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There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.
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 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?
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!
When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.
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?
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?
Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.
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.
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?
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?
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
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?
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?
Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?
Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?
What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
How many trapeziums, of various sizes, are hidden in this picture?
The Zargoes use almost the same alphabet as English. What does this birthday message say?
Put 10 counters in a row. Find a way to arrange the counters into five pairs, evenly spaced in a row, in just 5 moves, using the rules.
What could the half time scores have been in these Olympic hockey matches?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
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.
In how many ways can you stack these rods, following the rules?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?
Can you use this information to work out Charlie's house number?
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.?
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?
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
I like to walk along the cracks of the paving stones, but not the outside edge of the path itself. How many different routes can you find for me to take?
Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
Investigate the different ways you could split up these rooms so that you have double the number.
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
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!
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
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 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.