Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
In this maze of hexagons, you start in the centre at 0. The next
hexagon must be a multiple of 2 and the next a multiple of 5. What
are the possible paths you could take?
An investigation that gives you the opportunity to make and justify
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?
Find out what a "fault-free" rectangle is and try to make some of
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?
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
Can you replace the letters with numbers? Is there only one
solution in each case?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Can you find the chosen number from the grid using the clues?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Two children made up a game as they walked along the garden paths.
Can you find out their scores? Can you find some paths of your own?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
What happens when you round these three-digit numbers to the nearest 100?
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
This challenge is about finding the difference between numbers which have the same tens digit.
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.
What happens when you round these numbers to the nearest whole number?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
This challenge extends the Plants investigation so now four or more children are involved.
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Follow the clues to find the mystery number.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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
These eleven shapes each stand for a different number. Can you use
the multiplication sums to work out what they are?
If you hang two weights on one side of this balance, in how many
different ways can you hang three weights on the other side for it
to be balanced?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
This train line has two tracks which cross at different points. Can
you find all the routes that end at Cheston?
Can you find all the different ways of lining up these Cuisenaire
How many different triangles can you make on a circular pegboard that has nine pegs?
How many trains can you make which are the same length as Matt's,
using rods that are identical?
Can you make a train the same length as Laura's but using three
differently coloured rods? Is there only one way of doing it?
Alice's mum needs to go to each child's house just once and then
back home again. How many different routes are there? Use the
information to find out how long each road is on the route she
Penta people, the Pentominoes, always build their houses from five
square rooms. I wonder how many different Penta homes you can
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?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?
A package contains a set of resources designed to develop
students’ mathematical thinking. This package places a
particular emphasis on “being systematic” and is
designed to meet. . . .
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?