Number Operations - October 2005, All Stages

Problems

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Same Length Trains

Stage: 1 Challenge Level: Challenge Level:1

How many trains can you make which are the same length as Matt's, using rods that are identical?

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Making Trains

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

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

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Fractional Wall

Stage: 2 Challenge Level: Challenge Level:1

Using the picture of the fraction wall, can you find equivalent fractions?

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Fractions Made Faster

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

Use the fraction wall to compare the size of these fractions - you'll be amazed how it helps!

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Combining Cuisenaire

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

Can you find all the different ways of lining up these Cuisenaire rods?

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Fault-free Rectangles

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

Find out what a "fault-free" rectangle is and try to make some of your own.

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Rod Fractions

Stage: 3 Challenge Level: Challenge Level:1

Pick two rods of different colours. Given an unlimited supply of rods of each of the two colours, how can we work out what fraction the shorter rod is of the longer one?

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Colour Building

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

Using only the red and white rods, how many different ways are there to make up the other colours of rod?

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Harmonic Triangle

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

Can you see how to build a harmonic triangle? Can you work out the next two rows?

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Different by One

Stage: 4 Challenge Level: Challenge Level:1

Make a line of green and a line of yellow rods so that the lines differ in length by one (a white rod)

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Stretching Fractions

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

Imagine a strip with a mark somewhere along it. Fold it in the middle so that the bottom reaches back to the top. Stetch it out to match the original length. Now where's the mark?

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Data Chunks

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

Data is sent in chunks of two different sizes - a yellow chunk has 5 characters and a blue chunk has 9 characters. A data slot of size 31 cannot be exactly filled with a combination of yellow and. . . .

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Pythagorean Fibs

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

What have Fibonacci numbers got to do with Pythagorean triples?

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Fibonacci Fashion

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

What have Fibonacci numbers to do with solutions of the quadratic equation x^2 - x - 1 = 0 ?

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Plus or Minus

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

Make and prove a conjecture about the value of the product of the Fibonacci numbers $F_{n+1}F_{n-1}$.