Year 9 Visualising and Representing

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Fruity Totals

Age

7 to 16

Challenge level

In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?

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Special Numbers

Age

11 to 14

Challenge level

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?

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Picturing Triangular Numbers

Age

11 to 14

Challenge level

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

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How far does it move?

Age

11 to 14

Challenge level

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.

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Semi-regular Tessellations

Age

11 to 16

Challenge level

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

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Round and round and round

Age

11 to 14

Challenge level

Where will the point stop after it has turned through 30 000 degrees? I took out my calculator and typed 30 000 ÷ 360. How did this help?

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Reflecting Lines

Age

11 to 14

Challenge level

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.

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Translating Lines

Age

11 to 14

Challenge level

Investigate what happens to the equation of different lines when you translate them. Try to predict what will happen. Explain your findings.

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Diminishing Returns

Age

11 to 14

Challenge level

How much of the square is coloured blue? How will the pattern continue?

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At least one...

Age

11 to 14

Challenge level

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?

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Days and Dates

Age

11 to 14

Challenge level

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

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Growing Surprises

Age

11 to 14

Challenge level

Can you find the connections between linear and quadratic patterns?

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What's it worth?

Age

11 to 16

Challenge level

There are lots of different methods to find out what the shapes are worth - how many can you find?

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An Unusual Shape

Age

11 to 14

Challenge level

Can you maximise the area available to a grazing goat?

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Square coordinates

Age

11 to 14

Challenge level

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

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Mixing Paints

Age

11 to 14

Challenge level

Can you work out how to produce different shades of pink paint?

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Speeding up, slowing down

Age

11 to 14

Challenge level

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its speed at each stage.

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Triangle Numbers

Age

11 to 14

Challenge level

Take a look at the multiplication square. The first eleven triangle numbers have been identified. Can you see a pattern? Does the pattern continue?

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Tower of Hanoi

Age

11 to 14

Challenge level

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

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Opposite vertices

Age

11 to 14

Challenge level

Can you recreate squares and rhombuses if you are only given a side or a diagonal?

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Fill Me Up

Age

11 to 14

Challenge level

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

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What numbers can we make now?

Age

11 to 14

Challenge level

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

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Quadrilaterals in a Square

Age

11 to 14

Challenge level

What's special about the area of quadrilaterals drawn in a square?

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Counting Factors

Age

11 to 14

Challenge level

Is there an efficient way to work out how many factors a large number has?

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Impossibilities

Age

11 to 14

Challenge level

Just because a problem is impossible doesn't mean it's difficult...

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Legs Eleven

Age

11 to 14

Challenge level

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?

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Reversals

Age

11 to 14

Challenge level

Where should you start, if you want to finish back where you started?

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Funny Factorisation

Age

11 to 16

Challenge level

Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?

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Star Polygons

Age

11 to 14

Challenge level

Draw some stars and measure the angles at their points. Can you find and prove a result about their sum?

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Marbles in a box

Age

11 to 16

Challenge level

How many winning lines can you make in a three-dimensional version of noughts and crosses?

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The Farmers' Field Boundary

Age

11 to 14

Challenge level

The farmers want to redraw their field boundary but keep the area the same. Can you advise them?

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Alison's quilt

Age

11 to 14

Challenge level

Nine squares are fitted together to form a rectangle. Can you find its dimensions?

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Think of Two Numbers

Age

11 to 14

Challenge level

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

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Cuboids

Age

11 to 14

Challenge level

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?

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Efficient cutting

Age

11 to 14

Challenge level

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.

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Up and across

Age

11 to 14

Challenge level

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.

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Which solids can we make?

Age

11 to 14

Challenge level

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?