Can you substitute numbers for the letters in these sums?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Number problems at primary level that require careful consideration.
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?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
This task follows on from Build it Up and takes the ideas into three dimensions!
What happens when you round these three-digit numbers to the nearest 100?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
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.
What happens when you round these numbers to the nearest whole number?
What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?
Can you replace the letters with numbers? Is there only one solution in each case?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?
Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?
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?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
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?
The Zargoes use almost the same alphabet as English. What does this birthday message say?
Ben has five coins in his pocket. How much money might he have?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
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?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
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?
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.
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
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?
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost 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?
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?
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?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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.
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.
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
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 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?
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 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?