The purpose of bin packing is to pack a collection of objects into containers called bins. The bins are all the same size and the objects to be packed are different sizes. The aim is to pack the objects into the bins using the fewest possible bins. In this example students are asked to save computer files onto a CD...

In this resource students are asked to play the role of a local theatre manager, tasked with finding the best way to organise the audience to minimise the amount of space they take up. To solve the problem students must apply a series of first fit algorithms.

The resource includes a teacher presentation,...

This package of Core Maths resources explore how to solve bin packing problems using the first fit decreasing algorithm.

Bin Packing: Teacher guide
The teacher guide presentation contains an introduction to the topic through the plumber’s dilemma before working through the best possible...

The workbook contains a number of simulations designed to aid students understanding of the Binomial distribution.

Binomial distribution: simulated tossing a coin ten times. The probability of achieving 0,1,2… heads is calculated and displayed in a frequency table and a bar chart. The...

Most binomial questions define the binomial distribution and ask students to calculate the most likely value for x. In this activity, students are asked to explore whether the value for p can be found given the value for n and the most likely value for x. Subsequent pages of the presentation provide the solution to...

In this activity, students apply their knowledge of the binomial distribution to establish whether each of three rules, regarding the most likely outcome and the expected value, are true. The presentation contains a link to an applet which allows experimentation, and shows the binomial probabilities for various n...

This activity begins with the definition of the mean and the variance of a binomial distribution. Students are then challenged to take each definition and prove that they work for the binomial distribution B(3,p). The first task is for students to construct the probability distribution then calculate the mean and...

From the Integrating Mathematical Problem Solving project by Mathematics in Education and Industry (MEI), this activity for post-16 students demonstrates that if a link is suspected between a risk factor and an illness, statistical methods can be used to test whether such a link exists. Topic areas covered are:...

In this cluster of articles, students investigate aspects of plant biology and behaviour including chloroplast genes and how they have helped biologists understand plant evolution; how plants monitor the intensity, direction, colour and duration of the light they receive and if attacked by herbivores or pathogens...

In this activity the goal is for students to understand how the regression line is chosen. Autograph has a built-in facility for showing the squares of the residuals and is required to make this task work. Students are asked to explore what the lines that give the sum of the y-on-x residuals equal to zero have in...

In this activity, students are challenged to produce a scatter diagram consisting of ten points that give a product moment correlation coefficient of exactly 0.99. Students are expected to appreciate that the points will lie almost exactly on a straight line with at least one point being slightly out. The answer...

This Core Maths resource includes data from which students can calculate correlation coefficients. The resources includes a card sort that matches up scatter-graphs, data tables and product moment correlation coefficients. 

The teachers' notes give detailed teaching suggestions on how to introduce and...

This series of activities from NASA take a mathematical approach to looking at black holes. They are intended as supplementary problems for students looking for additional challenges in the maths and physical science post-16 curriculum. Problems consist of a student page and an answer sheet. Students need to be...

This Core Maths task involves substituting values into the BMI formula in order to make health decisions.

An introductory ...