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?
Investigate the different distances of these car journeys and find
out how long they take.
This challenge extends the Plants investigation so now four or more children are involved.
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?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
This is an adding game for two players.
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.
Can you explain how this card trick works?
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.
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
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.
Delight your friends with this cunning trick! Can you explain how
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
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.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
Find the sum of all three-digit numbers each of whose digits is
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?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
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.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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
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?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
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?
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
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
If the answer's 2010, what could the question be?
If each of these three shapes has a value, can you find the totals
of the combinations? Perhaps you can use the shapes to make the
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 article for teachers suggests ideas for activities built around 10 and 2010.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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?
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?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Find the next number in this pattern: 3, 7, 19, 55 ...
Is it possible to rearrange the numbers 1,2......12 around a clock
face in such a way that every two numbers in adjacent positions
differ by any of 3, 4 or 5 hours?
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
Vera is shopping at a market with these coins in her purse. Which
things could she give exactly the right amount for?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
Can you substitute numbers for the letters in these sums?
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Can you use the information to find out which cards I have used?