These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?
Sort the houses in my street into different groups. Can you do it in any other ways?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Use these head, body and leg pieces to make Robot Monsters which are different heights.
Find all the numbers that can be made by adding the dots on two dice.
My coat has three buttons. How many ways can you find to do up all the buttons?
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 ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. How many eggs are in each basket?
Take three differently coloured blocks - maybe red, yellow and blue. Make a tower using one of each colour. How many different towers can you make?
Can you find the chosen number from the grid using the clues?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
If you put three beads onto a tens/ones abacus you could make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?
In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?