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Syllabus Reference
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Steve Arnold
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Areas and PaperFolds
Download Student Worksheet file (PDF)
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Who would have thought that there could be so much mathematics in simply folding a piece of paper? This activity spans the years of secondary school, beginning with measurement, data collection and interpreting scatter plots in the early years, through linear functions, Pythagoras' Theorem and trigonometry, right through to calculus in the senior years.
The mathematical focus at each level is different - from finding the largest area to discovering functional relationships between the sides of a right-angled triangle, and on to optimisation. While algebra and calculus can be used to prove this result, it actually takes some geometry to understand why the final result is true.
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Perimeter and Area MS4.1
Uses formulae and Pythagoras’ theorem in calculating perimeter and area of circles and figures composed of rectangles and triangles
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Steve Arnold
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The Falling Ladder
Download Student Worksheet file (PDF)
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What does it feel like to be at the top of a ladder as the bottom begins to slide away? Do you fall at a steady rate? If not, then what is the nature of your motion - and when are you falling fastest?
This modelling problem is suitable for students across the secondary school, from consolidation of work on Pythagoras' Theorem in the early years, to optimization using differential calculus in the senior years. At all levels, it is a realistic and valuable task, which links a variety of mathematical skills and understandings with a practical real-world context.
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Perimeter and Area MS4.1
Uses formulae and Pythagoras' theorem in calculating perimeter and area of circles and figures composed of rectangles and triangles
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Steve Arnold
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The Beach Race
Download Student Worksheet file (PDF)
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This beach race begins from a point 4 kilometres out to sea from one end of a 6 kilometre beach, and finishes at the opposite end. Contestants must swim to a point along the beach, and then run to reach the finish line first. I can swim at 4 km/h and run at 10 km/h - where should I aim to land on the beach so as to minimize my total time for the race?
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Perimeter and Area MS4.1
Uses formulae and Pythagoras' theorem in calculating perimeter and area of circles and figures composed of rectangles and triangles
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Steve Arnold
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The Diminishing Square
Download Student Worksheet file (PDF)
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Study the diagram provided. A smaller square has been constructed inside a larger square, as shown.
A point x is located on the base of the larger square. (As shown) The smaller square is constructed using similar points on each of the remaining sides of the larger square. If x is the midpoint of the base, what is the ratio between the area of the larger square and the smaller square?
Explore the relationship between the position of this point and the area of the smaller square.
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Perimeter and Area MS4.1
Uses formulae and Pythagoras' theorem in calculating perimeter and area of circles and figures composed of rectangles and triangles
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Steve Arnold
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Cones and Witch's Hats
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From a sheet of cardboard 40 cm square, I need to make a conical witches hat for my child's party. If we assume she has a circular head of diameter 14 cm, what is the tallest hat I can make?
Assume I will make the cone by cutting a sector from a circle: what angle must I make this sector? |
Surface Area and Volume MS5.2.2
Applies formulae to find the surface area of right cylinders and volume of right pyramids, cones and spheres, and calculates the surface area and volume of composite solids
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