Analysing - June 2009, Stage 2&3

Analysing a problem in order to decide on appropriate mathematical procedures plays a key role in successful problem-solving. Do we estimate or approximate or do we use more accurate methods of calculation? Do we use diagrams or graphs? Do we manipulate numbers or use algebraic techniques? Do we check our working regularly? Do we record our work, our solutions and our conclusions in the most effective way? These are some of the important questions that we may need to ask ourselves.

Problems

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Cutting it Out

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

I cut this square into two different shapes. What can you say about the relationship between them?

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Holes

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

I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?

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Today's Date - 01/06/2009

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

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

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Which Scripts?

Stage: 2 Challenge Level: Challenge Level:1

There are six numbers written in five different scripts. Can you sort out which is which?

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The Magic Number and the Hepta-tree

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

Find the exact difference between the largest ball and the smallest ball on the Hepta Tree and then use this to work out the MAGIC NUMBER!

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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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Keep it Simple

Stage: 3 Challenge Level: Challenge Level:1

Can all unit fractions be written as the sum of two unit fractions?

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Egyptian Fractions

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

The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.

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The Greedy Algorithm

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

The Egyptians expressed all fractions as the sum of different unit fractions. The Greedy Algorithm might provide us with an efficient way of doing this.