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• Level: GCSE
• Subject: Maths
• Word count: 1031

# Maths Investigation- Grids

Extracts from this document...

Introduction

Karen Ng

10H

Maths Investigation- Grids

The first part of my task was to investigate the number of squares, which can be drawn on grids made from 11 lines.

I used 11 lines to make different grids on paper, alternating the use of lines. Starting with 1 horizontal and 10 vertical lines I work up (or down) so my grid then is 2 horizontal and 9 vertical. I counted the number of squares by outlining the shape of the square; this is shown in diagram 3.

Here is my table of results using 11 lines only.

 Lines Down Lines Across 1x1 square 2x2 Square 3x3 square 4x4 square Total Squares 0 0 0 0 0 0 0 10 1 0 0 0 0 0 9 2 8 0 0 0 8 8 3 14 6 0 0 20 7 4 18 10 4 3 35 6 5 20 12 6 2 40 5 6 20 12 6 2 40 4 7 18 10 4 3 35 3 8 14 6 0 0 20 2 9 8 0 0 0 8 1 10 0 0 0 0 0 0 0 0 0 0 0 0

As you can see, after the 6x5 result comes up, the rest of the results are exactly the

Middle

0

2

Total number of squares: 2

Best Combination: 3x2

This table of results is for 6 lines only

 Lines Down Lines across 1x1 squares 2x2 squares 3x3 squares 4x4 squares Total Squares 0 0 0 0 0 0 0 5 1 0 0 0 0 0 4 2 3 0 0 0 3 3 3 4 1 0 0 5

Total number of squares: 8

Best Combination 3x3

This table of results is for 7 lines only

 Lines Down Lines across 1x1 squares 2x2 squares 3x3 squares 4x4 squares Total Squares 0 0 0 0 0 0 0 6 1 0 0 0 0 0 5 2 4 0 0 0 4 4 3 6 2 0 0 8

Total number of squares: 12

Best Combination: 4x3

This table of results is for 8 lines only

 Lines Down Lines across 1x1 squares 2x2 squares 3x3 squares 4x4 squares Total Squares 0 0 0 0 0 0 0 7 1 0 0 0 0 0 6 2 5 0 0 0 5 5 3 8 3 0 0 11 4 4 9 4 1 0 14

Total number of squares: 30

Conclusion

## The more lines you have, the more squares you will get. The rules I found out are; if you were trying to find out how many 1x1 squares were in a 6x5 grid, you would do 6-1=5 and 5-1=4, then, you times the answer ( 5 and 4 ) together, and that number will be the amount of 1x1 squares you will get in the grid. To find out how many 2x2 squares are in a grid, you do exactly the same thing, except you subtract 2 instead of 1 because now there are 2 boxes missing from each side.

This student written piece of work is one of many that can be found in our GCSE T-Total section.

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