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Exploring Quadratic Modelling Through Waterslides and Real-World Scenarios

This exploration of quadratic modelling dives into different representations of mathematical concepts, focusing on practical applications like the motion of a stone hit into the air and the design of a rectangular playpen. Inspired by Herbert Simon’s insight on problem-solving, we examine how understanding algebra helps make solutions transparent. Through engaging scenarios, we will investigate equations determining height over time and derive quadratic equations from real-world measurements. Join us on a journey to discover the math behind everyday situations!

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Exploring Quadratic Modelling Through Waterslides and Real-World Scenarios

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Presentation Transcript

  1. QUADRATIC MODELLING A journey into different representations

  2. Waterslide

  3. Where’s the maths?

  4. Herbert SimonFather of problem solving research “solving a problem simply means representing it so as to make the solution transparent.” WHAT DOES THIS MEAN IN RELATION TO THE ALGBERA WE HAVE BEEN STUDYING?

  5. Two contexts… • Motion • http://dsc.discovery.com/videos/mythbusters-waterslide-wipeout/ • Design

  6. Modelling motion

  7. ‘mathematising’what are x and y?

  8. Tennis scenario • Jonah uses a tennis racket to hit a stone straight up into the air. The height, , in metres, of the stone after seconds is given by the formula . Use this equation to work out at what time the stone returns to the ground.

  9. Measurement scenario • The diagram shows a rectangular play-pen labelled ABCD. The perimeter is 36m and the area is 80m2. Form a quadratic equation and solve it to calculate .

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