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Mathematically Rich tasks to develop thinking and understanding as well as having a good time .

Mathematically Rich tasks to develop thinking and understanding as well as having a good time . Mitchell Howard. Before there was . . . . T here was . . . . Charles. Anthony. And Ian Lowe. And Doug Clarke. www.maths300.esa.edu.au. International Baccalaureate Middle Years Program (MYP).

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Mathematically Rich tasks to develop thinking and understanding as well as having a good time .

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  1. Mathematically Rich tasks to develop thinking and understanding as well as having a good time. Mitchell Howard

  2. Before there was . . . There was . . . Charles Anthony And Ian Lowe And Doug Clarke

  3. www.maths300.esa.edu.au

  4. International Baccalaureate Middle Years Program (MYP) Students learn best when: (p60) • their prior knowledge is considered to be important • learning is in context • contact is relevant • they can learn collaboratively • the learning environment is provocative • they get appropriate, formative feedback that supports their learning • diverse learning styles are understood and accommodated • they feel secure and their ideas are valued and respected • values and expectations are explicit continued

  5. Students learn best when: continued • there is a culture of curiosity at the school • they understand how learning is judged, and how to provide evidence of their learning • they become aware of and understand how they learn • structured inquiry, critical thinking, learning through experience and conceptual developments are central to teaching in the school • learning is engaging, challenging, rigorous, relevant and significant • they are encouraged in everything they do in school to become autonomous, lifelong learners.

  6. Working Mathematically • Working Mathematically means engaging students in learning to work like a mathematician.

  7. Being a Mathematician

  8. So what is a mathematically rich task?

  9. Protons and Antiprotons Why? this is a thinking lesson But I also have another reason to teach it to you

  10. Matter What is it? Can you use it in a sentence? Anti-Matter Does it Exist?

  11. Scientists in Geneva have created anti-matter, … the amount they created was hardly enough to detect and lasted barely a fraction of a second. Its creation, nevertheless is a landmark… "It really is proof that there is an anti-world," said Dr Walter Oerlert, one of the team that used the Low Energy Anti-proton Ring (Lear) at the European Laboratory for Particle Physics to create a few fleeting atoms of anti-hydrogen… Anti-particles have the same mass as normal particles but an opposite electric charge so when they meet they annihilate each other, releasing a burst of energy… The team of German, Italian and Swiss scientists say they were able to create anti-hydrogen - for about a 30-millionth of a second - by combining single anti-protons and positrons…

  12. Volunteers for demo • [2P, A] • [P, 2A] • [6P, 3A] • [6P, 3A, 3P] Mr H make up 20

  13. Challenge • [2P, 3P, 5A, 7P, 6A, 4A, 3P, 12A] Try Option 1

  14. Remember this one? • [6P, 3A, 3P] Why did this one turn out to have the same amount of Proton’s at the start as it did at the end? Are there other combinations which represent zero? How many other combinations are there So we can make any Proton/Anti-Proton pair we like.

  15. Try these • 3P + 2P = • 3P + 2A = • 3P – 2P = • 3P - 2A = DEMO Putting in the zeros is like turning the escaping energy back into matter. That’s still Science Fiction at the moment, but before 1995, the date of the article, the existence of anti-matter was science fiction too, so perhaps . . .

  16. Option 2 • Then make up 20 questions Challenge 2P + 3P + 5A + 7P – 6A - 4A +3P -12A =

  17. Building views • Need 30 blocks each • Build blocks like • Get out of chair, crouch down in front of your building cover one eye and observe. • It should look like . . . • Now rotate so you are looking at the side view.

  18. Reverse problem: • Remove any buildings you might have and count out exactly 15 blocks. • Sheet 2: Front and side views already given, your challenge is to recreate the design with exactly 15 blocks. • Check: 15 blocks, front view, side view • Challenge 1: How many more blocks can I add to keep the same view? Maximum • Challenge 2: How many locks can I take away? Minimum.

  19. Further extension • If you have found the maximum and the minimum, how many variations are there in between?

  20. Fraction Estimation • Need rope and three pegs

  21. Dice Difference

  22. Multo • 4 in a row horizontally • 4 in a row vertically • 4 in a row diagonally OR • all four corners

  23. What is the lowest number you can use? Why? • What is the highest number you can use? Why? • Are there any numbers you would never use? Why? • What are the best numbers to use? Why? • How often does each number occur? Why?

  24. maths300 • What to do now? • Check out sample lessons at www.maths300.esa.edu.au • Subscribe for each campus • Professional development available • Charles Lovitt clovitt@netspace.net.au • Doug Williams doug@blackdouglas.com.au • Tell your colleagues at other schools $Australian

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