Working systematically

Nine squares are fitted together to form a rectangle. Can you find its dimensions?

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

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?

How many different symmetrical shapes can you make by shading triangles or squares?

There are lots of ideas to explore in these sequences of ordered fractions.

Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

Can you arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?

How many trains can you make which are the same length as Matt's and Katie's, using rods that are identical?

How many different triangles can you draw on the dotty grid which each have one dot in the middle?