What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
How many different sets of numbers with at least four members can
you find in the numbers in this box?
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
56 406 is the product of two consecutive numbers. What are these
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
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 trains can you make which are the same length as Matt's,
using rods that are identical?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
"Ip dip sky blue! Who's 'it'? It's you!" Where would you position
yourself so that you are 'it' if there are two players? Three
I am thinking of three sets of numbers less than 101. They are the
red set, the green set and the blue set. Can you find all the
numbers in the sets from these clues?
Follow the clues to find the mystery number.
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
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?
Can you place the numbers from 1 to 10 in the grid?
Can you see how these factor-multiple chains work? Find the chain
which contains the smallest possible numbers. How about the largest
This package will help introduce children to, and encourage a deep
exploration of, multiples.
Becky created a number plumber which multiplies by 5 and subtracts
4. What do you notice about the numbers that it produces? Can you
explain your findings?
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
If you have only four weights, where could you place them in order
to balance this equaliser?
The discs for this game are kept in a flat square box with a square
hole for each disc. Use the information to find out how many discs
of each colour there are in the box.
Find the squares that Froggie skips onto to get to the pumpkin
patch. She starts on 3 and finishes on 30, but she lands only on a
square that has a number 3 more than the square she skips from.
Are these domino games fair? Can you explain why or why not?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
An investigation that gives you the opportunity to make and justify
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?
Ben’s class were making cutting up number tracks. First they
cut them into twos and added up the numbers on each piece. What
patterns could they see?
Nearly all of us have made table patterns on hundred squares, that
is 10 by 10 grids. This problem looks at the patterns on
differently sized square grids.
Help share out the biscuits the children have made.
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
Can you find the chosen number from the grid using the clues?
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
Pat counts her sweets in different groups and both times she has
some left over. How many sweets could she have had?
I throw three dice and get 5, 3 and 2. Add the scores on the three
dice. What do you get? Now multiply the scores. What do you notice?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
If there is a ring of six chairs and thirty children must either
sit on a chair or stand behind one, how many children will be
behind each chair?
Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
Andrew decorated 20 biscuits to take to a party. He lined them up
and put icing on every second biscuit and different decorations on
other biscuits. How many biscuits weren't decorated?
Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?
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?
On a farm there were some hens and sheep. Altogether there were 8
heads and 22 feet. How many hens were there?
There are ten children in Becky's group. Can you find a set of
numbers for each of them? Are there any other sets?
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?
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?
A game in which players take it in turns to choose a number. Can you block your opponent?
Complete the magic square using the numbers 1 to 25 once each. Each
row, column and diagonal adds up to 65.
Factor track is not a race but a game of skill. The idea is to go
round the track in as few moves as possible, keeping to the rules.