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Original “The Classroom” concept developed by Schools OUT UK

PYTHAGORAS’ THEOREM

Subject: Maths Key Stage 4

Helping you to deliver an LGBT+ INCLUSIVE CURRICULUM

Pythagoras’ Theorem | Maths | Key Stage 4

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KS4 Maths National Curriculum:

• Apply Pythagoras’ Theorem and trigonometric ratios to find angles and lengths in right-angled triangles (and, where possible, general triangles) in two (and three) dimensional figures.

Students can:

• State Pythagoras’ Theorem as a short equation. • Calculate the length of the hypotenuse using the equation. • Apply and rearrange the equation to real-life situations to find missing values.

Supplied:

• PowerPoint, with printable slide 4 Needed:

• Scientific Calculators • Scissors

1. Read the lesson plan and familiarise yourself with the PowerPoint and activities. 2. Print slide 4, one copy per two students.

Aims

Resources

Preparation

Learning Intentions

Pythagoras’ Theorem | Maths | Key Stage 4

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Time Slide(s) Activity Method

5 mins 5-7

Starter

Previous lesson recap. Easier: Where can we find examples of triangles being used? Harder: What do you know about the shape of triangles?

5 mins 8

9

Big Picture Learning Intentions

If a firefighter has to reach a window 12m above the ground and their ladder is 15m long, how far from the bottom of the wall should they put their ladder? (The Big Picture links lesson content to the real world and events happening outside of school. It acts as a point of interest to inspire conversations and engage students.) Opportunity to share the learning intentions, date and title.

5 mins 10 New Material Share the equation: a2 + b2 = c2 ASK: Over 2000 years ago Pythagoras made this discovery about triangles. How do you think we could prove this is correct?

10 mins 11-12 Prove It Give a printed diagram (from slide 4), and some scissors, to each student. All:

1. Carefully cut out the whole shape 2. Cut off squares A and B 3. Cut along the lines inside square B to split it into

four pieces 4. You should be able to arrange square A and the four

pieces of square B so they all fit inside of square C ASK: How would we calculate c?

10 mins 13-14 Review and Reflect All: Apply the equation to each triangle to calculate the length of the hypotenuse. a= 5cm b= 12cm c= ? (13cm) a= 4cm b= 2cm c= ? (4.47cm) a= 14cm b= 3cm c= ? (14.34cm)

Pythagoras’ Theorem | Maths | Key Stage 4

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5 mins 15-16

Whiteboards All: Rearrange a2 + b2 = c2for a and b

10 mins 17-18 Review and Reflect Easier: a= 15cm b= ? c= 17cm a= 4cm b= 8cm c= ? a= ? b= 10cm c= 12cm Harder: a= ? b= 13.5cm c= 14.6cm a= 3.4cm b= 7.1cm c= ? See slide 17 for third question Hardest: See slide 17 Answers on slide 18.

5 mins 19-22 Deepen Your Understanding

Easier: Justice’s house is exactly 502m from school. To get home they walk 480m South and then they walk West. How far West do they walk? Answer: 146.98m. Harder: Aisha and her girlfriend are buying a TV. It has a 34-inch screen and is 16 inches tall. Her TV cabinet is 19 inches wide. Will it fit? Answer: The TV is 30 inches wide so will not fit. Hardest: Mr and Mr Jacobs have an oddly shaped window in their home. It has the measurements shown (slide 21). They want to buy a curtain for the window, how wide should the curtain be? Answer: 52cm.

5 mins 23-24 Big Picture Students should be able to answer the big picture question with what they have learnt in this lesson. This can be used as the final progress measure. All: If a firefighter has to reach a window 12m above the ground and their ladder is 15m long, how far from the bottom of the wall should they put their ladder? Answer: 9m.