April 2002, Stage 2&3

Problems

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Dividing a Cake

Stage: 2 Challenge Level: Challenge Level:1

Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?

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Fractional Triangles

Stage: 2 Challenge Level: Challenge Level:1

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

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Fractions in a Box

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

The discs for this game are kept in a flat square box with a square hole for each disc. Use the information to find out how many discs of each colour there are in the box.

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Fun Time

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

On Saturday, Asha and Kishan's grandad took them to a Theme Park. Use the information to work out how long were they in the theme park.

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In the Money

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

There are a number of coins on a table. One quarter of the coins show heads. If I turn over 2 coins, then one third show heads. How many coins are there altogether?

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Farey Sequences

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

There are lots of ideas to explore in these sequences of ordered fractions.

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Great Granddad

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

Great Granddad is very proud of his telegram from the Queen congratulating him on his hundredth birthday and he has friends who are even older than he is... When was he born?

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Basically

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

The number 3723(in base 10) is written as 123 in another base. What is that base?