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### Take Three From Five

Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?

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### Which is cheaper?

When I park my car in Mathstown, there are two car parks to choose from. Can you help me to decide which one to use?

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### Steel Cables

Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?

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### Quadratic Patterns

Surprising numerical patterns can be explained using algebra and diagrams...

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### Speeding boats

Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?

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### Slick Summing

Watch the video to see how Charlie works out the sum. Can you adapt his method?

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### Speed-time problems at the Olympics

Have you ever wondered what it would be like to race against Usain Bolt?

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### Pythagoras Perimeters

If you know the perimeter of a right angled triangle, what can you say about the area?

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### Puzzling Place Value

Can you explain what is going on in these puzzling number tricks?

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### Plus Minus

Can you explain the surprising results Jo found when she calculated
the difference between square numbers?

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### Attractive Tablecloths

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

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### Terminology

Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?

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### Pick's Theorem

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

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### Painted Cube

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

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### Negatively Triangular

How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?

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### At right angles

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

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### Surprising Transformations

I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?

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### Mystic Rose

Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.