Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
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.
Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?
This task follows on from Build it Up and takes the ideas into three dimensions!
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?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
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!
Using the statements, can you work out how many of each type of rabbit there are in these pens?
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?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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 multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
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?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
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!
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
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 replace the letters with numbers? Is there only one solution in each case?
The Zargoes use almost the same alphabet as English. What does this birthday message say?
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?
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?
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.
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?
Can you use the information to find out which cards I have used?
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
This dice train has been made using specific rules. How many different trains can you make?
Can you find all the ways to get 15 at the top of this triangle of numbers?
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?