Year 9 Explaining, convincing and proving

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

How much can you read into a T-shirt?

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

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?

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

Some people offer advice on how to win at games of chance, or how to influence probability in your favour. Can you decide whether advice is good or not?

Engage in a little mathematical detective work to see if you can spot the fakes.

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?

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?

What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?

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

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?

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

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

Can you find ways to put numbers in the overlaps so the rings have equal totals?

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

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

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

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

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?

Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...

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?

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

Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

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

The clues for this Sudoku are the product of the numbers in adjacent squares.

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