Number problems at primary level that require careful consideration.
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?
Use these head, body and leg pieces to make Robot Monsters which are different heights.
Can you find the chosen number from the grid using the clues?
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?
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.
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?
In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?
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!
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?
Follow the clues to find the mystery number.
Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?
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.
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.
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!
Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?
What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?
The Zargoes use almost the same alphabet as English. What does this birthday message say?
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
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?
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?
Can you substitute numbers for the letters in these sums?
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?
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?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
This article for primary teachers suggests ways in which to help children become better at working systematically.
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?
Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?
Use the numbers and symbols to make this number sentence correct. How many different ways can you find?
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?
This challenge is about finding the difference between numbers which have the same tens digit.
Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
You have 5 darts and your target score is 44. How many different ways could you score 44?