Here are some challenges that you can work on and then see if you can convince someone that your solutions are right! Have a go!
![Two numbers under the microscope](/sites/default/files/styles/medium/public/thumbnails/content-id-8059-icon.gif?itok=srPls4bz)
problem
Two numbers under the microscope
This investigates one particular property of number by looking closely at an example of adding two odd numbers together.
![Even and odd](/sites/default/files/styles/medium/public/thumbnails/content-id-6895-icon.png?itok=koeHIdLD)
problem
Even and odd
This activity is best done with a whole class or in a large group. Can you match the cards? What happens when you add pairs of the numbers together?
![I Like ...](/sites/default/files/styles/medium/public/thumbnails/content-id-6962-icon.gif?itok=iN64Angn)
problem
I Like ...
Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?
![How Odd](/sites/default/files/styles/medium/public/thumbnails/content-id-7190-icon.gif?itok=ijrBovS8)
problem
How Odd
This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?
![In the Playground](/sites/default/files/styles/medium/public/thumbnails/content-id-7248-icon.jpg?itok=wuF2PZ05)
problem
In the Playground
What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school?
![Halving](/sites/default/files/styles/medium/public/thumbnails/content-03-07-cupboardlove3-icon.gif?itok=8OfwVTrn)
![Ring a Ring of Numbers](/sites/default/files/styles/medium/public/thumbnails/content-id-2782-icon.png?itok=90NvaFQb)
problem
Ring a Ring of Numbers
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
![Numbers as Shapes](/sites/default/files/styles/medium/public/thumbnails/content-id-5158-icon.jpg?itok=dIH4tpr_)
problem
Numbers as Shapes
Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?
![A Bag of Marbles](/sites/default/files/styles/medium/public/thumbnails/content-id-5930-icon.png?itok=JkPz4-Gt)
problem
A Bag of Marbles
Use the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
![Odd times Even](/sites/default/files/styles/medium/public/thumbnails/content-id-8062-icon.png?itok=AuQOnvzI)
problem
Odd times Even
This problem looks at how one example of your choice can show something about the general structure of multiplication.
![Lots of Lollies](/sites/default/files/styles/medium/public/thumbnails/content-id-2360-icon.png?itok=DhUS5VXQ)
problem
Lots of Lollies
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?