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?
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!
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Choose a symbol to put into the number sentence.
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?
Can you hang weights in the right place to make the equaliser
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
Can you use the numbers on the dice to reach your end of the number line before your partner beats you?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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?
If you have only four weights, where could you place them in order
to balance this equaliser?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Use the information about Sally and her brother to find out how many children there are in the Brown family.
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. . . .
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
This is an adding game for two players.
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
In this game, you can add, subtract, multiply or divide the numbers
on the dice. Which will you do so that you get to the end of the
number line first?
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?
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Use the number weights to find different ways of balancing the equaliser.
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?
A game for 2 or more players with a pack of cards. Practise your
skills of addition, subtraction, multiplication and division to hit
the target score.
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?
Who said that adding couldn't be fun?
Ben has five coins in his pocket. How much money might he have?
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?
Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?
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?
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.
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
A game for 2 or more players. Practise your addition and subtraction with the aid of a game board and some dried peas!
Find all the numbers that can be made by adding the dots on two dice.
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
Have a go at this game which involves throwing two dice and adding
their totals. Where should you place your counters to be more
likely to win?
A game for 2 players. Practises subtraction or other maths
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?