# Mathematics in the context of creative and digital technology

Many areas of mathematics are used in creative and digital technology. **Building the Digital Society** is a case study exploring how mathematics is used to convert digital data into information which is used to inform planning. The resource can be used as teacher inspiration or as part of a careers input.

**Analogue and Digital** explores difference between the two communication methods by looking at different codes building problem solving skills, mathematical reasoning and data handling skills. **Digital Designer** is a short film showing the importance of mathematics in the creative industries and can be used to emphasise the important part mathematics plays in their studies. The report **Digital Technologies and Mathematics Education** considers the role technology plays in the learning of mathematics and could provide stimulus for students to consider how they can combine their learning in mathematics with the work covered in their vocational course.

**Advancing the Digital Arts **considers the wealth of mathematics the computer animation industry relies on. **Maths and Numeracy - Exploring Digital Devices** explores the uses of the binary system in digital devices. **Computer Games Developer** is a short video detailing the mathematics used in the work of a computer games developer.

Many courses use **spreadsheets**. The remaining resources consist of a number of activities using spreadsheets in a mathematical context or applying the use of spreadsheets in the world of work.

### Building the Digital Society

This case study looks at how mathematics converts digital data into useful information for business, the government and the public. Computers and networks stuffed with ever-increasing amounts of data are transforming our society, creating a digital world with its own rules and behaviours. We need mathematicians who understand this new world and can turn data into useful information for the benefit of society as a whole. The resource can be used by teachers to guide their students or shared directly with students to inform them about careers using mathematics.

### Analogue and Digital

This activity introduces students to the differences between analogue and digital communication. An analogue signal can be rendered useless by small amounts of interference, whereas a digital signal remains coherent.

The activity is part of a full set of resources which look at Founding Communications and is supported by the following videos:

Communications of the future

Communications for safety

### Digital Designer

Simon Cam is a digital designer, working on interactive video production for an advertising agency. This video shows the importance of science and mathematics in a range of creative industries.

Simon works with film, special effects and 3D graphics, to develop a range of visual effects for the creative industries. This is as varied as creating an online 3D game to shooting a piece of film with miniature body cameras.

Simon describes his use of science and mathematics, "Even though I work in what is typically considered a creative field, my maths and science background has already helped me with the technical side of my career. If you’re creative, but also like maths and science, then this is the perfect job for you.”

### Digital Technologies and Mathematics Education

These resources, written in 2011, discuss the role that digital technologies might and should have in mathematics education. Consideration is given to the types of experiences students encounter and how best to develop the curriculum to engage students in using skills to explore a variety of aspects of mathematics.

Digital technologies and mathematics education - states that barriers to a more creative student-focussed use of digital technologies include a perception that they are an add-on to doing and learning mathematics, as well as current assessment practices, which do not allow the use of digital technologies.

### Advancing the Digital Arts

This case study looks at how mathematics is applied in the animation industry. The computer animation industry relies on a steady stream of mathematics to produce the fantastic images found on our cinema and television screens. Advanced mathematics also fuels developments in other areas of 3D modelling, such as car design. The resource can be used by teachers to guide their students or shared directly with students to inform them about careers using mathematics.

### Issue 3: Maths and Numeracy - Exploring Digital Devices

Exploring Digital Devices: Using the context of digital devices, this article explores how students might be helped to understand how decimal numbers work by considering binary numbers and manipulating them. Tables are used to explain the link between base 2 and base 10.

Brief descriptions of modern digital devices are used to introduce the terminology of bits, bytes and gigabytes, all of which are explained. Starting points for discussion and exploration are suggested, as are questions surrounding everyday digital devices such as laptop computers and music recorders.

Large numbers, powers and information about the way data is stored on a CD all suggest how everyday contexts could inform and be used to develop a deeper understanding of the mathematics behind them as well as making lessons more relevant and interesting to students.

Links are provided to further reading and sources of information which in turn could lead to other avenues of exploration and learning.

### Computer Games Developer

Simon works as a computer games developer, building scenarios for games using computer scripting language. This video shows how science, technology, engineering and mathematics (STEM) subjects can be the foundation for a career in the computer industry.

An understanding of mathematics forms an integral part to Simon's job. He says, "My official job title is Lead Scripter. As well as creating games we also test them, which is great fun."

"Maths and physics A-levels gave me a good grounding to do a games programming degree, and I use physics everyday. I did lots of computing at GCSE and A-level along with maths and physics. I love working in a fun environment with a really supportive team. It's a dream job.''

### Modelling with Spreadsheets

Modelling with Spreadsheets explains and illustrates both the principles of modelling and the use of computer spreadsheets. It describes several applications of modelling in detail and provides spreadsheet activities. The applications are mainly in the business/economics area and illustrate how modelling can be used to inform decision makers.

Modelling with a spreadsheet - provides an explanation of modelling in physical environments, such as wind tunnels and flight simulators, as well as the use of computer models for theoretical principles and logical assumptions. There are several examples of spreadsheets, which can be set up and used as tutorials, to develop awareness of the types of data and formulae, that are commonly used, and their adaptation.

Airline optimisation - presents an investigation of the consequences of altering the price charged for a plane journey, to establish what would be the best fare to charge. It uses information from a market research department and explains that, although the modelling process is a very powerful planning tool, no model is perfect and there is an art in using them effectively.

Analyses to try yourself - opportunities are provided to set up models based on background information similar to the airline investigation and include:

• The Orange Grove

• The Trucking Problem

• Selling Pocket Electronic Games

Optimising stock levels - frequent deliveries increases administrative costs, but if deliveries are made less often a large number of items have to be kept in stock and this is expensive too. The process of optimisation balances the trade-off between these two types of costs.

Warehouse location - positioning a warehouse is a classic problem and is studied in Human Geography and in Business Economics. There are a variety of approaches to finding the best location but spreadsheet techniques make it possible to explore this kind of analysis in a simple way.

Modelling traffic flow - applies the stopping distances of vehicles, given in the highway code, to the management of traffic speed through road works on the motorway to give the greatest flow of traffic along a single lane.

Processes and principles in modelling and optimisation - explains the ideas and principles which are characteristic of the activities described in this book and, although most of the ideas in this chapter have been introduced previously, they have been set out here to provide an overview.

### Spreadsheet Tasks

This resource contains ten instant maths ideas using spreadsheets to solve mathematical problems. Mathematical topics explored include:

• solving equations to complete a think of a number puzzle

• completion of magic squares

• exploring different sequences

• the ‘Rich Aunt’ problem

• an exploration of cubic graphs

Student resource sheets explain how spreadsheets can be used to perform the ‘Think of a number’ problem, the ‘How old are you?’ problem, the ‘boxes’ problem and an investigation to show how multiples are used to check that credit card numbers are valid.

### SMILE Spreadsheets

This resource contains 20 activities for using spreadsheets to solve mathematical problems in the classroom, rather than gaining spreadsheet skills in the computer room. By encouraging students to use spreadsheets when appropriate to the mathematics, they can be an aid to the development of mathematical thinking. Students should begin working with pencil, paper and a calculator, to allow them to get an understanding of the problem before using a spreadsheet to generate some results for analysis.

The activities:

Target 100 - place value and estimation

Dividing investigation - place value and decimals

Trick or treat - patterns and generalisations

Calculator trial and error - trial and improvement

A rich aunt - cumulative totals or constructing formulae

Again and again - sequences leading to limits

Consecutives - analysis of prime factors

Pamphlets - trial and improvement

Differences - sequences from polynomials leading to generalisations

Percentage problems - compound percentage increase or decrease

Jeans - effect of price increases on large quantities of material

Square root investigation - sequences formed by multiples of square roots

Strings - integer parts of a sequence

Averaging out - limits of sequences from the means of previous terms

What's recurring? - recurring and non-recurring decimal parts from fractions

String - open ended activity

A problem of power - calculating powers and modulos

Limits - iterative processes to find cube and square roots

Optimising - maximum volume

Converging sequences - limits of sequences leading to algebraic proof

### Spreadsheets Make Sense

This resource contains 21 activities for using spreadsheets to solve mathematical problems. Teachers' notes give advice on appropriate ways of using the activity and identifying particular support students may need when using a spreadsheet.

The activities are:

Favourite colours - carry out a survey and use ICT to display the data

Multiplication spreadsheet - create a multiplication table

Pocket money - perform repeated calculations quickly

Adding one - investigate the effect of adding or subtracting 1 from the numerator or denominator of a fraction

Dividing investigation - dividing integers by different numbers to categorise as terminating or recurring decimals

Planning a party - create a simple model using a variety of operations

142857 multiplication table - identify recurring decimals

Again and again - generate a sequence using an iterative process leading to limits

Spreadsheet grids - investigate the effect of the size of three or more numbers on their sum and product

Square roots investigation - identify a limit using patterns and algebra

Squidge - use brackets to create an algebraic expression to investigate sequences

A rich aunt - appreciate the power of a spreadsheet to solve real-life problem

Averaging out - use the mean to generate a sequence of numbers leading to a limit

Cuboids - create an algebraic expression for the formulas for surface area, total edge length and volume

Differences - between successive terms of sequences generated from linear, quadratic and cubic mappings

A problem of power - introduce students to modulo function

Marbles - use algebra to model a real life situation

Strings - numbers which are formed from the integer parts of terms of sequences

Converging sequences - the limit of a sequence formed from the ratios of corresponding terms

Geometry sequences - investigate infinite sequences with finite sums

Optimising - use algebraic and graphical methods to model and solve real life problems by manipulate mathematical formulas