Maths Investigation on Pond Borders Essay

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Maths- Garden Ponds and Fish Tank Investigation Plan: 1. First I am going to do different pond sizes and count the number of slabs around them and record the results in a table. I am going to go up to 10m by 10m. 2. Next I am going to find a pattern in my results and try to find out how many slabs are needed for a 100m by 100m pond. 3. After that I am going to find a formula for square ponds with the variable 'n' in it. 4. Then I am going to do the same with a rectangle and a triangle. 5. Finally I am going to do the fish tank using the same principals. Squares: n | Size of pond | Number of slabs | 1 | 1m by 1m | 8 | 2 | 2m by 2m | 12 | 3 | 3m by 3m | 16 | 4 | 4m by 4m | 20 | 5 | 5m by 5m | 24 | 6 | 6m by 6m | 28 | 7 | 7m by 7m | 32 | 8 | 8m by 8m | 36 | 9 | 9m by 9m | 40 | 10 | 10m by 10m | 44 | n | nm by nm | 4n+4 | Formula: The formula for squares is 4n+4. Prediction: I think that a 11m by 11m pond will have 48 slabs paving it. 1 | 48 | 47 | 46 | 45 | 44 | 43 | 42 | 41 | 40 | 39 | 38 | 37 | 2 | | | | | | | | | | | | 36 | 3 | | | | | | | | | | | | 35 | 4 | | | | | | | | | | | | 34 | 5 | | | | | | | | | | | | 33 | 6 | | | | | | | | | | | | 32 | 7 | | | | | | | | | | | | 31 | 8 | | | | | | | | | | | | 30 | 9 | | | | | | | | | | | | 29 | 10 | | | | | | | | | | | | 28 | 11 | | | | | | | | | | | | 27 | 12 | | | | | | | | | | | | 26 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | I now know that 100m by 100m is going to be worked out like this: 4x100+4=404, so the answer is 404 slabs are needed for a 100m by 100m pond. Rectangles: Height | Width | Slabs | 1 | 2 | 10 | 2 | 3 | 14 | 3 | 4 | 18 | 4 | 5 | 22 | 5 | 6 | 26 | 6 | 7

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