Investigate the different distances of these car journeys and find
out how long they take.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
A lady has a steel rod and a wooden pole and she knows the length
of each. How can she measure out an 8 unit piece of pole?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
There are 78 prisoners in a square cell block of twelve cells. The
clever prison warder arranged them so there were 25 along each wall
of the prison block. How did he do it?
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
What happens when you add the digits of a number then multiply the
result by 2 and you keep doing this? You could try for different
numbers and different rules.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
This article for teachers suggests ideas for activities built around 10 and 2010.
If the answer's 2010, what could the question be?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Find the sum of all three-digit numbers each of whose digits is
This is an adding game for two players.
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.
Using 3 rods of integer lengths, none longer than 10 units and not
using any rod more than once, you can measure all the lengths in
whole units from 1 to 10 units. How many ways can you do this?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
Which times on a digital clock have a line of symmetry? Which look
the same upside-down? You might like to try this investigation and
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
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Winifred Wytsh bought a box each of jelly babies, milk jelly bears,
yellow jelly bees and jelly belly beans. In how many different ways
could she make a jolly jelly feast with 32 legs?
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?
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
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?
Mr. Sunshine tells the children they will have 2 hours of homework.
After several calculations, Harry says he hasn't got time to do
this homework. Can you see where his reasoning is wrong?
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!
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!
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
This challenge extends the Plants investigation so now four or more children are involved.
Delight your friends with this cunning trick! Can you explain how
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 explain how this card trick works?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
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.
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
We can arrange dots in a similar way to the 5 on a dice and they
usually sit quite well into a rectangular shape. How many
altogether in this 3 by 5? What happens for other sizes?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Start with four numbers at the corners of a square and put the
total of two corners in the middle of that side. Keep going... Can
you estimate what the size of the last four numbers will be?
In this section from a calendar, put a square box around the 1st,
2nd, 8th and 9th. Add all the pairs of numbers. What do you notice
about the answers?
Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number.
Cross out the numbers on the same row and column. Repeat this
process. Add up you four numbers. Why do they always add up to 34?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.