Myths about teaching can hold you back
- Year 10•
- Higher
Applying Pythagoras' theorem in 3D
I can apply knowledge of Pythagoras' theorem to 3D problems.
- Year 10•
- Higher
Applying Pythagoras' theorem in 3D
I can apply knowledge of Pythagoras' theorem to 3D problems.
Lesson details
Key learning points
- For packing efficiency, it can be useful to know the length of the longest diagonal
- This would be from a bottom corner of a rectangular box, to the opposite top corner
- You can construct a right-angled triangle to calculate this
- You will need to know the length of the diagonal of the base of the box
- There is a formula you can deduce to calculate the longest diagonal
Keywords
Hypotenuse - The hypotenuse is the side of a right-angled triangle which is opposite the right angle.
Pythagoras' theorem - Pythagoras’ theorem states that the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of the hypotenuse.
Cross-section - A cross-section is a 2D face made from cutting straight through any plane of a 3D object.
Common misconception
Pythagoras' theorem cannot be applied to 3D shapes.
Pupils may benefit from imaging the cuboid is 'sliced' through and a triangle drawn on the now visible face.
To help you plan your year 10 maths lesson on: Applying Pythagoras' theorem in 3D, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 10 maths lesson on: Applying Pythagoras' theorem in 3D, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
Our video is a tool for planning, showing how other teachers might teach the lesson, offering helpful tips, modelled explanations and inspiration for your own delivery in the classroom. Plus, you can set it as homework or revision for pupils and keep their learning on track by sharing an online pupil version of this lesson.
Explore more key stage 4 maths lessons from the Right-angled trigonometry unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
Prior knowledge starter quiz
6 Questions
Q1.The relationship between the hypotenuse and the two short sides on a right-angled triangle is known as ' theorem.
Q2.Work out the the length of the hypotenuse, to 1 decimal place.

Q3.Work out the the length of the hypotenuse, to 1 decimal place.

Q4.Work out the length of the third side of the triangle, to 3 significant figures.

Q5.Work out the length of the third side of the triangle, to 3 significant figures.

Q6.A football pitch is 115 yards by 74 yards. What is the distance diagonally from one corner flag to the other? Give your answer to the nearest yard.
Assessment exit quiz
6 Questions
Q1.Which of these are right-angled triangles?



Q2.Given that DE = 6 cm and EH = 15 cm, what is the length of DH, to 1 decimal place?

Q3.Given that BG = 9 cm and GE = $$7\sqrt{2}$$ cm, what is the length of BE, to 1 decimal place?

Q4.If AF, FE and FH are known, which other length do we need, in order to calculate the volume of this cuboid?

Q5.Given that AF = 5 cm, FE = 12 cm and FH = 15 cm, work out the length of EH.

Q6.Given that AF = 5 cm, FE = 12 cm and FH = 15 cm, the volume of the cuboid ABCDEFGH is $$\text{ cm}^3$$
