Can you each work out the number on your card? What do you notice? How could you sort the cards?
Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
Noah saw 12 legs walk by into the Ark. How many creatures did he see?
A game for 2 or more players. Practise your addition and subtraction with the aid of a game board and some dried peas!
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?
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?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
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
This is an adding game for two players.
Can you find all the ways to get 15 at the top of this triangle of numbers?
On Planet Plex, there are only 6 hours in the day. Can you answer
these questions about how Arog the Alien spends his day?
This problem is based on the story of the 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!
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
Annie and Ben are playing a game with a calculator. What was
Annie's secret number?
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
At the beginning of May Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
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?
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
Can you draw a continuous line through 16 numbers on this grid so
that the total of the numbers you pass through is as high as
Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
Fill in the numbers to make the sum of each row, column and
diagonal equal to 15.
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
Fill in the numbers to make the sum of each row, column and
diagonal equal to 34. For an extra challenge try the huge American
Flag magic square.
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?
Can you arrange fifteen dominoes so that all the touching domino
pieces add to 6 and the ends join up? Can you make all the joins
add to 7?
How would you count the number of fingers in these pictures?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
In this game for two players, the aim is to make a row of four coins which total one dollar.
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
Can you find 2 butterflies to go on each flower so that the numbers
on each pair of butterflies adds to the same number as the one on
On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
Claire thinks she has the most sports cards in her album. "I have
12 pages with 2 cards on each page", says Claire. Ross counts his
cards. "No! I have 3 cards on each of my pages and there are. . . .
This challenge is about finding the difference between numbers which have the same tens digit.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Woof is a big dog. Yap is a little dog.
Emma has 16 dog biscuits to give to the two dogs.
She gave Woof 4 more biscuits than Yap.
How many biscuits did each dog get?