There are 366 different Starters of The Day, many to choose from. You will find in the left column below some starters on the topic of Pythagoras. In the right column below are links to related online activities, videos and teacher resources.

A lesson starter does not have to be on the same topic as the main part of the lesson or the topic of the previous lesson. It is often very useful to revise or explore other concepts by using a starter based on a totally different area of Mathematics.

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### Pythagoras Starters:

Bizarre Triangle: By how much would the area of this triangle increase if its base was enlarged to 8cm?

Red Lines: Either estimate the lengths of the red lines or, if you know how, calculate how long they are.

Square Thinkers: Can you find three square numbers where the third is the sum of the first two?

Coordinate Distance: Find k given that(-2,k) is 13 units away from (10,9)

Tan 22.5: Find an exact value for tan 22.5° without using a calculator.

Three Right Triangles: Calculate the lengths of the unlabelled sides of these right-angled triangles.

#### Pythagoras Basics

A drill and practice self marking exercise on the basics of Pythagoras' theorem.

Transum.org/go/?to=pythag

### Curriculum for Pythagoras:

#### Years 7 to 9

Pupils should be taught to apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides, including Pythagoras’ Theorem, and use known results to obtain simple proofs more...

Pupils should be taught to use Pythagoras’ Theorem and trigonometric ratios in similar triangles to solve problems involving right-angled triangles more...

#### Years 10 and 11

Pupils should be taught to apply Pythagoras’ Theorem and trigonometric ratios to find angles and lengths in right-angled triangles {and, where possible, general triangles} in 2 {and 3} dimensional figures more...

### Exam-Style Questions:

There are almost a thousand exam-style questions unique to the Transum website.

### Feedback:

Comment recorded on the s /Coordinate 'Starter of the Day' page by Greg, Wales:

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Comment recorded on the 19 June 'Starter of the Day' page by Nikki Jordan, Braunton School, Devon:

"Excellent. Thank you very much for a fabulous set of starters. I use the 'weekenders' if the daily ones are not quite what I want. Brilliant and much appreciated."

Comment recorded on the 9 October 'Starter of the Day' page by Mr Jones, Wales:

"I think that having a starter of the day helps improve maths in general. My pupils say they love them!!!"

Comment recorded on the 12 July 'Starter of the Day' page by Miss J Key, Farlingaye High School, Suffolk:

"Thanks very much for this one. We developed it into a whole lesson and I borrowed some hats from the drama department to add to the fun!"

Comment recorded on the s /Indice 'Starter of the Day' page by Busolla, Australia:

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Comment recorded on the 3 October 'Starter of the Day' page by S Mirza, Park High School, Colne:

"Very good starters, help pupils settle very well in maths classroom."

Comment recorded on the 23 September 'Starter of the Day' page by Judy, Chatsmore CHS:

"This triangle starter is excellent. I have used it with all of my ks3 and ks4 classes and they are all totally focused when counting the triangles."

Comment recorded on the 11 January 'Starter of the Day' page by S Johnson, The King John School:

"We recently had an afternoon on accelerated learning.This linked really well and prompted a discussion about learning styles and short term memory."

Comment recorded on the 17 November 'Starter of the Day' page by Amy Thay, Coventry:

"Thank you so much for your wonderful site. I have so much material to use in class and inspire me to try something a little different more often. I am going to show my maths department your website and encourage them to use it too. How lovely that you have compiled such a great resource to help teachers and pupils.
Thanks again"

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"A really awesome website! Teachers and students are learning in such a fun way! Keep it up..."

Comment recorded on the 9 April 'Starter of the Day' page by Jan, South Canterbury:

"Thank you for sharing such a great resource. I was about to try and get together a bank of starters but time is always required elsewhere, so thank you."

Comment recorded on the 28 May 'Starter of the Day' page by L Smith, Colwyn Bay:

"An absolutely brilliant resource. Only recently been discovered but is used daily with all my classes. It is particularly useful when things can be saved for further use. Thank you!"

Comment recorded on the 14 October 'Starter of the Day' page by Inger Kisby, Herts and Essex High School:

"Just a quick note to say that we use a lot of your starters. It is lovely to have so many different ideas to start a lesson with. Thank you very much and keep up the good work."

Comment recorded on the 26 March 'Starter of the Day' page by Julie Reakes, The English College, Dubai:

"It's great to have a starter that's timed and focuses the attention of everyone fully. I told them in advance I would do 10 then record their percentages."

Comment recorded on the 10 April 'Starter of the Day' page by Mike Sendrove, Salt Grammar School, UK.:

"A really useful set of resources - thanks. Is the collection available on CD? Are solutions available?"

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To the creator of this website and all of those teachers who have contributed to it, I would like to say a big THANK YOU!!! :)."

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"I would like to thank you for the excellent resources which I used every day. My students would often turn up early to tackle the starter of the day as there were stamps for the first 5 finishers. We also had a lot of fun with the fun maths. All in all your resources provoked discussion and the students had a lot of fun."

Comment recorded on the 7 December 'Starter of the Day' page by Cathryn Aldridge, Pells Primary:

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I rate this site as a 5!"

Comment recorded on the 1 August 'Starter of the Day' page by Peter Wright, St Joseph's College:

"Love using the Starter of the Day activities to get the students into Maths mode at the beginning of a lesson. Lots of interesting discussions and questions have arisen out of the activities.
Thanks for such a great resource!"

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"Find the starters wonderful; students enjoy them and often want to use the idea generated by the starter in other parts of the lesson. Keep up the good work"

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Keep it up and thank you!"

Comment recorded on the 19 October 'Starter of the Day' page by E Pollard, Huddersfield:

"I used this with my bottom set in year 9. To engage them I used their name and favorite football team (or pop group) instead of the school name. For homework, I asked each student to find a definition for the key words they had been given (once they had fun trying to guess the answer) and they presented their findings to the rest of the class the following day. They felt really special because the key words came from their own personal information."

Comment recorded on the 6 May 'Starter of the Day' page by Natalie, London:

"I am thankful for providing such wonderful starters. They are of immence help and the students enjoy them very much. These starters have saved my time and have made my lessons enjoyable."

Comment recorded on the 1 May 'Starter of the Day' page by Phil Anthony, Head of Maths, Stourport High School:

"What a brilliant website. We have just started to use the 'starter-of-the-day' in our yr9 lessons to try them out before we change from a high school to a secondary school in September. This is one of the best resources on-line we have found. The kids and staff love it. Well done an thank you very much for making my maths lessons more interesting and fun."

Comment recorded on the 14 September 'Starter of the Day' page by Trish Bailey, Kingstone School:

"This is a great memory aid which could be used for formulae or key facts etc - in any subject area. The PICTURE is such an aid to remembering where each number or group of numbers is - my pupils love it!
Thanks"

Comment recorded on the 1 February 'Starter of the Day' page by Terry Shaw, Beaulieu Convent School:

"Really good site. Lots of good ideas for starters. Use it most of the time in KS3."

Comment recorded on the 1 February 'Starter of the Day' page by M Chant, Chase Lane School Harwich:

"My year five children look forward to their daily challenge and enjoy the problems as much as I do. A great resource - thanks a million."

Comment recorded on the 21 October 'Starter of the Day' page by Mr Trainor And His P7 Class(All Girls), Mercy Primary School, Belfast:

"My Primary 7 class in Mercy Primary school, Belfast, look forward to your mental maths starters every morning. The variety of material is interesting and exciting and always engages the teacher and pupils. Keep them coming please."

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### Notes:

Pythagoras was a Greek philosopher, mathematician, and founder of the religious movement called Pythagoreanism. He is most famous for his theorem connecting the lengths of the sides of right angled triangles.

His theorem states that the squares of the lengths of the two shorter sides of any right-angled triangle will add up to the square of the length of the longest side (the hypotenuse).

This theorem can be used to calculate the length of any side of a right-angled triangle if the lengths of the other two sides are known.

Do you know when the next Pythagorean Day is? It will occur when the square of the day added to the square of the month equals the square of the last two digits of the year.

### Pythagoras Teacher Resources:

3D Trigonometry Presentation: A slide presentation (a poem) introducing using trigonometry (including Pythagoras' Theorem) to find lengths and angles on three dimensional shapes.

### Pythagoras Activities:

Pythagoras Basics: A drill and practice self marking exercise on the basics of Pythagoras' theorem.

Pythagoras: An online exercise to test your understanding of and ability to apply Pythagoras' Theorem.

Make Them Right: Arrange the measurements next to the sides of the triangles so that each diagram is correct according to Pythagoras' Theorem.

Where's Wallaby?: Find the hidden wallaby using the clues revealed at the chosen coordinates.

Trig-Pythag Fusion: Problems requiring multi-step solutions using both Trigonometry and Pythagoras' Theorem

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

Alternatively, for the more advanced student, there is an ever-growing collection of Exam-Style Questions with worked solutions on the topic of Pythagoras.

### Pythagoras Videos:

Transum's Pythagoras Video

Demonstrating Pythagoras: Short clip from QI: Stephen Fry demonstrates Pythagoras' theorem.

Pythagoras' Theorem Demonstration: Wheel with liquid demonstrates the Pythagorean theorem at Brentwood.

A Mathematical Fable: It's not just the squares on the sides of right angles triangles that add up!

Pythagoras' Theorem Video: The square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides.

Trigonometry and Pythagoras: A trigonometry and Pythagoras theorem revision song

Links to other websites containing resources for Pythagoras are provided for those logged into 'Transum Mathematics'. Subscribing also opens up the opportunity for you to add your own links to this panel. You can sign up using one of the buttons below:

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#### Pythagorean Probe

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

Transum.org/go/?to=pythagprobe

### Teaching Notes:

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QI,

Wednesday, June 12, 2019

"The Babylonians were using Pythagoras' Theorem over 1,000 years before Pythagoras was born."

Transum,

Wednesday, August 21, 2019

"Did you know that the area of the regular pentagon on the hypotenuse of a right-angled triangle is equal to the sum of the areas of the regular pentagons on the other two sides?

Can you prove that it is true?

Wikepedia,

Thursday, May 28, 2020

"Proof of the Pythagorean Theorem:
"

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