In this activity students are asked to investigate whether it is possible for a four-sided dice, with positive integer faces including odd numbers, to ever have expectation and variance the same. Sheet two carries a simulation with sheet three providing a search programme to find all possible solutions.

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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.

This resource, from Mathematics for Engineering Exemplars, shows how to build a mathematical model of liquid draining through a tank and how to use the model to determine the time required for a tank to completely drain. Bernoulli’s conservation of energy equation, which requires integration and differentiation, is...

Drinks cans are made by stamping out circular discs from a sheet of tin. Given the dimensions of the sheet of tin and the diameter of the circle stamped out, students are required to calculate the wastage and to investigate whether there is a more efficient method. The problem requires students to be able to...

This resource, from Mathematics for Engineering Exemplars, introduces mathematical models for the risk assessment of dropped load, which are used to analyse the safety of structures within nuclear power stations. Here students learn about the formulae which engineers use to calculate the maximum dynamic stress and...

This series of activities from NASA take a mathematical approach to looking at the Earth and its atmosphere. They are intended as supplementary problems for students looking for additional challenges in mathematics and physical science from age 11 to 19 years.

The problems were created to be authentic...

From the Integrating Mathematical Problem Solving project by Mathematics in Education and Industry (MEI), this activity shows how changing the price of a product changes the demand so putting the price up can reduce income. Modelling helps decision making. The mathematical ideas covered are:
• Percentage...

This series of activities from NASA take a mathematical approach to looking at electromagnetic radiation. They are intended as supplementary problems for students looking for additional challenges in mathematics and physical science from age 11 to 19 years. The problems were created to be authentic glimpses of...

In this problem students are given two circles with tangents that meet at a point P. The distance along the tangents from the circles to the point P are equal in length. The challenge is to describe the relationship between the x and y coordinates of the point P, given the coordinates of the centre of the circles...

This excel program is about finding the equation of straight lines in the form ax+by+c=0. The first two sheets deals with the equation of the line through two given points and the equation of the line through a point perpendicular to a given line. The resource is an...

This activity can be used to provide a simple introduction to the technique of Fermi estimation. The three files contain an overview, teacher notes and a student handout.

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Coding spreadsheet enables students to analyse the effect of coding data. Students can manipulate the values for x and the frequencies by which each value of x occurs. Students are required to understand and explain why the particular coding has been used. Once the question has been generated students calculate the...

Outlier tester is a very simple but fun spreadsheet that gives students the chance to explore the definition of an outlier using the interquartile range to determine the values beyond which outliers fall. Sheet two provides definitions for determining where outliers fall. By manipulating the outlier values and/or...

Playing with the quartiles for a small data set involves students using the values 1,3,5 and 7 on the spreadsheet to get the target quartile values for sample sizes of 20, 21, 22 and 23. The aim is to note by how much, or how little, difference to the quartiles is made by increasing the sample size by one. Sheet...

The many applications of mechanics make it an important topic of interest to applied mathematicians, scientists and engineers. This resource, produced by the Centre for Teaching Mathematics at the University of Plymouth, is designed to provide a more realistic view of mechanics and help the teaching of mechanics...