Functional Skills MathsAn introduction to Pythagoras’ theorem for building (roofing) students

Curriculum linksAdult NumeracyN1/L2.4: Evaluate expressions and make substitutions in given formulae in words and symbols to produce resultsUnderpins the following L2 Functional Maths coverage & range statementsUnderstand 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 http://www.excellencegateway.org.uk/sflcurriculum Ofqual (2009), Functional Skills criteria for English, Mathematics and ICT http://www2.ofqual.gov.uk/qualifications-assessments/89-articles/238-functional-skills-criteria

February 2013. Kindly contributed by Louise Dumbell. Search for Louise on www.skillsworkshop.org Please refer to the download page for this resource on skillsworkshop.org for detailed curriculum links and related resources.

Pythagoras’ Theorem

Please note this is an animated PPT and should be run full screen

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

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

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

Pythagoras’ Theorem

c2=a2+b2

Area = c x c = c2

Area = a x a = a2

Area = b x b = b2

Pythagoras’ Theorem

• If “c” is the hypotenuse and “a” and “b” are the other 2 sides then:

• c2=a2+b2

Pythagoras’ Theorem

• Calculate the missing lengths on these triangles:

13cm4cm 12cm

5cm

3cm 5 cm

Pythagoras’ Theorem

• What is the missing length?

24cm 26cm

10cm

Pythagoras’ Theorem

• Calculate the height of this triangle:

5cm

6cm

5cm

c2=a2+b2 so b2=c2-a2 =52-(6÷2)2 = 25-9 = 16

b=√16 = 4

Cut roofing

RafterRise

Span

Run

If you know the Rise of a roof and the Span (or Run) then you can calculate the Rafter length.

Rafter Lengths

• If a roof has a rise of 4m and a run of 3m, what length rafters do you need?

• Answer: 5m

Rafter Lengths

• If a roof has a rise of 6m and a run of 8m, what length rafters do you need?

• Answer:10m

To check a right angle:

4m

3m

5m

If you can make a triangle with the lengths shown then the angle between the short sides MUST be a right angle.