This page has been superseded by our Working Systematically - Primary Students page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.
list
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.
list
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.
problem
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
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?
problem
Half Time
Age
5 to 11
Challenge level
What could the half time scores have been in these Olympic hockey matches?
problem
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?
problem
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?
problem
Trebling
Age
7 to 11
Challenge level
Can you replace the letters with numbers? Is there only one solution in each case?
problem
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?
problem
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?
problem
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
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
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?
problem
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
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
Fifteen cards
Age
7 to 11
Challenge level
Can you use the information to find out which cards I have used?
game
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.
problem
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
Domino sets
Age
7 to 11
Challenge level
How do you know if your set of dominoes is complete?
problem
Six Ten Total
Age
7 to 11
Challenge level
This challenge combines addition, multiplication, perseverance and even proof.
problem
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
Six Numbered Cubes
Age
7 to 11
Challenge level
This task combines spatial awareness with addition and multiplication.
problem
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
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
Two Primes Make One Square
Age
7 to 11
Challenge level
Can you make square numbers by adding two prime numbers together?
problem
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
Make 37
Age
7 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?
problem
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
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?
problem
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
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
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
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
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
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
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
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
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?
problem
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.
problem
The Dice Train
Age
7 to 11
Challenge level
This dice train has been made using specific rules. How many different trains can you make?
problem
Cover the tray
Age
7 to 11
Challenge level
These practical challenges are all about making a 'tray' and covering it with paper.