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?
Small images of these Starters :: Index of Starters Pythagoras Advanced Starters:Coordinate Distance: Find k given that(2,k) is 13 units away from (10,9) Tan 22.5: Find an exact value for tan 22.50 without using a calculator. Three Right Triangles: Calculate the lengths of the unlabelled sides of these rightangled triangles.
Curriculum for Pythagoras:Years 7 to 9Pupils 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 rightangled triangles more... Years 10 and 11Pupils should be taught to apply Pythagoras’ Theorem and trigonometric ratios to find angles and lengths in rightangled triangles {and, where possible, general triangles} in 2 {and 3} dimensional figures more... Feedback:Comment recorded on the 8 May 'Starter of the Day' page by Mr Smith, West Sussex, UK: "I am an NQT and have only just discovered this website. I nearly wet my pants with joy. 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 17 June 'Starter of the Day' page by Mr Hall, Light Hall School, Solihull: "Dear Transum, Comment recorded on the 18 September 'Starter of the Day' page by Mrs. Peacock, Downe House School and Kennet School: "My year 8's absolutely loved the "Separated Twins" starter. I set it as an optional piece of work for my year 11's over a weekend and one girl came up with 3 independant solutions." 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 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." 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! Comment recorded on the 28 September 'Starter of the Day' page by Malcolm P, Dorset: "A set of real life savers!! 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 'starteroftheday' 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 online 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 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." Comment recorded on the 9 May 'Starter of the Day' page by Liz, Kuwait: "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 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?" 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 25 June 'Starter of the Day' page by Inger.kisby@herts and essex.herts.sch.uk, : "We all love your starters. It is so good to have such a collection. We use them for all age groups and abilities. Have particularly enjoyed KIM's game, as we have not used that for Mathematics before. Keep up the good work and thank you very much 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 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 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 2 May 'Starter of the Day' page by Angela Lowry, : "I think these are great! So useful and handy, the children love them. 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 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. 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 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 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 3 October 'Starter of the Day' page by Fiona Bray, Cams Hill School: "This is an excellent website. We all often use the starters as the pupils come in the door and get settled as we take the register." 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 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 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 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 5 April 'Starter of the Day' page by Mr Stoner, St George's College of Technology: "This resource has made a great deal of difference to the standard of starters for all of our lessons. Thank you for being so creative and imaginative." Comment recorded on the 19 November 'Starter of the Day' page by Lesley Sewell, Ysgol Aberconwy, Wales: "A Maths colleague introduced me to your web site and I love to use it. The questions are so varied I can use them with all of my classes, I even let year 13 have a go at some of them. I like being able to access Starters for the whole month so I can use favourites with classes I see at different times of the week. Thanks." 
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. 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. Alternatively, for the more advanced student, there is an evergrowing collection of ExamStyle Questions with worked solutions on the topic of Pythagoras. Pythagoras Videos:Demonstrating Pythagoras' theorem: 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 rightangled triangle is equal to the sum of the squares of the other two sides. Trigonometry and Pythagoras: A trigonometry and Pythagoras theorem revision song Pythagoras External Links: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: SearchThe activity you are looking for may have been classified in a different way from the way you were expecting. You can search the whole of Transum Maths by using the box below.

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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 rightangled 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?
What about other shapes?"
Wikepedia,
Thursday, May 28, 2020
"Proof of the Pythagorean Theorem:
"