Exploring and noticing

problem

Bundles of Cubes

Age

7 to 11

Challenge level

2 out of 3

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?
problem

Making Squares

Age

7 to 11

Challenge level

3 out of 3

Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?
problem

Lost Books

Age

7 to 11

Challenge level

3 out of 3

While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?
problem

Difference

Age

7 to 11

Challenge level

3 out of 3

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
problem

Marvellous Matrix

Age

7 to 11

Challenge level

3 out of 3

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

3 out of 3

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

3 out of 3

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

Sticks and Triangles

Age

7 to 11

Challenge level

3 out of 3

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

More Pebbles

Age

7 to 11

Challenge level

3 out of 3

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

Polygonals

Age

7 to 11

Challenge level

3 out of 3

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