Year 9 Visualising and Representing

problem

Favourite

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.

problem

Favourite

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?

problem

Favourite

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?

problem

Favourite

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.

problem

Favourite

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.

problem

Favourite

Diminishing Returns

Age

11 to 14

Challenge level

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

problem

Favourite

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?

problem

Favourite

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...

problem

Favourite

Growing Surprises

Age

11 to 14

Challenge level

Can you find the connections between linear and quadratic patterns?

problem

Favourite

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?

problem

Favourite

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.

problem

Favourite

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?

problem

Favourite

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.

problem

Favourite

Opposite vertices

Age

11 to 14

Challenge level

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

problem

Favourite

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?

problem

Favourite

Quadratic Patterns

Age

11 to 14

Challenge level

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

problem

Favourite

Quadrilaterals in a Square

Age

11 to 14

Challenge level

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

problem

Favourite

Impossibilities

Age

11 to 14

Challenge level

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

problem

Favourite

Reversals

Age

11 to 14

Challenge level

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

problem

Favourite

Counting Factors

Age

11 to 14

Challenge level

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

problem

Favourite

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?

problem

Favourite

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?

problem

Favourite

Alison's quilt

Age

11 to 14

Challenge level

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

problem

Favourite

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?

problem

Favourite

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?

problem

Favourite

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?

problem

Favourite

An Unusual Shape

Age

11 to 14

Challenge level

Can you maximise the area available to a grazing goat?

problem

Favourite

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?

problem

Favourite

Mixing Paints

Age

11 to 14

Challenge level

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

problem

Favourite

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.