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Introduction to Pythagoras' Theorem for Building Students

This resource provides an introduction to Pythagoras' Theorem and its application in roofing calculations. It covers the square and square root of numbers, as well as calculating missing lengths in triangles. It also explains how to determine rafter lengths and check for right angles in roofing. Suitable for Functional Skills Maths, with curriculum links provided.

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Introduction to Pythagoras' Theorem for Building Students

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

  2. Pythagoras’ Theorem Please note this is an animated PPT and should be run full screen

  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

  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

  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

  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 12cm 5cm 3cm 5 cm

  9. Pythagoras’ Theorem • What is the missing length? 24cm 26cm 10cm

  10. Pythagoras’ Theorem • Calculate the height of this triangle: 5cm 5cm 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 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

  13. Rafter Lengths • If a roof has a rise of 6m and a run of 8m, what length rafters do you need? • Answer:10m

  14. To check a right angle: 3m 4m 5m If you can make a triangle with the lengths shown then the angle between the short sides MUST be a right angle.

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