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For younger learners

  • Early Years Foundation Stage

Working Systematically - Lower Primary

Mathematicians often talk about the importance of working systematically. This means that rather than working in a haphazard and random way, there is a methodical, organised and logical approach. The problems below will challenge you to work systematically and will help you appreciate the benefits of working in this way.

Scroll down to see our complete collection of Lower Primary problems, or explore the two sub-collections.

We also have a collection of Upper Primary problems that lend themselves to working systematically.

Primary teachers may like to read our article Encouraging Primary Children to Work Systematically.

Age 5 to 7
Challenge Level Yellow star

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.

Age 5 to 7
Challenge Level Yellow star

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.



Inside Triangles

Age 5 to 7
Challenge Level Yellow star

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

Sort the Street

Age 5 to 7
Challenge Level Yellow star

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

Button-up

Age 5 to 7
Challenge Level Yellow star

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

Pairs of Numbers

Age 5 to 7
Challenge Level Yellow star

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?

Let's Investigate Triangles

Age 5 to 7
Challenge Level Yellow star

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

Robot Monsters

Age 5 to 7
Challenge Level Yellow star

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

Two Dice

Age 5 to 7
Challenge Level Yellow star

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

A City of Towers

Age 5 to 7
Challenge Level Yellow star

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?

Same Length Trains

Age 5 to 7
Challenge Level Yellow star

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

Triangle Animals

Age 5 to 7
Challenge Level Yellow starYellow star

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

Ladybirds in the Garden

Age 5 to 7
Challenge Level Yellow starYellow star

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?

Three Ball Line Up

Age 5 to 7
Challenge Level Yellow starYellow star

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

Age 5 to 7
Challenge Level Yellow starYellow star

If you put three beads onto a tens/ones abacus you can make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?

Eggs in Baskets

Age 5 to 7
Challenge Level Yellow starYellow star

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?

The Tall Tower

Age 5 to 7
Challenge Level Yellow starYellow starYellow star

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

Sitting Round the Party Tables

Age 5 to 11
Challenge Level Yellow star

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

Growing Garlic

Age 5 to 11
Challenge Level Yellow star

Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?

Beads and Bags

Age 5 to 11
Challenge Level Yellow star

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?

One of Thirty-six

Age 5 to 7
Challenge Level Yellow starYellow star

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

3 Blocks Towers

Age 5 to 7
Challenge Level Yellow starYellow star

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?

Teddy Town

Age 5 to 11
Challenge Level Yellow starYellow star

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?

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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