Working Systematically - Upper Primary Students

This page has been superseded by our Working Systematically - Primary Students page

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 Upper Primary problems, or explore the two sub-collections.

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

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

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Finding all possibilities Upper Primary

Age

7 to 11

Challenge level

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

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Ordered Ways of Working Upper Primary

Age

7 to 11

Challenge level

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

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Favourite

Sitting round the party tables

Age

5 to 11

Challenge level

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

problem

Favourite

Beads and bags

Age

5 to 11

Challenge level

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?

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Favourite

Half time

Age

5 to 11

Challenge level

What could the half time scores have been in these Olympic hockey matches?

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Favourite

Make 37

Age

5 to 11

Challenge level

Four bags contain a large number of 1s, 3s, 5s and 7s. Can you pick any ten numbers from the bags so that their total is 37?

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Favourite

School fair necklaces

Age

5 to 11

Challenge level

How many possible symmetrical necklaces can you find? How do you know you've found them all?

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Favourite

Plenty of pens

Age

7 to 11

Challenge level

Amy's mum had given her £2.50 to spend. She bought four times as many pens as pencils and was given 40p change. How many of each did she buy?

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Favourite

Trebling

Age

7 to 11

Challenge level

Can you replace the letters with numbers? Is there only one solution in each case?

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Favourite

A square of numbers

Age

7 to 11

Challenge level

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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Favourite

A mixed-up clock

Age

7 to 11

Challenge level

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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Favourite

Nine-pin triangles

Age

7 to 11

Challenge level

How many different triangles can you make on a circular pegboard that has nine pegs?

problem

Favourite

First connect three

Age

7 to 11

Challenge level

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

problem

Favourite

What do you need?

Age

7 to 11

Challenge level

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

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Cubes here and there

Age

7 to 11

Challenge level

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

problem

Favourite

Magic Vs

Age

7 to 11

Challenge level

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

problem

Favourite

Fifteen cards

Age

7 to 11

Challenge level

Can you use the information to find out which cards I have used?

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First connect three for two

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

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Favourite

Buying a balloon

Age

7 to 11

Challenge level

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

problem

Favourite

Domino sets

Age

7 to 11

Challenge level

How do you know if your set of dominoes is complete?

problem

Favourite

Six ten total

Age

7 to 11

Challenge level

This challenge combines addition, multiplication, perseverance and even proof.

problem

Favourite

All the digits

Age

7 to 11

Challenge level

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

problem

Favourite

Six numbered cubes

Age

7 to 11

Challenge level

This task combines spatial awareness with addition and multiplication.

problem

Favourite

Reach 100

Age

7 to 11

Challenge level

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

problem

Favourite

Factor lines

Age

7 to 14

Challenge level

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

problem

Favourite

Two primes make one square

Age

7 to 11

Challenge level

Can you make square numbers by adding two prime numbers together?

problem

Favourite

Sealed solution

Age

7 to 11

Challenge level

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

problem

Favourite

Finding fifteen

Age

7 to 11

Challenge level

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

problem

Favourite

Light the lights again

Age

7 to 11

Challenge level

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

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Favourite

Button-up some more

Age

7 to 11

Challenge level

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

problem

Favourite

This Pied Piper of Hamelin

Age

7 to 11

Challenge level

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

problem

Favourite

Maze 100

Age

7 to 11

Challenge level

Can you go through this maze so that the numbers you pass add to exactly 100?

problem

Favourite

Prison cells

Age

7 to 11

Challenge level

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

problem

Favourite

Counting cards

Age

7 to 11

Challenge level

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

problem

Favourite

5 on the clock

Age

7 to 11

Challenge level

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

problem

Favourite

Curious number

Age

7 to 11

Challenge level

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

problem

Favourite

Inky cube

Age

7 to 14

Challenge level

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

problem

Favourite

Dice in a corner

Age

7 to 11

Challenge level

How could you arrange at least two dice in a stack so that the total of the visible spots is 18?

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Tea cups

Age

7 to 14

Challenge level

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.