List

Year 9 Visualising and Representing

Fruity Totals
problem
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Fruity totals

Age
7 to 16
Challenge level
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In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?

At least one...
problem
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At least one...

Age
11 to 14
Challenge level
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Imagine flipping a coin a number of times. Can you work out the probability you will get a head on at least one of the flips?

Days and Dates
problem
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Days and dates

Age
11 to 14
Challenge level
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Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
Growing Surprises
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Growing surprises

Age
11 to 14
Challenge level
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Can you find the connections between linear and quadratic patterns?
What's it worth?
problem
Favourite

What's it worth?

Age
11 to 16
Challenge level
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There are lots of different methods to find out what the shapes are worth - how many can you find?

Special Numbers
problem
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Special numbers

Age
11 to 14
Challenge level
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My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

Picturing Triangular Numbers
problem
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Picturing triangular numbers

Age
11 to 14
Challenge level
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Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
How far does it move?
problem
Favourite

How far does it move?

Age
11 to 14
Challenge level
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Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects the distance it travels at each stage.

Round and round and round
problem
Favourite

Round and round and round

Age
11 to 14
Challenge level
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Where will the point stop after it has turned through 30 000 degrees? I took out my calculator and typed 30 000 รท 360. How did this help?
Reflecting Lines
problem
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Reflecting lines

Age
11 to 14
Challenge level
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Investigate what happens to the equations of different lines when you reflect them in one of the axes. Try to predict what will happen. Explain your findings.
Translating Lines
problem
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Translating lines

Age
11 to 14
Challenge level
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Investigate what happens to the equation of different lines when you translate them. Try to predict what will happen. Explain your findings.
Diminishing Returns
problem
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Diminishing returns

Age
11 to 14
Challenge level
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How much of the square is coloured blue? How will the pattern continue?
Fill Me Up
problem
Favourite

Fill me up

Age
11 to 14
Challenge level
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Can you sketch graphs to show how the height of water changes in different containers as they are filled?

What numbers can we make now?
problem
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What numbers can we make now?

Age
11 to 14
Challenge level
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Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

Quadrilaterals in a Square
problem
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Quadrilaterals in a square

Age
11 to 14
Challenge level
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What's special about the area of quadrilaterals drawn in a square?
Impossibilities
problem
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Impossibilities

Age
11 to 14
Challenge level
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Just because a problem is impossible doesn't mean it's difficult...

Reversals
problem
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Reversals

Age
11 to 14
Challenge level
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Where should you start, if you want to finish back where you started?
Counting Factors
problem
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Counting factors

Age
11 to 14
Challenge level
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Is there an efficient way to work out how many factors a large number has?
The Farmers' Field Boundary
problem
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The farmers' field boundary

Age
11 to 14
Challenge level
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The farmers want to redraw their field boundary but keep the area the same. Can you advise them?
Legs Eleven
problem
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Legs eleven

Age
11 to 14
Challenge level
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Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?
Alison's quilt
problem
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Alison's quilt

Age
11 to 14
Challenge level
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Nine squares are fitted together to form a rectangle. Can you find its dimensions?
Funny Factorisation
problem
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Funny factorisation

Age
11 to 16
Challenge level
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Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?
Marbles in a box
problem
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Marbles in a box

Age
11 to 16
Challenge level
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How many winning lines can you make in a three-dimensional version of noughts and crosses?
Think of Two Numbers
problem
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Think of two numbers

Age
11 to 14
Challenge level
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Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
An Unusual Shape
problem
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An unusual shape

Age
11 to 14
Challenge level
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Can you maximise the area available to a grazing goat?
Mixing Paints
problem
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Mixing paints

Age
11 to 14
Challenge level
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Can you work out how to produce different shades of pink paint?
Speeding up, slowing down
problem
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Speeding up, slowing down

Age
11 to 14
Challenge level
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Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its speed at each stage.

Triangle Numbers
problem
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Triangle numbers

Age
11 to 14
Challenge level
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Take a look at the multiplication square. The first eleven triangle numbers have been identified. Can you see a pattern? Does the pattern continue?
Tower of Hanoi
problem
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Tower of Hanoi

Age
11 to 14
Challenge level
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The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

Which solids can we make?
problem
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Which solids can we make?

Age
11 to 14
Challenge level
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Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?

Nine Colours
problem
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Nine colours

Age
11 to 16
Challenge level
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Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
Triangles to Tetrahedra
problem
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Triangles to tetrahedra

Age
11 to 14
Challenge level
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Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
Cuboids
problem
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Cuboids

Age
11 to 14
Challenge level
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Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
Efficient cutting
problem
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Efficient cutting

Age
11 to 14
Challenge level
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Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.
Up and across
problem
Favourite

Up and across

Age
11 to 14
Challenge level
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Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its vertical and horizontal movement at each stage.

Mixing More Paints
problem
Favourite

Mixing more paints

Age
14 to 16
Challenge level
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Can you find an efficent way to mix paints in any ratio?