Ratio and Proportion - February 2006, All Stages

Problems

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Scale Draw

Stage: 1 Challenge Level: Challenge Level:1

Use the grids to draw pictures to different scales.

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Little Man

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?

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Blackcurrantiest

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you decide whose drink has the strongest blackcurrant flavour from these pictures?

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Once Upon a Time

Stage: 2 Challenge Level: Challenge Level:1

Can you work out the height of Baby Bear's chair and whose bed is whose if all the things the three bears have are in the same proportions?

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Nutty Mixture

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Use the ratio of cashew nuts to peanuts to find out how many peanuts Rachel has. What would the ratio be if Rachel and Marianne mixed their bags?

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Rod Ratios

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?

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Cereal Mix

Stage: 3 Challenge Level: Challenge Level:1

A farmer is supplying a mix of seeds, nuts and dried apricots to a manufacturer of crunchy cereal bars. What combination of ingredients costing £5 per kg could he supply?

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Mixing Paints

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

A decorator can buy pink paint from two manufacturers. What is the least number he would need of each type in order to produce different shades of pink.

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Mixing More Paints

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Is it always possible to combine two paints made up in the ratios 1:x and 1:y and turn them into paint made up in the ratio a:b ? Can you find an efficent way of doing this?

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A Change in Code

Stage: 4 Challenge Level: Challenge Level:1

There are two sets of numbers. The second is the result of the first after an increase by a constant percentage. How can you find that percentage if one set of numbers is in code?

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Tin Tight

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

What's the most efficient proportion for a 1 litre tin of paint?

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Orbiting Billiard Balls

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?

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Squareflake

Stage: 5 Challenge Level: Challenge Level:1

A finite area inside and infinite skin! You can paint the interior of this fractal with a small tin of paint but you could never get enough paint to paint the edge.

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Sierpinski Triangle

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

What is the total area of the triangles remaining in the nth stage of constructing a Sierpinski Triangle? Work out the dimension of this fractal.

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Von Koch Curve

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Make a poster using equilateral triangles with sides 27, 9, 3 and 1 units assembled as stage 3 of the Von Koch fractal. Investigate areas & lengths when you repeat a process infinitely often.