Year 9 Visualising and representing

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

Can you find the connections between linear and quadratic patterns?

Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?

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

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?

What do you notice about the sum of two identical triangular numbers?

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.

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?

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.

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

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

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?

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

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

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

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?

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

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

Can you minimise the amount of wood needed to build the roof of my garden shed?

Can you find and prove the relationship between the area of a trapezium and the area of a triangle constructed within it?

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

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

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

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

Can you maximise the area available to a grazing goat?

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

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

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

Can you make sense of these three proofs of Pythagoras' Theorem?

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

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

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

Can you do a little mathematical detective work to figure out which number has been wiped out?

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

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?

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

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?

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.

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.

An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

Can you find an efficent way to mix paints in any ratio?