Exploring and noticing

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

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?

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?

In sheep talk the only letters used are B and A. A sequence of words is formed by following certain rules. What do you notice when you count the letters in each word?

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

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?

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

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

Like a bit of help getting into the game? Then have a look at this.