Maths-hidden faces

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Mathematics GCSE coursework: hidden faces              Tina Harris

Aim: 

To find a rule in algebra to reveal how many hidden faces there are in a row of cubes, and to use dimensions and the number of shown faces to work out the number of hidden faces in cuboids.

Part 1-Investigating the number of hidden faces in rows of cubes

Introduction: 

This part of the investigation is about how many hidden faces there are in a row of cubes. I will be investigating how to work out the number of hidden faces in a row of cubes in algebra, whilst using the number of cubes in a row in the expression, e.g. Number of hidden faces = number of cubesa specific number. I will also be showing how to work out the number of hidden faces in a row without counting, but instead by using an expression. To prove the expression works I will test and predict the amount of hidden face in a row of cubes by using the rule in algebra. If the rule works then I will be able to explain it and draw diagrams to test the rule in algebra.

Results:

Rule: h=3n–2

Key: h=hidden faces, n=number of cubes

Explanation of rule:

I found my rule by looking at the number of hidden faces on the row of cubes. For each cube in the middle of the row, there are three faces showing and three faces hidden so the first part of my rule was 3n. At the end of each row there are only 2 hidden faces so that is why you have to –2 from the total number of hidden faces.

1.) Test and predict:

Predict:

Number of cubes=9

Using the rule, I predict that for 9 cubes there will be 25 hidden faces.

9x3=27-2=25

Test: I drew out the number of cubes showing the hidden faces, which gave the same answer as my prediction, which proves that my rule is correct.

Predict:

Number of cubes=10

Using the rule, I predict that for 10 cubes there will be 28 hidden faces.

10x3=30-2=28

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Test: I drew a diagram showing that a row of 10 cubes has 28 hidden faces, so yet again this confirms the fact that the rule h=3n-2 is correct.  

2nd Rule: h=2(n-1)+n

Key: h=hidden faces, n=number of cubes

Predict:

Number of cubes=11

Using this rule, I predict that for 11 cubes there will be 31 hidden faces.

2(11-1) =22-2=20+11=31

Test: I drew another diagram showing that a row of 11 cubes has 31 hidden faces, so this confirms the fact that the rule 2(n-1) +n also works.  

Explanation of rule:

The same rules and explanations apply to this rule as ...

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