• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

To see if three horizontal rectangle numbers e.g. “12,13,14” – have the same result when you multiply the middle number by 2 and add the 1st and last number together.

Extracts from this document...

Introduction

image00.png

Diagram.1

image01.png

Case.1:

To see if three horizontal rectangle numbers e.g. “12,13,14” – have the same result when you multiply the middle number by 2 and add the 1st and last number together.

Testing:

image04.png

image00.png

Conclusion:

This happens because the mean of the 1st and last number is equal to the middle number i.e.:        

Mean of 12 and 14 = 13

Middle number = 13

The next part of the scenario was to multiply the middle number by 2 and plus the 1st and last number together;

...read more.

Middle

image00.png

Conclusion:

The original formula (Case.1) also works for Variable.2.

Case.3:

Investigate what happens when Mary draws a rectangle around five numbers.

Testing:

I first tried to see if the formula for Case.1 applied for Case.3:

image06.png

Conclusion:

The formula for Case.3 also works for rectangles with 5 squares whether it is diagonal, horizontal or vertical.

Case.4

Investigate if the formula also works for any amount of rectangle squares:

image00.png

Testing:

image07.png

Conclusion:

After doing the previous scenarios I have realised that

...read more.

Conclusion

71,73,93,91=image02.png

image03.png

Conclusion:

We found out that it is possible to find out the middle number by finding the sum of the parameter and then dividing it by the parameter (squares on the outside.) Another way of finding the middle number was to take two diagonally opposite corners and divide by 2. This works as it is the same as diagonal rectangles (see case.2)


image00.png

Formula:

n.b         = parameter.

 = Sum of parameter.

Error! Not a valid link. = Middle number.

Error! Not a valid link. =

Or

Error! Not a valid link. = Two diagonally opposite corners  2

...read more.

This student written piece of work is one of many that can be found in our GCSE Consecutive Numbers section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related GCSE Consecutive Numbers essays

  1. GCSE Maths Coursework - Maxi Product

    5+5+4 --> 5x5x4 =100 I am now going to use decimal numbers as I have found the highest possible result in whole numbers. I will see in decimal numbers if I can retieve a higher result than 100 when three numbers are multiplied together.

  2. Investigate the Maxi Product of numbers

    (6 2/13, 6 11/13)=13 à 6 2/13+6 11/13 à 6 2/13x6 11/13=42.13 (2dp) I have found that 6.5 and 6.5 are the two numbers which added together make 13 and when multiplied together make 42.25 which is the highest possible answer which is retrieved when two numbers added together equal 13 are multiplied.

  1. Consecutive Numbers Investigation

    = 11*11 = 121 Difference 57 18, 21 182 = 18*18 = 324 212 = 21*21 = 441 Difference 117 It would appear that it works every time, I have tried it three times and it works all right so far.

  2. In this investigation I will explore the relationship between a series of straight, non-parallel, ...

    In this diagram there are: Number of Lines (n) Cross-Over Points Open Regions Closed Regions Total Regions 1 0 2 0 2 2 1 4 0 4 3 3 6 1 7 4 6 8 3 11 Diagram 5: (all 5 lines cross each other, regions are depicted with numbers, crossover points are high-lighted with red circles)

  1. I am to conduct an investigation involving a number grid.

    now calculated the 5 x 5 boxes using a 10 x 10 grid and have learned that the number which I predicted was accurate and correct. This determines that the formula that I chose to use was the proper one to do this certain part of the investigation with.

  2. Borders and squares

    Sequence of 7: 61+20+4= 85 Sequence of 8: 85+24+4=113 Sequence of 9: 113+28+4=145 Sequence of 10: 145+32+4=181 Sequence of 11: 181+36+4=221 Sequence of 12: 221+40+4=265 61 85 113 145 181 221 265 24 28 32 36 40 44 +4 +4 +4 +4 +4 From all of these we can see that the formula is right.

  1. Investigating a Sequence of Numbers.

    - 1! + (2 + 2)! - 2! + (3 + 2)! - 3! + (n + 2)! - n! = (n + 1)! + (n + 2)! - 3 Tn = c1 + c2 + c3 + c4 + c5 + ......

  2. To investigate consecutive sums. Try to find a pattern, devise a formulae and establish ...

    + 16 = 45 15 + 16 + 17 = 48 16 + 17 + 18 = 51 17 + 18 + 19 = 54 18 + 19 + 20 = 57 19 + 20 + 21 = 60 Prediction Although possibly premature, as it is common practice to use

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work