# Great problems for new classes - September 2011, Stage 2&3

This month we have chosen a selection of problems ideal for beginning problem-solving at the start of a new school year. These tasks help to break the ice and stimulate mathematical discussions. We hope they will help new classes to develop good mathematical habits of mind.

## Problems

### Plants

##### Age 5 to 11 Challenge Level:

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

### Spot Thirteen

##### Age 7 to 11 Challenge Level:

Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?

### Fifteen Cards

##### Age 7 to 11 Challenge Level:

Can you use the information to find out which cards I have used?

### American Billions

##### Age 11 to 14 Challenge Level:

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

### Summing Consecutive Numbers

##### Age 11 to 14 Challenge Level:

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

### Changing Areas, Changing Perimeters

##### Age 11 to 14 Challenge Level:

How can you change the area of a shape but keep its perimeter the same? How can you change the perimeter but keep the area the same?

### Non-transitive Dice

##### Age 11 to 14 Challenge Level:

Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea?

### Changing Areas, Changing Volumes

##### Age 11 to 14 Challenge Level:

How can you change the surface area of a cuboid but keep its volume the same? How can you change the volume but keep the surface area the same?

### Ideas for the Secondary Classroom

##### Age 11 to 18

Articles about mathematics which can help to invigorate your classroom