Being Curious - Secondary Students

This activity is based on data in the book 'If the World Were a Village'. How will you represent your chosen data for maximum effect?

Try out this number trick. What happens with different starting numbers? What do you notice?

Follow the clues to find the mystery number.

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

Explore ways of colouring this set of triangles. Can you make symmetrical patterns?

Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

Watch this animation. What do you see? Can you explain why this happens?

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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

What do you think is going to happen in this video clip? Are you surprised?

These clocks have only one hand, but can you work out what time they are showing from the information?

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

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?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

Can you find a way to identify times tables after they have been shifted up or down?

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

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

Can you find the values at the vertices when you know the values on the edges?

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

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

Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?

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

What's the largest volume of box you can make from a square of paper?

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

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?

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

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

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?

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.

Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

This problem challenges you to sketch curves with different properties.

Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

Can you make a curve to match my friend's requirements?