# January 2010, All Stages

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

### Scaling Clowns

##### Stage: 1 Challenge Level:

These five clowns work in pairs. What is the same and what is different about each pair's faces?

### Making Longer, Making Shorter

##### Stage: 1 Challenge Level:

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

### 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?

### Mixing Lemonade

##### 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.

### 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?

### Maths Filler

##### Stage: 4 Challenge Level:

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

### Fair Shares?

##### Stage: 4 Challenge Level:

A mother wants to share a sum of money by giving each of her children in turn a lump sum plus a fraction of the remainder. How can she do this in order to share the money out equally?

### Immersion

##### Stage: 4 Challenge Level:

Various solids are lowered into a beaker of water. How does the water level rise in each case?

### Ratios and Dilutions

##### Stage: 4 Challenge Level:

Scientists often require solutions which are diluted to a particular concentration. In this problem, you can explore the mathematics of simple dilutions

### Physnrich

##### Stage: 4 and 5 Challenge Level:

PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics

### Bionrich

##### Stage: 4 and 5 Challenge Level:

bioNRICH is the area of the stemNRICH site devoted to the mathematics underlying the study of the biological sciences, designed to help develop the mathematics required to get the most from your. . . .

### Core Scientific Mathematics

##### Stage: 4 and 5 Challenge Level:

This is the area of the advanced stemNRICH site devoted to the core applied mathematics underlying the sciences.

### Vector Walk

##### Stage: 4 and 5 Challenge Level:

Starting with two basic vector steps, which destinations can you reach on a vector walk?

### Chemnrich

##### Stage: 4 and 5 Challenge Level:

chemNRICH is the area of the stemNRICH site devoted to the mathematics underlying the study of chemistry, designed to help develop the mathematics required to get the most from your study. . . .

### Advanced Scientific Mathematics

##### Stage: 5 Challenge Level:

This is the section of stemNRICH devoted to the advanced applied mathematics underlying the study of the sciences at higher levels

### Engnrich

##### Stage: 5 Challenge Level:

engNRICH is the area of the stemNRICH Advanced site devoted to the mathematics underlying the study of engineering

### Curve Match

##### Stage: 5 Challenge Level:

Which curve is which, and how would you plan a route to pass between them?

### Brimful

##### Stage: 5 Challenge Level:

Can you find the volumes of the mathematical vessels?