Working Systematically

Mathematicians try to work systematically so they can see how they worked something out, and see patterns which messy work might not reveal. Scroll down to see our complete collection of lower primary problems that require you to work systematically, or explore the two sub-collections.
Stage: 1 Challenge Level: Challenge Level:1

Finding All Possibilities Lower Primary

These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

Stage: 1 Challenge Level: Challenge Level:1

Ordered Ways of Working Lower Primary

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.




Sort the Street

KS 1 Challenge Level:

Challenge Level:1

Sort the houses in my street into different groups. Can you do it in any other ways?

Pairs of Numbers

KS 1 Challenge Level:

Challenge Level:1

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?

Robot Monsters

KS 1 Challenge Level:

Challenge Level:1

Use these head, body and leg pieces to make Robot Monsters which are different heights.

Two Dice

KS 1 Challenge Level:

Challenge Level:1

Find all the numbers that can be made by adding the dots on two dice.

Same Length Trains

KS 1 Challenge Level:

Challenge Level:1

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

Weighted Numbers

KS 1 Challenge Level:

Challenge Level:1

Use the number weights to find different ways of balancing the equaliser.

Button-up

KS 1 Challenge Level:

Challenge Level:1

My coat has three buttons. How many ways can you find to do up all the buttons?

3 Blocks Towers

KS 1 Challenge Level:

Challenge Level:2 Challenge Level:2

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?

Three Ball Line Up

KS 1 Challenge Level:

Challenge Level:2 Challenge Level:2

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

6 Beads

KS 1 Challenge Level:

Challenge Level:2 Challenge Level:2

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?

A City of Towers

KS 1 Challenge Level:

Challenge Level:2 Challenge Level:2

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?

One of Thirty-six

KS 1 Challenge Level:

Challenge Level:2 Challenge Level:2

Can you find the chosen number from the grid using the clues?

Ladybirds in the Garden

KS 1 Challenge Level:

Challenge Level:2 Challenge Level:2

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?

Triangle Animals

KS 1 Challenge Level:

Challenge Level:2 Challenge Level:2

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

Eggs in Baskets

KS 1 Challenge Level:

Challenge Level:2 Challenge Level:2

There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?

The Tall Tower

KS 1 Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

Growing Garlic

KS 1 Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

Inside Triangles

KS 1 Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

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

Getting the Balance

KS 1 Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

Beads and Bags

KS 1 & 2 Challenge Level:

Challenge Level:1

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?

Sitting Round the Party Tables

KS 1 & 2 Challenge Level:

Challenge Level:1

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

Teddy Town

KS 1, 2 & 3 Challenge Level:

Challenge Level:2 Challenge Level:2

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?