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NZAMT 2019

Embrace joy in teaching math by employing engaging activities, anecdotes, and proofs to make learning enjoyable. Explore various mathematical problems and theorems from Pythagoras to place value, enhancing classroom experiences. Join in to discover the fun in math!

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NZAMT 2019

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  1. NZAMT 2019

  2. The Joy in Teaching Mathematics • Teaching mathematics is like an echo, what you put in is what bounces back. Certainly angst and discord are to be found at every turn, but so is joy. If you feel bored or uninterested with the subject, your lessons will reflect this. You have to remember that joy is there and look for it. • In this workshop, I will present activities, initiators, hook-ins, and engaging problems. To bring the exercises to life, I will also share anecdotes and stories that flesh out the amazing characters in mathematics. I have used these activities and problems over the years with my own classes, and I have graded them from Y9 to Y13. • Relax and enjoy the experience of getting inside these problems and the people who gave us the theorems and ideas.

  3. PROBLEM 1 Which is the better fit i) a square peg in a round hole or ii) a round peg in a square hole ?

  4. PYTHAGORAS THEOREM There are hundreds of proofs for this theorem, these two proofs are suitable for pupils working at level 5, they use basic algebra and are visually interesting See the back of page 3 for a couple of proofs.

  5. QUESTION 2 Find an expression for the hypotenuse of a right angle in terms of its Area (A) and its Perimeter (P) only

  6. QUESTION 3 An equilateral triangle and a regular Hexagon have the same perimeter, if the Triangle has an area of 2 what is the area of the hexagon ?

  7. QUESTION 4 Join the vertices of a regular Pythagorean proof to form the flat shape shown Refer to the handout

  8. USING MATERIALS QUESTION 5 Find the ratio that is halfway between 1:1 and 1:2

  9. QUESTION 6 Use Materials to prove i) 9÷4 =2 ii) show 7 is prime Show iii) of is iv) += v) ÷ = 1 vi) ÷=

  10. QUESTION 7 The 1089 problem – using place value

  11. QUESTION 8: VISUALISING IN 3-D REFER TO THE HANDOUT AND THE CUBES

  12. QUESTION 9 5 FISHERMEN RETURN FROM A TRIP WITH A MEAN CATCH OF 3 FISH AND A MEDIAN CATCH OF 2 FISH. EXPLORE THE DISTRIBUTIONS FOR THE CATCH THEY COULD HAVE ACHIEVED – THERE ARE A NUMBER OF POSSIBILITIES!!

  13. A Bonus Problem Is 2333 + 3222 divisible by 5 as it stands a poorly conceived problem but it has potential - explore

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