# January 2010, Stage 3&4

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

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

Can you work out which drink has the stronger flavour?

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

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

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

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

##### Age 11 to 14 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?

##### 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?

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

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

##### 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

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

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

##### 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. . . .

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

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

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

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

##### 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. . . .

## Articles & Games

The second of three articles on the History of Trigonometry.

Which dilutions can you make using 10ml pipettes and 100ml
measuring cylinders?

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?