Math

"A cube has all of its faces painted red. The cube is cut into 243 smaller cubes. Investigate how many cubes have 0, 1, 2, 3 faces painted."

State that your are going to look at simpler cases and show your working out in detail for all of them.

"I am going to look at a cube cut into 27 smaller cubes first."

Be consistent in your use of letters and symbols - this shows you are able to express yourself mathematically.

"I am going to use x to stand for the number of cubes along each edge."

After you've round about 5 or 6 results, draw a table and show any values you've used or worked out for each case. Now look for patterns. A good way to find algebraic rules is to look at the differences between values. I'm not going to use the example of the painted cube here because it is often used as a GCSE task so it wouldn't be fair to give you any more help with it. To look at differences, I'm just going to use a sequence of values:

x 1 2 3 4 5 6 7 8 9

Results 4 11 18 25 32 39 46 53 60

1st difference 7 7 7 7 7 7 7 7

The first difference is 7. This tells us that we have to multiply x by 7. Next work out what we need to add or subtract to get the algebraic relationship:

7 x 1 = 7, 7 - 3 = 4 7 x 2 = 14, 14 - 3 = 11 7 x 3 = 21, 21 - 3 = 18

The rule is multiply by 7 and subtract 3, or x maps onto 7x - 3, y = 7x -3.

For algebra involving powers, it gets a bit more complicated:

x 1 2 3 4 5 6 7 8 9

Results