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Activity 1 - Pythagoras’ Theorem dissection proof
Activity 1 - Pythagoras’ Theorem dissection proof
Today we will begin to piece together the wonderful formula generated many years ago, Pythagoras’ Theorem. To do so, we are going to use some hands on materials.
You will need to have the following things ready before you start:
A4 piece of paper
pencil
ruler
scissors.
Task 1 - Why Pythagoras' Theorem?
Task 1 - Why Pythagoras' Theorem?
Watch the video, Pythagoras' Theorem (1 of 3: Introduction).
Pythagoras' Theorem (1 of 3: Introduction)
Duration: 5:40
Task 2- Pythagoras' Theorem Dissection
Task 2- Pythagoras' Theorem Dissection
Watch the video Pythagoras' Theorem (2 of 3: Dissection Proof) and follow the instructions in the video, to create a visual representation of Pythagoras’ Theorem.
Paste your completed representation into your workbook or add it to your folder.
Pythagoras' Theorem (2 of 3: Dissection Proof)
Duration: 9:42
Activity 2 - Pythagorean triads
Activity 2 - Pythagorean triads
Task 1 - Pythagoras' Theorem summary
Task 1 - Pythagoras' Theorem summary
Watch the video, Pythagoras' Theorem (3 of 3: Summary).
Write the formula and the Pythagorean triad example in your workbook or folder
Pythagoras' Theorem (3 of 3: Summary)
Duration: 5:40
Task 2 - Pythagorean triads
Task 2 - Pythagorean triads
See if you can discover more Pythagorean triads using the Geogebra applet.
Open the applet in a new tab by clicking on the image.
Write your new triads in your workbook or folder
Need help?
Need help?
Check out the Maths is Fun website Pythagorean Triples if you are getting stuck.
The first one included was 32+42=52.
Activity 3 - Practicing triads
Activity 3 - Practicing triads
Task 1 - More triads
Task 1 - More triads
Visit the Make Them Right page on Transum.org.
Click on the image link to open the activity in a new tab.
Try to match the Pythagorean triads to the sides of the triangles
Task 2 - Other proofs - just for interest.
Task 2 - Other proofs - just for interest.
Watch the video, How many ways are there to prove the Pythagorean theorem?
How many ways are there to prove the Pythagorean theorem?
Duration: 5:16
Activities too easy?
Activities too easy?
Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. (Definition from Fractal Foundation website.)
The Pythagoras tree fractal interactive on Geogebra is a fractal made up of squares arranged to form a right angle triangle using the Pythagoras relationship.
Play around with the fractal and if you feel like it have a go at calculating the area at each stage, so for n=1, n=2, n=3 and so on.
Handing in your work
Handing in your work
Don't forget to hand in the work you completed today!
Your teacher will have told you to do one of the following:
Upload any digital documents you created and any photos you took of your written work to your Learning Management system (MS Teams, Google Classroom for example).
Email any digital documents you created and any photos you took of your written work to your teacher.
Make sure you keep any hand written work you did in your exercise book or folder as your teacher may need to see these when you are back in class.
Student reflection
Student reflection
Let us know how you feel about this lesson.
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