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?
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?
Follow the clues to find the mystery number.
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
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?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
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....?
Can you find the chosen number from the grid using the clues?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
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?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
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.
This challenge extends the Plants investigation so now four or more children are involved.
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?
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?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
An investigation that gives you the opportunity to make and justify
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
These eleven shapes each stand for a different number. Can you use
the multiplication sums to work out what they are?
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
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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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?
Find out what a "fault-free" rectangle is and try to make some of
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.
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
A dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?
Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
Can you find all the different ways of lining up these Cuisenaire
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
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?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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
How many different triangles can you make on a circular pegboard
that has nine pegs?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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 make a train the same length as Laura's but using three
differently coloured rods? Is there only one way of doing it?
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. . . .