Interpreting and evaluating - July 2009, Stage 2&3

This month our problems involve aspects of the process of interpreting the information in a question and examining in various ways the solution or methods used to get the solution. For example, are the assumptions and arguments made correct or appropriate? How does the solution relate to the initial problem? Can we make sense of someone else's finding? Can we compare strategies used?

Problems

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Hexpentas

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

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

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The Mathemagician's Seven Spells

Stage: 2 Challenge Level: Challenge Level:1

"Tell me the next two numbers in each of these seven minor spells", chanted the Mathemagician, "And the great spell will crumble away!" Can you help Anna and David break the spell?

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Six Is the Sum

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

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

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Factor Lines

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

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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Cycling Squares

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

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

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Inside Seven Squares

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

What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?

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Parallel Lines

Stage: 3 Challenge Level: Challenge Level:1

How does the position of the line affect the equation of the line? What can you say about the equations of parallel lines?

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How Steep Is the Slope?

Stage: 3 Challenge Level: Challenge Level:1

On the grid provided, we can draw lines with different gradients. How many different gradients can you find? Can you arrange them in order of steepness?

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At Right Angles

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

Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?