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

problem icon

Scaling Clowns

Stage: 1 Challenge Level: Challenge Level:1

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

problem icon

Making Longer, Making Shorter

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

It Was 2010!

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

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

problem icon

Once Upon a Time

Stage: 2 Challenge Level: Challenge Level:1

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?

problem icon

Sticks and Triangles

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

problem icon

More and More Buckets

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

problem icon

Mixing Lemonade

Stage: 3 Challenge Level: Challenge Level:1

Can you work out which drink has the stronger flavour?

problem icon

Farey Sequences

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

Peaches Today, Peaches Tomorrow....

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?

problem icon

Maths Filler

Stage: 4 Challenge Level: Challenge Level:1

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

problem icon

Fair Shares?

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?

problem icon

Immersion

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

Ratios and Dilutions

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

problem icon

Physnrich

Stage: 4 and 5 Challenge Level: Challenge Level:1

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

problem icon

Bionrich

Stage: 4 and 5 Challenge Level: Challenge Level:1

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. . . .

problem icon

Core Scientific Mathematics

Stage: 4 and 5 Challenge Level: Challenge Level:1

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

problem icon

Chemnrich

Stage: 4 and 5 Challenge Level: Challenge Level:1

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. . . .

problem icon

Advanced Scientific Mathematics

Stage: 5 Challenge Level: Challenge Level:1

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

problem icon

Engnrich

Stage: 5 Challenge Level: Challenge Level:1

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

problem icon

Vector Walk

Stage: 5 Challenge Level: Challenge Level:1

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

problem icon

Curve Match

Stage: 5 Challenge Level: Challenge Level:1

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

problem icon

Brimful

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Can you find the volumes of the mathematical vessels?

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
Copyright © 1997 - 2012. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project.