Dijkstra's algorithm finds the shortest path for a given problem. Dijkstra's algorithm can be used to find the shortest route between two cities. This algorithm is so powerful that it not only finds the shortest path from a chosen source to a given destination, it also finds all of the shortest paths from the...

This exercise is designed to ensure that students know how to find the expected value, E(X), and the variance, Var(X) for a discrete random variable, and that the probabilities in a probability distribution always add to one. Students are given a selection of numbers and are challenged to establish those...

In this activity students consider a population growth problem which leads to a power series. The presentation can be used to introduce the topic and use of spreadsheets would enable students to model and draw graphs of the situation.

The Nuffield Foundation provides this activity which uses examples in the context of shape and space to help students understand how big errors may be, and how errors accumulate when measurements are used in calculations. This is particularly important in scientific contexts. Students are required to find the upper...

In this activity, students examine changes to forests in cross-border regions of Africa and Borneo using Google Earth Pro to help identify features shown in satellite images and make measurements. The context allows students to explore the factors which put pressure on forested areas, and what is being done to...

The Nuffield Foundation provide this resource for students to collect data and then use statistical methods to analyse the results. The activities require that students investigate the extent to which people follow the advice from the Department of Health, which recommends that everyone eats at least five portions...

Students work in teams to design and make a prototype device that can design and make a prototype of a simple device (to be sold in stores like B&Q) that will allow homeowners to remove water from their house during periods of flooding.

In this challenge the device will have to move 100ml of water from...

The network flow problem involves finding the optimum route through a flow network; a directed graph where each arc has a capacity and each arc receives a flow. Typical examples include: evacuation plans and delivery services. The problem involves students analysing the plan of a school canteen and deciding whether...

In this lesson plan and associated presentation from CensusAtSchool, students are asked to remember how many frogs are on a slide when they have only had a few seconds to look at this. A student who has not been present is then asked to question the students about how many frogs were on the slide. Students will...

The Nuffield Foundation provide this activity which uses graphical methods to find a suitable model to connect two sets of data. There are a variety of ways in which the data could be used, depending on the focus required. It is possible to use a log graph to find an exponential model, which is the intended focus...

From the Integrating Mathematical Problem Solving project by Mathematics in Education and Industry (MEI), this activity for post-16 students demonstrates that the efficiency of a river can be measured using the hydraulic radius; this depends on the cross-sectional area of the river and the wetted perimeter of the...

In this resource the head of a circular snowman rolls around its circular body to make one trip back to where it started. The ratio of the diameters of the circles is given. The challenge is to find how many times the head will revolve throughout the journey, and find a general rule.

The resource contains a...

This activity from the Nuffield Foundation introduces the use of moving averages and weighted moving averages to smooth out seasonal fluctuations in UK house prices, enabling the yearly trend to be identified. The data provided is adapted from The Halifax House Price Index spreadsheet and although the arithmetic...

This activity focuses on the link between the UK’s current water usage and the predicted increase expected in the future. Looking at a water board website, students think about how the website is set up and the formulae that are being used. They then work in groups to...

From the Integrating Mathematical Problem Solving project by Mathematics in Education and Industry (MEI), this activity for post-16 students shows how regular sampling of a variety of prices is used to get a measure of inflation. There is more than one possible way to do this. A measure of inflation is used to...