This page has been superseded by our Working Systematically - Primary Students page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.
Finding all possibilities upper primary
Ordered ways of working upper primary
Half time
Sitting round the party tables
Beads and bags
School fair necklaces
Make 37
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?
Fifteen cards
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.
Buying a balloon
Domino sets
How do you know if your set of dominoes is complete?
Plenty of pens
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?
Trebling
Can you replace the letters with numbers? Is there only one solution in each case?
A square of numbers
A mixed-up clock
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?
Nine-pin triangles
How many different triangles can you make on a circular pegboard that has nine pegs?
First connect three
What do you need?
Cubes here and there
Magic Vs
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
This Pied Piper of Hamelin
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Maze 100
Prison cells
Six ten total
All the digits
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?
Six numbered cubes
Reach 100
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.
Factor lines
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Two primes make one square
Can you make square numbers by adding two prime numbers together?
Sealed solution
Finding fifteen
Light the lights again
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?
Button-up some more
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Dice in a corner
How could you arrange at least two dice in a stack so that the total of the visible spots is 18?
Tea cups
The dice train
Cover the tray
Counting cards
5 on the clock
Curious number
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?
Inky cube
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?