These activities are part of our Primary collections, which are problems grouped by topic.
![Multiplication Square Jigsaw](/sites/default/files/styles/medium/public/thumbnails/content-id-5573-icon.png?itok=kBx8oZ5E)
![Multiplication Squares](/sites/default/files/styles/medium/public/thumbnails/content-02-10-penta1-icon.gif?itok=xvTs90p3)
problem
Multiplication Squares
Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.
![What's in the Box?](/sites/default/files/styles/medium/public/thumbnails/content-id-5576-icon.png?itok=RCNWwyq5)
problem
What's in the Box?
This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?
![Ordering cards](/sites/default/files/styles/medium/public/thumbnails/content-id-8058-icon.png?itok=dNwJ9YCR)
problem
Ordering cards
This problem is designed to help children to learn, and to use, the two and three times tables.
![Let us divide!](/sites/default/files/styles/medium/public/thumbnails/content-id-8308-icon.png?itok=aX9M_8zD)
problem
Let us divide!
Look at different ways of dividing things. What do they mean? How might you show them in a picture, with things, with numbers and symbols?
![Shape Times Shape](/sites/default/files/styles/medium/public/thumbnails/content-id-5714-icon.png?itok=Pu4-NNY7)
problem
Shape Times Shape
These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?
![Multiply Multiples 1](/sites/default/files/styles/medium/public/thumbnails/content-id-10421-icon.gif?itok=ySiKdv96)
problem
Multiply Multiples 1
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
![Sweets in a box](/sites/default/files/styles/medium/public/thumbnails/content-00-12-bbprob1-icon.jpg?itok=WT5n0fd-)
problem
Sweets in a box
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?
![Multiply Multiples 2](/sites/default/files/styles/medium/public/thumbnails/content-id-10424-icon.gif?itok=Zz3B3N4F)
![What Do you Need?](/sites/default/files/styles/medium/public/thumbnails/content-id-5950-icon.png?itok=wgqMJ7pg)
problem
What Do you Need?
Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?
![Multiply Multiples 3](/sites/default/files/styles/medium/public/thumbnails/content-id-10478-icon.png?itok=qv1fEc6v)
problem
Multiply Multiples 3
Have a go at balancing this equation. Can you find different ways of doing it?
![Highest and Lowest](/sites/default/files/styles/medium/public/thumbnails/content-99-04-penta5-icon.jpg?itok=Ikk6pjwc)
problem
Highest and Lowest
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
![Which is quicker?](/sites/default/files/styles/medium/public/thumbnails/content-03-09-letme2-icon.gif?itok=Txz6gtCb)
problem
Which is quicker?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
![Three Dice](/sites/default/files/styles/medium/public/thumbnails/content-id-6719-icon.png?itok=cahapRQD)
problem
Three Dice
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
![Division Rules](/sites/default/files/styles/medium/public/thumbnails/content-id-10490-icon.jpg?itok=EFtWRK68)
problem
Division Rules
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
![Zios and Zepts](/sites/default/files/styles/medium/public/thumbnails/content-00-06-penta2-icon.png?itok=rhaJFIAE)
problem
Zios and Zepts
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?
![Trebling](/sites/default/files/styles/medium/public/thumbnails/content-03-11-penta1-icon.gif?itok=Gu7SmX2J)
![Times Tables Shifts](/sites/default/files/styles/medium/public/thumbnails/content-id-6863-icon.jpg?itok=2WjKpBW7)
problem
Times Tables Shifts
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
![Always, Sometimes or Never? Number](/sites/default/files/styles/medium/public/thumbnails/content-id-12672-icon.png?itok=UuM6k13s)
problem
Always, Sometimes or Never? Number
Are these statements always true, sometimes true or never true?
![Abundant Numbers](/sites/default/files/styles/medium/public/thumbnails/content-00-07-penta3-icon.gif?itok=onfyrFo1)
problem
Abundant Numbers
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
![A Square of Numbers](/sites/default/files/styles/medium/public/thumbnails/content-03-11-penta2-icon.gif?itok=wlJ1dBta)
problem
A Square of Numbers
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
![How do you do it?](/sites/default/files/styles/medium/public/thumbnails/content-id-6901-icon.gif?itok=DU3xchZB)
problem
How do you do it?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
![Picture Your Method](/sites/default/files/styles/medium/public/thumbnails/content-id-14736-icon.jpg?itok=S45wDqrO)
problem
Picture Your Method
Can you match these calculation methods to their visual representations?
![Odd Squares](/sites/default/files/styles/medium/public/thumbnails/content-id-2280-icon.gif?itok=NA7OpQi-)
problem
Odd Squares
Think of a number, square it and subtract your starting number. Is the number you're left with odd or even? How do the images help to explain this?
![Compare the Calculations](/sites/default/files/styles/medium/public/thumbnails/content-id-14739-icon.png?itok=YPXkXLlg)
problem
Compare the Calculations
Can you put these four calculations into order of difficulty? How did you decide?
![Flashing Lights](/sites/default/files/styles/medium/public/thumbnails/content-00-09-penta1-icon.png?itok=gokrIswu)
problem
Flashing Lights
Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?
![Up and Down Staircases](/sites/default/files/styles/medium/public/thumbnails/content-id-2283-icon.png?itok=sT8Zghu_)
problem
Up and Down Staircases
One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?
![4 by 4 Mathdokus](/sites/default/files/styles/medium/public/thumbnails/content-id-15106-icon.png?itok=6Zyctoxi)
![The Moons of Vuvv](/sites/default/files/styles/medium/public/thumbnails/content-01-07-penta3-icon.gif?itok=xHgSC_ox)
problem
The Moons of Vuvv
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
![Carrying Cards](/sites/default/files/styles/medium/public/thumbnails/content-id-2726-icon.png?itok=BG7Qhv6t)
problem
Carrying Cards
These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?
![Xavi's T-shirt](/sites/default/files/styles/medium/public/thumbnails/content-id-15208-icon.png?itok=p09ReWyq)
![An Easy Way to Multiply by 10?](/sites/default/files/styles/medium/public/thumbnails/content-id-2772-icon.jpg?itok=jiT2oq21)
problem
An Easy Way to Multiply by 10?
Do you agree with Badger's statements? Is Badger's reasoning 'watertight'? Why or why not?
![Follow the numbers](/sites/default/files/styles/medium/public/thumbnails/content-id-7127-icon.png?itok=501qbvoG)
problem
Follow the numbers
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.
![Music to my Ears](/sites/default/files/styles/medium/public/thumbnails/content-id-5483-icon.png?itok=b-g_edt0)
problem
Music to my Ears
Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?
![Journeys in Numberland](/sites/default/files/styles/medium/public/thumbnails/content-id-7285-icon.jpg?itok=G_TGMSH-)
problem
Journeys in Numberland
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
![All the Digits](/sites/default/files/styles/medium/public/thumbnails/content-02-09-penta1-icon.png?itok=nuAeRKtn)
problem
All the Digits
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
![Factor track](/sites/default/files/styles/medium/public/thumbnails/content-id-7468-icon.png?itok=Vg8AApCS)
problem
Factor track
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.
![Factor Lines](/sites/default/files/styles/medium/public/thumbnails/content-02-10-penta5-icon.gif?itok=RIygcdS8)
problem
Factor Lines
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
![Factor-Multiple Chains](/sites/default/files/styles/medium/public/thumbnails/content-id-5578-icon.png?itok=_LqJl9mK)
problem
Factor-Multiple Chains
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
![Two Primes Make One Square](/sites/default/files/styles/medium/public/thumbnails/content-03-01-penta2-icon.gif?itok=UNPMgYqh)
problem
Two Primes Make One Square
Can you make square numbers by adding two prime numbers together?
![Four Go](/sites/default/files/styles/medium/public/thumbnails/content-id-5633-icon.png?itok=3yVpdfOW)
problem
Four Go
This challenge is a game for two players. Choose two of the numbers to multiply or divide, then mark your answer on the number line. Can you get four in a row?
![Pebbles](/sites/default/files/styles/medium/public/thumbnails/content-98-08-bbprob1-icon.png?itok=wyHJ2vWm)
problem
Pebbles
Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
![Cycling Squares](/sites/default/files/styles/medium/public/thumbnails/content-03-01-penta3-icon.gif?itok=HWC6En86)
problem
Cycling Squares
Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?
![Picture a Pyramid ...](/sites/default/files/styles/medium/public/thumbnails/content-id-5809-icon.png?itok=wCvbMZ8_)
problem
Picture a Pyramid ...
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
![Round and round the circle](/sites/default/files/styles/medium/public/thumbnails/content-01-02-bbprob1-icon.gif?itok=HVb00dyR)
problem
Round and round the circle
What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
![Remainders](/sites/default/files/styles/medium/public/thumbnails/content-96-11-six4-icon.png?itok=5cZcyZQE)
problem
Remainders
I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?
![Make 100](/sites/default/files/styles/medium/public/thumbnails/content-00-07-penta5-icon.jpg?itok=FYf8VMSG)
problem
Make 100
Find at least one way to put in some operation signs to make these digits come to 100.
![Table patterns go wild!](/sites/default/files/styles/medium/public/thumbnails/content-id-6924-icon.png?itok=_L0q3bAS)
problem
Table patterns go wild!
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.
![Counting Cogs](/sites/default/files/styles/medium/public/thumbnails/content-id-6966-icon.gif?itok=-yx-oxgg)
problem
Counting Cogs
Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
![Light the Lights Again](/sites/default/files/styles/medium/public/thumbnails/content-id-7035-icon.gif?itok=E1T6ZYZN)
problem
Light the Lights Again
Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?
![Mystery Matrix](/sites/default/files/styles/medium/public/thumbnails/content-01-09-penta2-icon.png?itok=QvnkPfB_)
problem
Mystery Matrix
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
![Multiples Grid](/sites/default/files/styles/medium/public/thumbnails/content-id-5429-icon.png?itok=S2WRt3VQ)
problem
Multiples Grid
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?
![One Wasn't Square](/sites/default/files/styles/medium/public/thumbnails/content-02-07-penta1-icon.gif?itok=IHembGmh)
problem
One Wasn't Square
Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.
![So it's times!](/sites/default/files/styles/medium/public/thumbnails/content-id-7517-icon.png?itok=Lf5eout9)
problem
So it's times!
How will you decide which way of flipping over and/or turning the grid will give you the highest total?
![Cubes within Cubes](/sites/default/files/styles/medium/public/thumbnails/content-03-02-penta2-icon.gif?itok=zwjIUBuI)
problem
Cubes within Cubes
We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
![Four goodness sake](/sites/default/files/styles/medium/public/thumbnails/content-01-11-penta3-icon.gif?itok=5ecUxTWW)
problem
Four goodness sake
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
![Curious number](/sites/default/files/styles/medium/public/thumbnails/content-id-7218-icon.png?itok=yakj4l75)
problem
Curious number
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?