Year 10 Visualising and Representing

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Take three from five

Age

11 to 16

Challenge level

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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Hollow squares

Age

14 to 16

Challenge level

Which armies can be arranged in hollow square fighting formations?

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Isosceles seven

Age

14 to 16

Challenge level

Is it possible to find the angles in this rather special isosceles triangle?

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Pair products

Age

14 to 16

Challenge level

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

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Speeding boats

Age

14 to 16

Challenge level

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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Speed-time problems at the Olympics

Age

14 to 16

Challenge level

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

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Which is cheaper?

Age

14 to 16

Challenge level

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

Age

14 to 16

Challenge level

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

Age

14 to 16

Challenge level

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

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Pythagoras perimeters

Age

14 to 16

Challenge level

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

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Puzzling place value

Age

14 to 16

Challenge level

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

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Plus minus

Age

14 to 16

Challenge level

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

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Attractive tablecloths

Age

14 to 16

Challenge level

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

Age

14 to 16

Challenge level

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

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Pick's theorem

Age

14 to 16

Challenge level

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

Age

14 to 16

Challenge level

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

Age

14 to 16

Challenge level

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

Age

14 to 16

Challenge level

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

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Surprising transformations

Age

14 to 16

Challenge level

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

Age

14 to 16

Challenge level

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

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Filling the gaps

Age

14 to 16

Challenge level

Which numbers can we write as a sum of square numbers?

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For younger learners

Year 10 Visualising and Representing

Take three from five

Hollow squares

Isosceles seven

Pair products

Speeding boats

Speed-time problems at the Olympics

Which is cheaper?

Steel cables

Quadratic patterns

Pythagoras perimeters

Puzzling place value

Plus minus

Attractive tablecloths

Terminology

Pick's theorem

Painted cube

Negatively triangular

At right angles

Surprising transformations

Mystic rose

Filling the gaps