Exploring and noticing

problem
Favourite

Four goodness' sake

Age

7 to 11

Challenge level

Use 4 four times in a calculation. What answers can you get?
problem
Favourite

Fitted

Age

7 to 11

Challenge level

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?
problem

Marvellous matrix

Age

7 to 11

Challenge level

Follow the directions for circling numbers in the matrix. Add all the circled numbers together. Note your answer. Try again with a different starting number. What do you notice?
problem

One million to seven

Age

7 to 11

Challenge level

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
problem

Triangle pin-down

Age

7 to 11

Challenge level

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
problem
Favourite

Board block challenge

Age

7 to 11

Challenge level

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?
problem

Sticks and triangles

Age

7 to 11

Challenge level

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?
problem
Favourite

Fraction fascination

Age

7 to 11

Challenge level

This problem challenges you to work out what fraction of the whole area of these pictures is taken up by various shapes.
problem

More pebbles

Age

7 to 11

Challenge level

Have a go at this 3D extension to the Pebbles problem.
problem

Polygonals

Age

7 to 11

Challenge level

Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.