# January 2010, Stage 4&5

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

### Fair Shares?

##### Age 14 to 16 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

##### Age 14 to 16 Challenge Level:

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

### Ratios and Dilutions

##### Age 14 to 16 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

##### Age 14 to 18 Challenge Level:

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

### Bionrich

##### Age 14 to 18 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

##### Age 14 to 18 Challenge Level:

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

### Vector Walk

##### Age 14 to 18 Challenge Level:

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

### Chemnrich

##### Age 14 to 18 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. . . .

##### Age 16 to 18 Challenge Level:

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

### Engnrich

##### Age 16 to 18 Challenge Level:

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

### Curve Match

##### Age 16 to 18 Challenge Level:

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

### Brimful

##### Age 16 to 18 Challenge Level:

Can you find the volumes of the mathematical vessels?