# Maths Dots Investigation

Extracts from this document...

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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