Topic 8 Year 9 Mathematics
Mathematics | |||
Topic | Pythagoras' Theorem | ||
No of lessons | 8 | ||
When is it happening | Term 2 | ||
What will students learn |
Understand that radical notation can be used to describe slanted non_x0002_integer lengths and how this relates to squares and right-angled triangles. Be able to find any missing length of a right-angled triangle by knowing that the square of the hypotenuse is equal to the sum of the squares of the other two sides. Be able to identify opportunities to use Pythagoras’s theorem in non-obvious contexts. Understand that perpendicular lines are often an opportunity to use Pythagoras’ theorem |
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Key Knowledge that students should know at the end of 'Topic' | This is the knowledge that students will meet for the first time in this topic | Radicals are used to express side lengths of tilted squares. Students look at and compare representations for the side lengths. Students connect tilted squares to right-angled triangles. The hypotenuse is introduced and students look at methods of finding the length of a hypotenuse. Pythagoras’ theorem is formally introduced with a geometric representation. The formula is used to find the length of the hypotenuse. Students look at undoing Pythagoras’ theorem to find the non-hypotenuse sides (catheti) of a right-angled triangle. Non-routine contexts for Pythagoras’ theorem are introduced, such as isosceles triangles, rectangles, and a context that is a focus later in the week – the Cartesian plane. After looking at non-routines contexts with drawn hypotenuses in lesson 1, students begin trying to spot opportunities to find the hidden opportunities to use Pythagoras’ theorem. | |
This is knowledge that students may have met before but will need to deepen their understanding | Students revise squares and square roots | ||
Key Skills that students should be able to demonstrate at the end of 'Topic' | This is the skills that students will meet for the first time in this topic | Identify right angled triangles, | |
This is skills that students may have met before but will need to develop | Squares & roots of a number | ||
Key vocabulary that students should know and understand | |||
The Big Question | What is Pythagoras? | ||
Key questions that students should be able to answer at the end of the 'Topic' |
Can you find the area of squares on squared paper and use the area to find the side length? | ||
Can you identify, describe and define the hypotenuse of a right-angled triangle? | |||
Can you find the length of the hypotenuse if the other two sides are given? | |||
Can you find any missing side length of a right-angled triangle? | |||
Can you use Pythagoras’ theorem to find the diagonal of a rectangle and height of an isosceles triangle? | |||
Can you edit and annotate diagrams to find opportunities for using Pythagoras’ theorem to find out new information? | |||
Can you use Pythagoras to find distances in 3D shapes? | |||
Can you find the distance between any two coordinate pairs – using Pythagoras? |