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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

...read more.

Middle

Rule-no. Of dots joined

                           2

Prediction-I predict that when 20 dots are joined the area will be 10cmimage00.png.

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(cmimage00.png)

               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 11cmimage00.png.

My prediction was correct.

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

                 A= Area                                     2  

Jonathan parsonage

 investigation four.

...read more.

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(cmimage00.png)

               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 12cmimage00.png.

                   My prediction was correct.

Formula- D= Dots joined     A= D +4

                 A= Area                      2

...read more.

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