used the trial and error strategy- we trialed different weights in the problem, and if they didn't work we took them out and replaced them with other weights. E.g. we did not need 30kg because we could use 10kg and 20kg to make 30kg.
We were constantly checking and rechecking to ensure that we had correct combinations.
We also worked as a group and so communication was very important.
What answers did you come up with?
The weights were - 10kg, 20kg, 40kg, 80kg and 160kg.
The maximum weight that we could lift using the counterweights was 310kg,. this was a combination of all the weights.
We also found out that the weights doubled every new weight.
The combinations we came up with were:
10kg= 10kg
20kg= 20kg
30kg= 10kg + 20kg
40kg= 40kg
50kg= 10kg + 40kg
60kg= 20kg + 40kg
70kg= 40kg + 20kg + 10kg
80kg= 80kg
90kg= 80kg + 10kg
100kg= 80kg + 20kg
110kg= 80kg + 20kg + 10kg
120kg= 80kg + 40kg
130kg= 80kg + 40kg + 10kg
140kg= 80kg + 40kg + 20kg
150kg= 80kg + 40kg + 20kg + 10kg
160kg= 160kg
170kg= 160kg + 10kg
180kg= 160kg + 20kg
190kg= 160kg + 20kg + 10kg
200kg= 160kg + 40kg
210kg= 160kg + 40kg + 10kg
220kg= 160kg + 40kg + 20kg
230kg= 160kg + 40kg + 20kg + 10kg
240kg= 160kg + 80kg
250kg= 160kg + 80kg + 10kg
260kg= 160kg + 80kg + 20kg
270kg= 160kg + 80kg + 20kg + 10kg
280kg= 160kg + 80kg + 40kg
290kg= 160kg + 80kg + 40kg + 10kg
300kg= 160kg + 80kg + 40kg + 20kg
310kg= 160kg + 80kg + 40kg + 20kg +10kg
Marc, Nader & Amit from Carlton PS
What did you have to find out?
We had to find out the masses of the five weights that can counterbalance the maximum possible load. We also had to find out what the maximum load was. Finally we had to find out the combinations of the the weights to counterweight any load.
What materials did you use?
We used the Investigation Sheet supplied, White Board Markers, Whiteboard, our computer, weights to test our solution, a set of scales and our extensive knowledge of Mathematics.
How did you think? What strategies did you use? How did you solve this problem?
We thought using the formula of ( Powers of 2 can summate up to every consecutive whole numeral from the total of the powers and subjacent)so we used the first five powers of 2 which are 1(2 to the power of 0), 2, 4, 8, 16 and since they are multiples of 10, we multiplied them by 10.
What answers did you come up with?
Using the formula mentioned previously, the counterweights weigh 10kg, 20kg, 40kg, 80kg and 160kg. This would mean that the maximum load would be 310kg. The combinations for summating up to every multiple of ten up to 310 are the following weights: 10kg, 20kg, 40kg, 80kg, 160kg.
10=10kg
20=20kg
30=10+20kg
40=40kg
50=40+10kg
60=40+20kg
70=40+10+20kg
80=80kg
90=80+10kg
100=80+20kg
110=80+10+20kg
120=80+40kg
130=80+40+10kg
140=80+40+20kg
150=80+40+20+10kg
160=160kg
170=160+10kg
180=160+20kg
190=160+20+10kg
200=160+40kg
210=160+40+10kg
220=160+40+20kg
230=160+40+20+10kg
240=160+80kg
250=160+80+10kg
260=160+80+20kg
270=160+80+20+10kg
280=160+80+40kg
290=160+80+40+10kg
300=160+80+40+20kg
310=160+80+40+20+10kg
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