These activities are part of our Primary collections, which are problems grouped by topic.
![Approaching Midnight](/sites/default/files/styles/medium/public/thumbnails/content-id-10776-icon.png?itok=PJ8lSHiV)
list
Approaching Midnight
Here's a strategy game with lots to explore. Can you find out enough to guarantee a win, no matter what the settings?
![Discuss and Choose](/sites/default/files/styles/medium/public/thumbnails/content-id-7449-icon.png?itok=5CkEbXRM)
problem
Discuss and Choose
This activity challenges you to decide on the 'best' number to use in each statement. You may need to do some estimating, some calculating and some research.
![Clocks](/sites/default/files/styles/medium/public/thumbnails/content-03-07-letme1-icon.gif?itok=AfiG27hg)
![Brush Loads](/sites/default/files/styles/medium/public/thumbnails/content-id-4911-icon.jpg?itok=P72P2b_V)
problem
Brush Loads
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
![Torn Shapes](/sites/default/files/styles/medium/public/thumbnails/content-id-4963-icon.jpg?itok=9xYJk5iR)
problem
Torn Shapes
These rectangles have been torn. How many squares did each one have inside it before it was ripped?
![Twice as Big?](/sites/default/files/styles/medium/public/thumbnails/content-id-5561-icon.png?itok=1fSrouE1)
problem
Twice as Big?
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
![Area and perimeter](/sites/default/files/styles/medium/public/thumbnails/content-id-7280-icon.png?itok=acOMB1ep)
problem
Area and perimeter
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
![Olympic Starters](/sites/default/files/styles/medium/public/thumbnails/content-id-8170-icon.png?itok=vIghhxZ8)
problem
Olympic Starters
Look at some of the results from the Olympic Games in the past. How do you compare if you try some similar activities?
![Wonky Watches](/sites/default/files/styles/medium/public/thumbnails/content-00-05-penta4-icon.jpg?itok=JgEjEJ81)
problem
Wonky Watches
Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.
![Numerically Equal](/sites/default/files/styles/medium/public/thumbnails/content-01-03-penta2-icon.jpg?itok=kI4KaqDe)
problem
Numerically Equal
Can you draw a square in which the perimeter is numerically equal to the area?
![Two Clocks](/sites/default/files/styles/medium/public/thumbnails/content-id-4806-icon.png?itok=W95kmVAi)
problem
Two Clocks
These clocks have only one hand, but can you work out what time they are showing from the information?
![How Much Did it Cost?](/sites/default/files/styles/medium/public/thumbnails/content-id-5949-icon.png?itok=uEtvooD9)
problem
How Much Did it Cost?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
![Oh! Harry!](/sites/default/files/styles/medium/public/thumbnails/content-id-5979-icon.png?itok=AAhYlqkp)
problem
Oh! Harry!
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
![Next size up](/sites/default/files/styles/medium/public/thumbnails/content-id-6931-icon.png?itok=5dh9oKgq)
![The time is ...](/sites/default/files/styles/medium/public/thumbnails/content-id-7384-icon.png?itok=D5YO9EPa)
problem
The time is ...
Can you put these mixed-up times in order? You could arrange them in a circle.
![Through the Window](/sites/default/files/styles/medium/public/thumbnails/content-id-10344-icon.png?itok=BPH4RXuq)
problem
Through the Window
My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?
![Number Lines in Disguise](/sites/default/files/styles/medium/public/thumbnails/content-id-13452-icon.jpg?itok=w1sVtOJy)
problem
Number Lines in Disguise
Some of the numbers have fallen off Becky's number line. Can you figure out what they were?
![Making Boxes](/sites/default/files/styles/medium/public/thumbnails/content-01-05-bbprob1-icon.gif?itok=Tbi6F4AQ)
problem
Making Boxes
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
![Fitted](/sites/default/files/styles/medium/public/thumbnails/content-03-09-six3-icon.gif?itok=fv1mqjJW)
problem
Fitted
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?
![5 on the clock](/sites/default/files/styles/medium/public/thumbnails/content-98-10-penta1-icon.gif?itok=pvYbgg49)
problem
5 on the clock
On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?
![Ribbon Squares](/sites/default/files/styles/medium/public/thumbnails/content-id-9939-icon.png?itok=-o4AD6iA)
problem
Ribbon Squares
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
![Watch the clock](/sites/default/files/styles/medium/public/thumbnails/content-00-01-penta2-icon.jpg?itok=dg4uLtYD)
problem
Watch the clock
During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?