What happens when you round these three-digit numbers to the nearest 100?
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 complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Can you substitute numbers for the letters in these sums?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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.
You have been given nine weights, one of which is slightly heavier
than the rest. Can you work out which weight is heavier in just two
weighings of the balance?
What happens when you round these numbers to the nearest whole number?
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?
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
Let's suppose that you are going to have a magazine which has 16
pages of A5 size. Can you find some different ways to make these
pages? Investigate the pattern for each if you number the pages.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
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 do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
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 happens when you add three numbers together? Will your answer be odd or even? How do you know?
Can you replace the letters with numbers? Is there only one
solution in each case?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
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?
Can you work out some different ways to balance this equation?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
How many different journeys could you make if you were going to
visit four stations in this network? How about if there were five
stations? Can you predict the number of journeys for seven
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
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.
An investigation that gives you the opportunity to make and justify
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Follow the clues to find the mystery number.
Using different numbers of sticks, how many different triangles are
you able to make? Can you make any rules about the numbers of
sticks that make the most triangles?
How many models can you find which obey these rules?
Investigate the different ways you could split up these rooms so
that you have double the number.
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?
My two digit number is special because adding the sum of its digits
to the product of its digits gives me my original number. What
could my number be?
The ancient Egyptians were said to make right-angled triangles
using a rope with twelve equal sections divided by knots. What
other triangles could you make if you had a rope like this?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
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?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
On a digital clock showing 24 hour time, over a whole day, how many
times does a 5 appear? Is it the same number for a 12 hour clock
over a whole day?
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?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
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.
Take 5 cubes of one colour and 2 of another colour. How many
different ways can you join them if the 5 must touch the table and
the 2 must not touch the table?