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Pythagorean Probe

Use Pythagoras' Theorem to help find all of the measurements of these right angles triangles.

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This is level 1: given the lengths of two sides. The diagrams are not drawn to scale. Include the letters 'cm' when labelling sides but the units of perimeters and areas are already typed for you.

1

Perimeter =

cm

Area =

cm2

2

Perimeter =

cm

Area =

cm2

3

Perimeter =

cm

Area =

cm2

4

Perimeter =

cm

Area =

cm2

5

Perimeter =

cm

Area =

cm2

6

Perimeter =

cm

Area =

cm2

Check

This is Pythagorean Probe level 1. You can also try:
Level 2 Level 3 Level 4 Level 5 Level 6

Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

Why am I learning this?

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 10 September 'Starter of the Day' page by Carol, Sheffield PArk Academy:

"3 NQTs in the department, I'm new subject leader in this new academy - Starters R Great!! Lovely resource for stimulating learning and getting eveyone off to a good start. Thank you!!"

Comment recorded on the 16 March 'Starter of the Day' page by Mrs A Milton, Ysgol Ardudwy:

"I have used your starters for 3 years now and would not have a lesson without one! Fantastic way to engage the pupils at the start of a lesson."

Whose Idea Was This?

Did you enjoy doing this 'Pythagorean Probe' activity? Are you curious about who originally came up with this idea in Maths? Discover more about one of the mathematicians who is associated with this concept.

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Description of Levels

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Pythagoras' Theorem Exercise - This would be a good place to start if you are a Pythagoras beginner.

Level 1 - Given the lengths of two sides

Suitable for
Years 8 to 10

Level 2 - Given two sides in different units

Level 3 - Given one short side and the area

Level 4 - Given two measurements

Suitable for
Years 11 to 13

Level 5 - Given algebraic expressions for sides

Level 6 - Given expressions for the perimeter and area

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

More on this topic including lesson Starters, visual aids, investigations and self-marking exercises.

This exercise was inspired by a recource shared on Twitter by Nathan Day @nathanday314

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

Help

Did you do the main Pythagoras' Theorem Exercise yet? This is the video that mas made to help you with that exercise.

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen. A tick or a cross will only appear if something has been typed into all of the input boxes for that question.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Log in Sign up

This exercise was inspired by a recource shared on Twitter by Nathan Day @nathanday314

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