Can you make a cycle of pairs that add to make a square number
using all the numbers in the box below, once and once only?
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
Choose a symbol to put into the number sentence.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
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?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
Can you substitute numbers for the letters in these sums?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
If you have only four weights, where could you place them in order
to balance this equaliser?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
Find all the numbers that can be made by adding the dots on two dice.
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
If each of these three shapes has a value, can you find the totals
of the combinations? Perhaps you can use the shapes to make the
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Can you use the information to find out which cards I have used?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
There are to be 6 homes built on a new development site. They could
be semi-detached, detached or terraced houses. How many different
combinations of these can you find?
Can you hang weights in the right place to make the equaliser
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
Use these head, body and leg pieces to make Robot Monsters which are different heights.
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.
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
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?
Use the 'double-3 down' dominoes to make a square so that each side has eight dots.
Use these four dominoes to make a square that has the same number of dots on each side.
Who said that adding couldn't be fun?
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
Ben has five coins in his pocket. How much money might he have?
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
An old game but lots of arithmetic!
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
Number problems at primary level that require careful consideration.