# January 2010, Stage 2&3

This month, we are celebrating the launch of the stemNRICH section of the website for Stages 4 and 5, which embeds mathematical problem-solving into science, technology and engineering contexts. Proportional reasoning and Volume are important concepts in science as well as maths, and feature in several of our problems at all stages this month.

## Problems

### It Was 2010!

##### Stage: 1 and 2 Challenge Level:

If the answer's 2010, what could the question be?

### Once Upon a Time

##### Stage: 2 Challenge Level:

Can you work out the height of Baby Bear's chair and whose bed is whose if all the things the three bears have are in the same proportions?

### Sticks and Triangles

##### Stage: 2 Challenge Level:

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

### More and More Buckets

##### Stage: 2 Challenge Level:

In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?

##### Stage: 3 Challenge Level:

Can you work out which drink has the stronger flavour?

### Farey Sequences

##### Stage: 3 Challenge Level:

There are lots of ideas to explore in these sequences of ordered fractions.

### Maths Filler

##### Stage: 3 Challenge Level:

Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?

### Peaches Today, Peaches Tomorrow....

##### Stage: 3 and 4 Challenge Level:

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?