Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Have a go at balancing this equation. Can you find different ways of doing it?
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?
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?
Can you use the information to find out which cards I have used?
Follow the clues to find the mystery number.
What happens when you round these three-digit numbers to the nearest 100?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Can you substitute numbers for the letters in these sums?
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?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Can you work out some different ways to balance this equation?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Can you replace the letters with numbers? Is there only one
solution in each case?
Using all ten cards from 0 to 9, rearrange them to make five prime
numbers. Can you find any other ways of doing it?
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 put the numbers 1-5 in the V shape so that both 'arms' have the same total?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
An investigation that gives you the opportunity to make and justify
A merchant brings four bars of gold to a jeweller. How can the
jeweller use the scales just twice to identify the lighter, fake
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!
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Stuart's watch loses two minutes every hour. Adam's watch gains one
minute every hour. Use the information to work out what time (the
real time) they arrived at the airport.
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 many different shaped boxes can you design for 36 sweets in one
layer? Can you arrange the sweets so that no sweets of the same
colour are next to each other in any direction?
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?
Can you order the digits from 1-6 to make a number which is
divisible by 6 so when the last digit is removed it becomes a
5-figure number divisible by 5, and so on?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
The discs for this game are kept in a flat square box with a square
hole for each disc. Use the information to find out how many discs
of each colour there are in the box.
Can you draw a square in which the perimeter is numerically equal
to the area?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
Your challenge is to find the longest way through the network
following this rule. You can start and finish anywhere, and with
any shape, as long as you follow the correct order.
This challenge is to design different step arrangements, which must
go along a distance of 6 on the steps and must end up at 6 high.
My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?
In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?
This task depends on groups working collaboratively, discussing and reasoning to agree a final product.
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?