Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
This article for primary teachers suggests ways in which to help children become better at working systematically.
I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?
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?
The Zargoes use almost the same alphabet as English. What does this birthday message say?
What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?
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.
Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?
Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?
Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.
My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?
On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?
10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
How many possible necklaces can you find? And how do you know you've found them all?
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
How many different rectangles can you make using this set of rods?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
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?
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?
The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?
Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?
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?
What could the half time scores have been in these Olympic hockey matches?
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
You have 5 darts and your target score is 44. How many different ways could you score 44?