1. Functional Skills Maths An introduction to Pythagoras’ theorem for building (roofing) students
February Kindly contributed by Louise Dumbell.
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Please refer to the download page for this resource on skillsworkshop.org for detailed curriculum links and related resources.
Curriculum links
Adult Numeracy
N1/L2.4: Evaluate expressions and make substitutions in given formulae in words and symbols to produce results
Underpins the following L2 Functional Maths coverage & range statements
Understand and use simple formulae and equations involving one- or two-step operations.
Carry out calculations with numbers of any size in practical contexts, to a given number of decimal places
References: Excellence Gateway (2009), Skills for Life, Core Curriculum
Ofqual (2009), Functional Skills criteria for English, Mathematics and ICT
Feb Kindly contributed to by Louise Dumbell.

2. Please note this is an animated PPT and should be run full screen
Pythagoras’ Theorem
Please note this is an animated PPT and should be run full screen
Feb Kindly contributed to by Louise Dumbell.
This PowerPoint was used to introduce Pythagoras Theorem to E3 and L1 college students whose main course work is to do with the Building Trades. The last 4 slides therefore deal with using Pythagoras to calculate the length of roof rafters.

3. Square and square root of numbers
What does 32 mean?
3 x 3 = 9
What does 42 mean?
4 x 4 = 16
What does 102 mean?
10 x 10 = 100
Feb Kindly contributed to by Louise Dumbell.

4. Square and square root of numbers
What does the symbol mean?
Square root – i.e. What number do you multiple by itself to get the original number?
What is √4 ?
2x2=4 so the √4 is 2
What is √9 ?
3x3=9 so the √9 is 3
Feb Kindly contributed to by Louise Dumbell.

5. Pythagoras’ Theorem What is Pythagoras’ Theorem used for?
Given 2 sides of a right angled triangle to calculate the 3rd.
What is a right angled triangle?
What is the side opposite the right angle called?
Hypotenuse
Feb Kindly contributed to by Louise Dumbell.

6. Pythagoras’ Theorem c2=a2+b2 Area = c x c = c2 Area = a x a = a2
Area = b x b = b2

7. Pythagoras’ Theorem
If “c” is the hypotenuse and “a” and “b” are the other 2 sides then:
c2=a2+b2

8. Pythagoras’ Theorem Calculate the missing lengths on these triangles:
13cm
4cm cm
5cm
3cm cm
Feb Kindly contributed to by Louise Dumbell.

9. Pythagoras’ Theorem What is the missing length? 24cm 26cm 10cm
Feb Kindly contributed to by Louise Dumbell.

10. Pythagoras’ Theorem Calculate the height of this triangle: 5cm 5cm
Feb Kindly contributed to by Louise Dumbell.
c2=a2+b2 so b2=c2-a2 =
52-(6÷2)2 = 25-9 = 16
b=√16 = 4
6cm

11. Cut roofing Rafter Rise Run Span
Feb Kindly contributed to by Louise Dumbell.
Span
If you know the Rise of a roof and the Span (or Run) then you can calculate the Rafter length.

12. Rafter Lengths
If a roof has a rise of 4m and a run of 3m, what length rafters do you need?
Answer: 5m
Feb Kindly contributed to by Louise Dumbell.

13. Rafter Lengths
If a roof has a rise of 6m and a run of 8m, what length rafters do you need?
Answer:10m
Feb Kindly contributed to by Louise Dumbell.

14. To check a right angle: 3m 4m 5m
Feb Kindly contributed to by Louise Dumbell.
If you can make a triangle with the lengths shown then the angle between the short sides MUST be a right angle.