Using the statements, can you work out how many of each type of rabbit there are in these pens?
This task follows on from Build it Up and takes the ideas into three dimensions!
You have 5 darts and your target score is 44. How many different ways could you score 44?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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?
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.
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
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?
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant 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?
This is an adding game for two players.
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?
Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?
Investigate the different distances of these car journeys and find out how long they take.
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
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?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
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?
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.
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 jugs.
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Use these head, body and leg pieces to make Robot Monsters which are different heights.
Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.
If the answer's 2010, what could the question be?
Can you go through this maze so that the numbers you pass add to exactly 100?
This activity is best done with a whole class or in a large group. Can you match the cards? What happens when you add pairs of the numbers together?
What is happening at each box in these machines?
Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
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?
Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?
How many starfish could there be on the beach, and how many children, if I can see 28 arms?
Sam got into an elevator. He went down five floors, up six floors, down seven floors, then got out on the second floor. On what floor did he get on?
Can you substitute numbers for the letters in these sums?
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?
Can you score 100 by throwing rings on this board? Is there more than way to do it?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
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?
A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?
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?
Number problems at primary level that require careful consideration.