# From Introduction to Deeper Understanding

These tasks all encourage you to explore and describe number patterns, and in particular to use what you know about factors and multiples. They would be best done in the order below as you will find that the later tasks build on ideas from the earlier ones.

As a set, these activities will give you opportunities to work on all five key ingredients that make a successful mathematician: understanding, skills, problem solving, reasoning and attitude. To find out more about these five ingredients and suggestions about how you can reflect on becoming a better mathematician, take a look at our short article What Makes a
Good Mathematician?.

##### Age 5 to 7

Challenge Level

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?

##### Age 7 to 11

Challenge Level

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

##### Age 7 to 11

Challenge Level

Can you find any two-digit numbers that satisfy all of these statements?

##### Age 7 to 14

Challenge Level

You'll need to know your number properties to win a game of Statement Snap...

##### Age 11 to 16

Challenge Level

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?