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Introduction

Jonathan Parsonage

11A1

Maths Coursework

Mrs.

Johnson

Introduction

The task that I am set is to find a formula connecting the area of a shape to the number of dots that lie inside the shape. I am going to do a number  of mini investigations to help me find a suitable formula. I must use as many investigations as I need to discover a formula and will show all the necessary investigations I need. First of all I will start off with the shapes with no dots inside and try to find

Middle

Rule-no. Of dots joined

2

Prediction-I predict that when 20 dots are joined the area will be 10cm .

My prediction was correct.

Formula- D= No. Of dots joined          A=D

A= Area                                     2

Jonathan parsonage

investigation three. Two dots inside shape.

Number of dots joined          Area(cm )

6                                   4

8                                        5

106

12                                7

14                                 8

16                                 9

prediction   20                                 11

Rule- no. Of dots joined  +1

2

Prediction-I predict that when 20 dots are joined,

the area will be 11cm .

My prediction was correct.

Formula- D= No. Of dots joined         A= D +1

A= Area                                     2

Jonathan parsonage

investigation four.

Conclusion

No. Of dots inside              Formula

0D -1

2

1D

2

2D +1

2

3D  +2

2

Rule-dots joined + dots inside -1

2

Formula- D= Dots joined                  A= D+ I -1

I= Dots inside                         2

A= Area

Prediction- I predict that when a shape with five dots inside increases in area, then the formula for it will be D+4.

2

Jonathan Parsonage

investigation for prediction made in conclusion (five dots joined)

Number of dots joined          Area(cm )

16                                 6

18                                 7

208

22                                9

24                                 10

prediction    28                                 12

Rule- No. Of dots joined +4

2

Prediction- I predict that when 28 dots are joined,

the area will be 12cm .

My prediction was correct.

Formula- D= Dots joined     A= D +4

A= Area                      2

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