Year 9 Being curious

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?

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

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

Which set of numbers that add to 100 have the largest product?

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?

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.

How does the position of the line affect the equation of the line? What can you say about the equations of parallel lines?

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

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?

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

By selecting digits for an addition grid, what targets can you make?

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?

Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?

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 greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?

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?

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?

Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?

Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?

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?

Take a look at the video and try to find a sequence of moves that will untangle the ropes.

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

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

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