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</script>This page contains all of our guidance for Teachers who wish to engage in some sort of cross-curricular STEM activity.</p>
<br></br>
<p><strong>At the heart of stemNRICH</strong> are the students who will have a range of interests across STEM subjects and, in this ever more technological and cross-disciplinary world, are likely to leave school needing a range of skills and the ability to make links between traditional school STEM subjects.</p>
<p><strong>The key goals of the stemNRICH are:</strong> To create inspiring, stimulating and engaging rich scientific mathematics classroom resources and guidance which facilitate the forging of links between mathematics and SET for students aged 11-16, reinforcing the learning in all subjects and linking into <a href="http://nrich.maths.org/stemnrich">stemNRICH</a> at KS5.</p>
<p> </p>
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<div style="width: 50%; font-size: 10pt;">
<h2 style="width: 200pt;">New and featured content</h2>
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</div>
<h3>News</h3>
<div id="sidebar">
<ul class="menu">
<li class="leaf2">Our next STEM initiative will be to convene the STEM teachers group again to reflect on the <a href="http://nrich.maths.org/stemtiday1">first STEM TI day</a>, look ahead to the second one, and generally work on moving the STEM agenda in schools forward.</li>
<li class="leaf2">Our first <a href="http://mmp.maths.org/STEM_TI">STEM Teacher Inspiration day</a> was a great success! Thanks to all the teachers who attended and created such a buzz of excitement.</li>
<li class="leaf2">The cross disciplinary <a href="http://nrich.maths.org/7528&part=">DT/Maths focus group</a> proved enormously helpful in providing ideas to develop the Technology pages on the site.</li>
<li class="leaf2">Our cross disciplinary <a href="http://nrich.maths.org/7325&part=">science/maths focus group</a> in February 2011 was a great success, giving us many ideas for our practical teacher support.</li>
<li class="leaf2">The resources in stemNRICH are new, exciting and different. Please get <a href="mailto:jag55@cam.ac.uk">in touch</a> with your stories, comments and suggestions for future developments.</li>
<li class="leaf2">We have funding to continue work on the resources and teacher support until September 2012.</li>
<li class="leaf2"> </li>
</ul>
</div>
</div>
<p><strong>Our STEM guidance material can be accessed through the following links, which will be updated periodically as we work on the project:</strong></p>
<br></br>
<ol>
<li><a href="#" id="hideShow0">What is hoped to be gained by doing all of this?</a>
<div id="hidden0" style="display: none;">
<ul>
<li>Teachers feeling supported and able to increase student motivation in and enjoyment of STEM.</li>
<li>Make students better prepared for GCSE, A-levels and university - making them happier, more skilled and better informed.</li>
<li>Enrichment of maths and SET classrooms, making full use of the varied histories and experiences of teachers, such as non-subject specialists teaching maths/science.</li>
</ul>
</div>
</li>
<li><a href="#" id="hideShow1">Three levels of STEM engagement in the classroom</a>
<div id="hidden1" style="display: none;">
<p>We suggest that there are three levels at which students/teachers can be engaged in this process in schools; the table below indicates the types of activity which will fall into each level. All are important and we suggest that a diet of lots of level 1, some of level 2 and a little level 3 will have great impact on students.</p>
<p><strong>NRICH will create tasks and guidance documents to provide examples at each of these levels across a range of topics.</strong></p>
<table style="width: 631px;" border="1">
<tbody>
<tr>
<td colspan="2" style="width: 631px; height: 16px;">
<p>Three levels of STEM engagement</p>
</td>
</tr>
<tr>
<td rowspan="2" style="width: 44px; height: 20px;">
<p>ONE</p>
</td>
<td style="width: 587px; height: 20px;">
<p><strong>Raise awareness of general connections</strong> across subjects</p>
</td>
</tr>
<tr>
<td style="width: 587px; height: 261px;">
<ul>
<li>"Mr. Dalton tells me that this is very useful in chemistry"</li>
<li>"Physicists make heavy use of equations"</li>
<li>"Historically maths and physics often developed together"</li>
<li>"You will need to know plenty of maths to do science at A-level"</li>
<li>"The history of astronomy programme is on tonight"</li>
<li>"Scientific notation is used in science because the numbers can be so big or small, for example ...."</li>
<li>"When I did my biology degree I used statistics very frequently"</li>
<li>"Look at the beautiful symmetry/mathematical structure in this image from nature"</li>
<li>"Negative numbers are used to measure temperatures - the lowest possible temperature is about -273K."</li>
<li>Designers need to be able to use ideas of scale and proportion.</li>
<li>etc. etc.</li>
</ul>
</td>
</tr>
<tr>
<td rowspan="2" style="width: 44px; height: 40px;">
<p>TWO</p>
</td>
<td style="width: 587px; height: 40px;"><strong>Active reference in lessons to timetabled curriculum links</strong> across departments as will be encountered by the students</td>
</tr>
<tr>
<td style="width: 587px; height: 91px;">
<ul>
<li>"You will see the Hooke's law graphs when you do linear equations in maths next term"</li>
<li>"You will use trigonometry when you do the parallax module next week in physics"</li>
<li>"The way we are creating graphs for this experiment is different to the way you are creating graphs when doing lines of best fit in maths at the moment. Why? For these reasons ..."</li>
<li>"You will use equations like this in science this term"</li>
<li>When you want to adapt a pattern or a recipe for a different size or a different number of people, you will need to use proportion and fractions.</li>
<li>You often need to do a survey to find out what people want for a design brief.</li>
<li>etc.</li>
</ul>
</td>
</tr>
<tr>
<td rowspan="2" style="width: 44px; height: 25px;">
<p><strong>THREE</strong></p>
</td>
<td style="width: 587px; height: 25px;">
<p><strong>Use of cross-curricular tasks in the learning of the standard curriculum</strong></p>
</td>
</tr>
<tr>
<td style="width: 587px; height: 59px;">
<ul>
<li>Analysis in maths lessons of data collected in science/D&T lessons.</li>
<li>Testing in science of a mathematical model created in a maths lesson.</li>
<li>Using D&T or science contexts to contextualise a range of mathematical techniques, eg. proportion, ratio, fractions, percentages, averages and spread.</li>
<li>Termly review of SET books for maths content and maths books for SET content.</li>
<li><em>'See the General Ideas for Lessons and Learning' in this document.</em></li>
</ul>
</td>
</tr>
</tbody>
</table>
<p> </p>
</div>
</li>
<li><a href="#" id="hideShow2">Key elements of good STEM practice</a>
<div id="hidden2" style="display: none;">
<p><strong>Summary: COMMUNICATION, RESPECT AND EMPATHY FOR THE INTERESTS AND GOALS OF OTHERS</strong></p>
<ul>
<li>Respect for different departments and no sense of any subject being better or more important or more fundamental than any other: differences are great, but there are also commonalities.</li>
<li>Use positive language when talking about mathematics: it is unfortunately seen as OK to dismiss maths as un-cool, pointless or geeky and this has a very negative impact on subject perceptions amongst students.</li>
<li>Build on learning from other subjects, rather than trying to teach things from scratch that students might have encountered elsewhere.</li>
<li>Realise that all SET teachers will have to teach maths at some points in the curriculum.</li>
<li>Don't assume that the maths is easy for students when it is located in a context where they wouldn't expect to find it.</li>
<li>Try to find the hidden gems in any topic area, even if it is not your personal favourite.</li>
<li>Be aware that the important role of the teacher is as a learning facilitator in many cross-curricular activities, rather than the transmitter of all of the knowledge.</li>
<li>It is OK not to know 'all' the answers. In fact, it is desirable to provide contexts in which you do not know all the answers to all possible questions!</li>
<li>Always use units.</li>
<li>Awareness of differing uses of notation/terminology</li>
<li>Awareness of key confusables (e.g. weight/mass)</li>
<li>Stress to students that subject barriers are merely a teaching convenience.</li>
<li>Be aware that the mathematisation of the natural world is both subtle and amazing!</li>
</ul>
</div>
</li>
<li><a href="#" id="hideShow3">Key differences between maths and SET</a>
<div id="hidden3" style="display: none;">
<p>There are some differences in the ways maths and SET approach particular topics/terminology. It would be good to be aware of these. Some of the most important differences which can lead to confusion in students are:</p>
<ul>
<li>In maths a line of best fit on a scattergraph will be a straight line at KS3 and 4; in SET there are various ways in which graphs are constructed, depending on the purpose for the data.</li>
<li>Differences in approaches to algebra: e.g. balance method in mathematics vs formula triangles in science.</li>
<li>'Investigation' means different things in different departments.</li>
<li>'Evaluation', 'Proof' have specific mathematical meanings.</li>
<li>'Weight' is often mis-used in maths as being synonymous with 'mass'.</li>
<li>Notation for symbols can be confusing to students: in maths straight line graphs are often y-against-x; students often do not make the link to straight line graphs with other variable names.</li>
<li>Maths often uses neat, tidy and idealised diagrams, data and numbers; SET often makes use of real, noisy data and numbers.</li>
<li>Use of mathematical symbols is particularly important for older students who are planning on studying mathematics or physics at university.
<ul>
<li>$\approx$ means 'approximately equal to' (safe to use)</li>
<li>$\therefore$ means 'Therefore'</li>
<li>$\sim$ means many things, but most basically means 'is the same order of magnitude as'</li>
<li>$\equiv$ means 'equal by definition'</li>
<li>$\Rightarrow$ is the implication symbol (use carefully or avoid if unsure)</li>
</ul>
</li>
</ul>
</div>
</li>
<li><a href="#" id="hideShow4">Key obstacles hindering cross-curricular teaching</a>
<div id="hidden4" style="display: none;">
<p><strong>NRICH will design tasks which naturally fit into the curriculum in both maths and SET</strong>.</p>
<ul>
<li>Teacher knowledge outside their standard subject knowledge.</li>
<li>Teachers afraid of ceasing to be an 'established expert'.</li>
<li>Pupil inertia and disjointed '50 minute' thinking.</li>
<li>Both teachers and students feeling that they have to 'know' the answers or know exactly what to do before feeling safe and comfortable.</li>
<li>Cross-curricular coordination needed to provide links across departmental SoWs. E.g. Y9 are being taught the parallax error months before maths has covered any trigonometry.</li>
<li>Possible differences between exam boards specifications at KS4 as to content relevance.</li>
<li>Some of the maths used in SET at secondary school (e.g. time and reading scales) is left behind at primary school.</li>
<li>Assumptions that certain concepts and content are being covered 'elsewhere'.</li>
<li>Specification issues: e.g. changes to Science spec in 2011, new Maths spec only scheduled to run until 2012</li>
<li>Differences in 'abilities' or interests of students in different STEM subjects. D&T often taught in mixed ability groups, where maths and science are set.</li>
<li>Different teaching groups for maths, science and technology lessons.</li>
<li>Timetabling and the matching of topics across subject areas</li>
<li>Ease of communication between staff, especially if there exist departmental staffrooms.</li>
<li>Some key teachers resistant to change or sceptical about the value and importance of the 'other' subject(s).</li>
<li>Even if teachers are on board, timetabling might make meeting to plan difficult.</li>
<li>Often need technology provision for STEM lessons</li>
<li>MONEY - how do we fund, for example, cross-curricular planning meetings?</li>
<li>TIME - how do we find time to talk to other STEM colleagues?</li>
<li>Physical location of necessary resources in large school</li>
<li>Differences in time allocated to matching topics across subjects.</li>
<li>Students complaining that they've done something before in another subject.</li>
<li>Students claiming 'this isn't maths!' or 'this isn't science!'</li>
<li>Need the backing and understanding of SLT.</li>
</ul>
</div>
</li>
<li><a href="#" id="hideShow5">Practical ways for the departments and teachers to work together</a>
<div id="hidden5" style="display: none;">
<p><strong>NRICH will help by providing notes for teachers to accompany key problems from stemNRICH. We will also include key facts and cross-curricular information to help with planning outside of your subject specialism.</strong></p>
<p>Some general tips, many of which might be implements during start of year planning, are as follows:</p>
<ul>
<li>Knowing roughly what is taught, to whom, and when. </li>
<li>Knowing some of the ways particular key topics are introduced in different departments so that these methods can be referred to.</li>
<li>Include different levels of activity in schemes of work which will allow teacher and student comfort to grow as they progress from levels 1 to 3 above: be sure staff are comfortable with the small things before attempting more complex tasks</li>
<li>Spend some time in a staff meeting to learn the 'STEM history' of your staff, TAs and lab workers - do any staff have particularly strong practical or educational backgrounds in engineering, technology or science? This is an opportunity for 'non-specialists' to shine.</li>
<li>Observe a cross-departmental lesson or attend a planning meeting of another department.</li>
<li>Learn from humanities teachers who often work in a cross-curricular fashion.</li>
<li>Ask someone for help!</li>
</ul>
</div>
</li>
<li><a href="#" id="hideShow6">General ideas for lessons and learning</a>
<div id="hidden6" style="display: none;">
<p><strong>Many of the stemNRICH tasks can be used in the ways described here. We will provide guidance and suggestions for appropriate use in the teachers' notes to the tasks.</strong></p>
<ol>
<li>Data collection in SET then analysis of the data in maths; possibly with a feedback into SET.</li>
<li>Create an equation/make a prediction/do a calculation for a physical process in a maths lesson and then test out the prediction by performing the experiment in science.</li>
<li>Introduce a task in a SET lesson (to ensure the pupils all have the SET knowledge required), continuing to work on it in a maths lesson (using maths skills) and then complete it for a double homework - marked by both maths and SET teacher with their particular subject focus.</li>
<li>Introduce a short, regular and scheduled 'discussion' or circle time in both maths and SET lessons (perhaps 10 minutes a fortnight). Give students a chance to comment on the SET that they have noted in maths and vice versa and also to ask teachers/other students of wider questions concerning the mathematics they have seen in SET or the SET that they have seen in maths.</li>
<li>Set a half-termly cross-curricular review homework:
<ol style="list-style-type: lower-alpha;">
<li>Maths: Review SET books for mathematical content; make links with the mathematics that they have learnt during the term.</li>
<li>SET: Review maths books and suggest SET links or connections with the material covered. Look for parts of maths which have the most common uses.</li>
</ol>
</li>
<li>Joint poster project: Choose a theme and work on the same poster in both a maths and SET lesson, where the focus is finding the maths/SET related to a big theme, such as global warming.</li>
<li>Use snippets of problems/weekly challenges as starters when students enter room. Choose topic to give a flavour of the main theme of the day and plan for appropriate content in schemes of work.</li>
<li>Include some cross-curricular display material in corridors and classrooms.</li>
<li>Ask student newspaper to interview members of science and maths departments to find out their 'STEM history' in terms of the STEM experience at university, hobbies or other jobs.</li>
<li>Build on the clear links between 'investigation cycles' in science, 'design pentagon' in D&T and 'data handling cycles' in maths.</li>
<li>Use data loggers, light sensors, paper and other patterns, and other hands-on technology in maths.</li>
<li>Show a picture of an experiment/activity as used in SET to act as stimulated recall in maths at the appropriate time.</li>
<li>Have meaningful end of term cross-curricular activites.</li>
<li>Have <em>AsSTEMblies</em> - assemblies which focus on some aspect of STEM</li>
<li>Form a STEM club or a maths club or both. Form links between these clubs and clubs from other schools.</li>
</ol>
</div>
</li>
<li><a href="#" id="hideShow7">Curriculum area offering rich opportunities for collaboration</a>
<div id="hidden7" style="display: none;">
<p>These are the main curriculum areas offering natural STEM links as identified by our focus group of science and maths teachers - this will be enlarged after our focus group of D&T and maths teachers has met in July 2011.</p>
<ul>
<li>Graphs</li>
<li>Data handling and representation</li>
<li>Formula rearranging</li>
<li>Units of measurement</li>
<li>Standard form</li>
<li>Percentages, ratio and proportion</li>
<li>Scale drawing</li>
<li>The topics covered in functional skills</li>
<li>The historical links between mathematics and SET</li>
<li>The present day links between mathematics and SET</li>
</ul>
</div>
</li>
<li><a href="#" id="hideShow8">Specific examples of curriculum links by year</a>
<div id="hidden8" style="display: none;">
<p>These examples will hopefully give you an idea of some of the natural cross-over points between subjects at specific points during the year.</p>
<p><em>This will also be augmented after our Maths/D&T focus group has met.</em></p>
<table style="width: 659px;" border="1">
<tbody>
<tr>
<td> </td>
<td>
<p>Science</p>
</td>
<td style="width: 322px;">
<p>Maths</p>
</td>
</tr>
<tr>
<td>
<p>Y7</p>
</td>
<td>
<p>Variation (Y7 Biology)</p>
</td>
<td style="width: 322px;">
<p>Bar charts/line graphs (L3-6)<br></br>
Interpreting graphs (L4-6)</p>
</td>
</tr>
<tr>
<td>
<p>Y7</p>
</td>
<td>
<p>Mass & Weight, Speed, Pressure (all years Physics)</p>
</td>
<td style="width: 322px;">
<p>Reading scales (L3-4)<br></br>
Distance/time and mass/weight graphs (L5-6)<br></br>
Rates of change and compound measures (L7-8, Unit 2 GCSE)</p>
</td>
</tr>
<tr>
<td>
<p>Y7</p>
</td>
<td colspan="2" style="width: 610px;">
<p>Forces :Hooke's Law, Friction, Speed. Direct proportion as a concept appearing. From a maths viewpoint links to initial use of equations and basic algebraic substitution.</p>
</td>
</tr>
<tr>
<td>
<p>Y7</p>
</td>
<td colspan="2" style="width: 610px;">
<p>Classification & food webs -Could link the idea of classification in Science to classification of 2D shapes or quadrilaterals in maths. Statistics built in with the science content through use of data collection with quadrants, calculating averages when investigating the food webs. Possible connections to area as well e.g. estimating areas of different size leaves.</p>
</td>
</tr>
<tr>
<td>
<p>Y7</p>
</td>
<td colspan="2" style="width: 610px;">
<p>In KS3 Sc uses trolleys and light-gates to calculate speed. Sc could make a video of this the next time it happens for Ma to use to help the pupils recall this. </p>
</td>
</tr>
<tr>
<td>
<p>Y7/8</p>
</td>
<td colspan="2" style="width: 610px;">
<p>Negative numbers for boiling and melting points of elements; which stay solid for largest range of temperatures? This incorporates differences between negative numbers.</p>
</td>
</tr>
<tr>
<td>
<p>Y7/8</p>
</td>
<td style="width: 288px;">
<p>Balancing Equations (Y7 & 8 Chem)</p>
</td>
<td style="width: 322px;">
<p>Ratios<br></br>
Unitary method (L3-4)<br></br>
Simplify ratios, divide quantities into two parts (L4-5)<br></br>
Divide into quantities of more than two parts (L5-6, Unit 2 GCSE)<br></br>
Interpret ratios in a range of contexts (L6-7, Unit 2 GCSE)</p>
</td>
</tr>
<tr>
<td>
<p>Y8</p>
</td>
<td style="width: 288px;">
<p>Solar System (Y8 Physics)<br></br>
Swirling water tub with balls to demonstrate orbits.<br></br>
Relative sizes, distances from the sun, temperatures, orbital period</p>
</td>
<td style="width: 322px;">
<p>Loci (all levels)<br></br>
Circumference/area of a circle (L6-7, Unit 2/3 GCSE)<br></br>
Standard form<br></br>
Orbits (KS5)</p>
</td>
</tr>
<tr>
<td>
<p>Y8</p>
</td>
<td colspan="2" style="width: 610px;">
<p>Graphing, sequences from experiments such as measurement of temperature.</p>
</td>
</tr>
<tr>
<td>
<p>Y8</p>
</td>
<td style="width: 288px;">
<p>Liquid soap: how watered down does soap need to be before just slipping of hands/surfaces at various angles.</p>
</td>
<td style="width: 322px;">
<p>Angles of elevation, ratios, rearranging, averages from repeated measurements.</p>
</td>
</tr>
<tr>
<td>
<p>Y9</p>
</td>
<td colspan="2" style="width: 610px;">
<p>Building on the clear links between the Investigation Cycle in science and the Data Handling Cycle in maths by having a joint maths/sci project in Yr 9.</p>
</td>
</tr>
<tr>
<td>
<p>Y9/10</p>
</td>
<td colspan="2" style="width: 610px;">
<p>Attach data loggers to a pupil and watch as they attempt to create particular distance/time graphs. Pupils are used to seeing the <em>x</em> and <em>y</em> axes as spatial axes, which means the graph creates a picture of what we would see in real life. A distance/time graph is different, but some pupils assume it shows someone climbing a hill, for example.</p>
</td>
</tr>
<tr>
<td>
<p>Y9</p>
</td>
<td colspan="2" style="width: 610px;">
<p>Dinosaurs, percentages, ratio, scales and scale drawing; timelines. There could be links to Y7 fossils in science.</p>
</td>
</tr>
<tr>
<td>
<p>Y9</p>
</td>
<td colspan="2" style="width: 610px;">
<p>Pressures, forces & moments, formulae rearranging</p>
</td>
</tr>
<tr>
<td>
<p>Y9</p>
</td>
<td colspan="2" style="width: 610px;">
<p>Chemical Patterns, concentration of solutions, ratio.</p>
</td>
</tr>
<tr>
<td>
<p>Y9</p>
</td>
<td colspan="2" style="width: 610px;">
<p>Reaction Times,Drugs & Behaviour/Quest for Y9 Intelligence data handling. Science look at the effects of caffeine on reaction times. In maths could have a data handling project where collecting reactions times provides one set of data to investigate hypotheses comparing boys' and girls' 'abilities'</p>
</td>
</tr>
<tr>
<td>
<p>Y10+</p>
</td>
<td>
<p>Air Quality/pollutants (GCSE Chem, 21<sup>st</sup> Century)</p>
</td>
<td style="width: 322px;">
<p>Averages, range, outliers, repetition of trials (probability), reliability of results/comments and comparisons of results (Unit 1 GCSE)</p>
</td>
</tr>
<tr>
<td>
<p>Y10+</p>
</td>
<td>
<p>Risk (IAS 5 21<sup>st</sup> Century)</p>
</td>
<td style="width: 322px;">
<p>Percentages, ratio, proportionality, sampling (Unit 2 GCSE)</p>
</td>
</tr>
<tr>
<td>
<p>Y10+</p>
</td>
<td colspan="2" style="width: 610px;">
<p>Parallax Error, trigonometry. Linking initial discovery into trigonometrical ratios with this. Also could be developing concept of accuracy and bounds.</p>
</td>
</tr>
<tr>
<td>
<p>Y10+</p>
</td>
<td colspan="2" style="width: 610px;">
<p>Standard Form, Astronomical distances / cell biology. </p>
</td>
</tr>
<tr>
<td>
<p>Y10+</p>
</td>
<td colspan="2" style="width: 610px;">
<p>Lens formula, focal points / telephoto lens &enlargements. Interesting area, with links to formulae, angles and transformations.</p>
</td>
</tr>
<tr>
<td>
<p>Y10+</p>
</td>
<td colspan="2" style="width: 610px;">
<p>Crystal formation, 3D coordinates, angles between bonds, 3D Geometry. </p>
</td>
</tr>
<tr>
<td>
<p>Y10+</p>
</td>
<td colspan="2" style="width: 610px;">
<p>Kinematic Equations, rearranging formulae / real-life formulae</p>
</td>
</tr>
<tr>
<td>
<p>Y10+</p>
</td>
<td>
<p>Samples (Health Studies 21<sup>st</sup> Century)</p>
</td>
<td style="width: 322px;">
<p>Sampling (Unit 1 GCSE) [NB Sci just random, Ma includes stratified]</p>
</td>
</tr>
<tr>
<td>
<p>Y10+</p>
</td>
<td>
<p>Electrical Circuits (P5 21<sup>st</sup> Century)</p>
</td>
<td style="width: 322px;">
<p>Transposition of formulae, straight line graphs (Unit 2 GCSE)</p>
</td>
</tr>
<tr>
<td>
<p>Y10+</p>
</td>
<td>
<p>Correlation and cause (IAS2 21<sup>st</sup> Century)</p>
</td>
<td style="width: 322px;">
<p>Lines of best fit, correlation, types of graph (Unit 1 GCSE)</p>
</td>
</tr>
<tr>
<td>
<p>Y10+</p>
</td>
<td>
<p>Energy and the Environment (all levels Chem)</p>
</td>
<td style="width: 322px;">
<p>Scale drawing, percentages, graph skills, budgeting, area (all levels)</p>
</td>
</tr>
</tbody>
</table>
</div>
</li>
<li><a href="#" id="hideShow11">Common mathematical content important throughout KS3 and 4</a>
<div id="hidden11" style="display: none;">
<p>Some mathematical content runs throughout science at key stages 3, 4 and 5. It is worth remembering that good lessons in these areas can indirectly benefit students in other subjects, particularly if students are made aware of the connections in lessons.</p>
<p><em>This will also be augmented after our Maths/D&T focus group has met.</em></p>
<p><strong>Converting units of length, mass, capacity</strong></p>
<p>The use of units is a key issue in science. Dimension-ful answers should always be given with units (otherwise they are meaningless). The ability to convert between units is extremely important. nm and microns need to be recognised in Sc; mm, m, cm, km need to be converted between.</p>
<p>In Ma we use 1000 as the usual conversion between adjacent units, recognising that cm are an anomaly.</p>
<p>In Sc converting periods of time is important, eg to turn a number of minutes and seconds into a number of seconds.</p>
<p><strong>Standard index form</strong></p>
<p>In Sc this links closely with the conversion of units. For example, MW (megawatts) are 10<sup>6</sup> Watts, nm are 10<sup>-9</sup>m, etc.</p>
<p>In Ma standard form tends to be introduced and used with reference to measurements, for example to record very large distances (solar system data) or very small measurements (size of microbes), but then proceeds to abstract calculations.</p>
<p><strong>Using and converting compound measures</strong></p>
<p>Speed and density are used in Ma. Are pupils made aware that speed cannot be measured directly, but has to be calculated from the ratio between the distance travelled and the time taken'</p>
<p>Sc uses other compound measures too (pressure, work, etc).</p>
<p>The units can be used to help remember the formulas (eg m/s has metres ÷ seconds, so we need the distance ÷ time).</p>
<p><strong>Rounding/approximation/estimation</strong></p>
<p>In Sc rounding to sig figs and dp are both important, including knowing when it is appropriate to round and to what degree. </p>
<p>In Ma: approximation is done by rounding figures (and maybe then carrying out calculations on them), whereas estimation involves deciding on a value for something.</p>
<p>'The length of my classroom is about 6m' is an estimate.</p>
<p>In Sc when there is lots of data we might talk about the 'best estimate' for the 'true value'.</p>
<p>In Ma, at KS4, pupils need to realise that measurements have already been rounded by their very nature, whether this is explicitly stated or not. They need to be able to work out the upper/lower bounds for measurements. They also need to play the examination game, realising that if they are given a triangle and asked to work out the area, or to use trigonometry then they should
treat the measurements as being accurate?</p>
<p><strong>Using indices</strong> Sc: positive whole number powers, eg for volume formulas. <em>x</em><sup>-1</sup> for rate calculations (higher tier GCSE). Again there is a link with units (volume units are m<sup>3</sup>, etc, so they involve multiplying three lengths together).</p>
<p><strong>Proportion and ratio</strong> Sc: direct and inverse proportion only. Ma: higher GCSE includes square and inverse square too. In Sc the links between the graph and the proportion it implies are important.</p>
<p><strong>Using algebra</strong> In Sc this includes substituting, rearranging, solving equations etc. NB: the units are still important! Formula triangles are often used in Sc (eg for speed, density, etc) and in Ma (for trigonometrical formulae).</p>
<p><strong>Drawing graphs</strong> In Sc this involves: Drawing and labelling axes; plotting graphs; reading values from graphs; creating scatter graphs and the line of best fit; relating a table of values to a graph; drawing graphs for a particular proportional relationship; bar charts</p>
<p><strong>The data handling cycle and the investigation cycle</strong> There are considerable links between these, with initial hypotheses being expressed in both, then data collected, analysis of the data (using graphs and calculations) and an evaluation of what it means, perhaps then leading to a new hypothesis and a second cycle.</p>
<p><strong>Calculations, including using fractions/decimals/percentages</strong> Sc: in Yr 11 percentages are particularly important</p>
<p><strong>Use of a calculator</strong> Entering calculations in the correct order, finding the right keys (eg for cube root) and using brackets as appropriate.</p>
<p><strong>Converting units of area/volume</strong> Ma: important at KS4</p>
<p><strong>Calculating perimeters, areas and volumes</strong> Important for Sc and for Ma</p>
<p><strong>The mean and range</strong> These are used in Ma and Sc; Sc does not use mode/modal/median</p>
<p><strong>Probability</strong> In Ma pupils must use fractions (or an equivalent) to describe probabilities and may not use words. In Sc pupils can explain, using the language of probability, how likely it is that a particular result true or meaningful.</p>
<p> </p>
</div>
</li>
<li><a href="#" id="hideShow9">Content uses specific to university biology/chemistry</a>
<div id="hidden9" style="display: none;">
<p>If you take a look at the bigger picture then many students will choose to study science at university and the mathematics they learn at school will become fundamentally important to them. Here we give a comprehensive list of the important subjects in mathematics compiled from all of the NRICH maths content tags by a second-year undergraduate - NRICH has the capability to be searched according
to these tags. This list will be relevant to KS3/4/5 science and should be made known to students who might consider studying biology or chemistry at university.</p>
<table style="border:none;">
<tbody>
<tr>
<td nowrap="nowrap" style="height: 18px;">
<h2>Maths content</h2>
</td>
<td nowrap="nowrap" style="height: 18px;">
<h2>Applications</h2>
</td>
</tr>
<tr>
<td colspan="2" style="height: 18px;">
<h3>Extremely important</h3>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Processing and representing data</p>
</td>
<td style="height: 18px;">
<p>Many various</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Interpreting data</p>
</td>
<td style="height: 18px;">
<p>Many various</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Handling data</p>
</td>
<td style="height: 18px;">
<p>Many various</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Data logging</p>
</td>
<td style="height: 18px;">
<p>Many various</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Data collection</p>
</td>
<td style="height: 18px;">
<p>Many various</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Sampling</p>
</td>
<td style="height: 18px;">
<p>Many various</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Types of data</p>
</td>
<td style="height: 18px;">
<p>Many various</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Experimental design</p>
</td>
<td style="height: 18px;">
<p>Many various</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Working systematically</p>
</td>
<td style="height: 18px;">
<p>A very important skill to have!</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Calculating with ratio and proportion</p>
</td>
<td style="height: 18px;">
<p>Generally very important</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p> </p>
<h3>Very important</h3>
</td>
<td style="height: 18px;">
<p> </p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Game theory</p>
</td>
<td style="height: 18px;">
<p>Behaviour</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Speed</p>
</td>
<td style="height: 18px;">
<p>Rate of reaction, physiology</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Volume and capacity</p>
</td>
<td style="height: 18px;">
<p>Related to surface area</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Surface and surface areas</p>
</td>
<td style="height: 18px;">
<p>Uptake of nutrients etc</p>
</td>
</tr>
<tr>
<td style="height: 25px;">
<p>Angle properties of shapes</p>
</td>
<td style="height: 25px;">
<p>Bond angles</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Angles at a point or line</p>
</td>
<td style="height: 18px;">
<p>Bond angles</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Angles</p>
</td>
<td style="height: 18px;">
<p>Bond angles</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Laws of logs</p>
</td>
<td style="height: 18px;">
<p>Various</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Log functions</p>
</td>
<td style="height: 18px;">
<p>Many various</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Exponential function</p>
</td>
<td style="height: 18px;">
<p>Many various</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Exp growth and decay</p>
</td>
<td style="height: 18px;">
<p>Cooling curves, modelling,</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Sketching</p>
</td>
<td style="height: 18px;">
<p>Many various</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Gradients</p>
</td>
<td style="height: 18px;">
<p>Many various</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Graphs</p>
</td>
<td style="height: 18px;">
<p>Data handling, modelling</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Trial and improvement</p>
</td>
<td style="height: 18px;">
<p>Modelling, experiment</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Investigations</p>
</td>
<td style="height: 18px;">
<p>Experiment</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Selecting and using information</p>
</td>
<td style="height: 18px;">
<p>Designing experiments</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Recording mathematics</p>
</td>
<td style="height: 18px;">
<p>Experiment</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Making and testing hypotheses</p>
</td>
<td style="height: 18px;">
<p>Experiment, investigation</p>
</td>
</tr>
<tr>
<td colspan="2" style="height: 18px;">
<p> </p>
<h3>Some understanding needed</h3>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Cartesian equations of lines</p>
</td>
<td style="height: 18px;">
<p>Modelling</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Co ordinates</p>
</td>
<td style="height: 18px;">
<p>Data handling</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Cubic functions</p>
</td>
<td style="height: 18px;">
<p>Modelling</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Composition of functions</p>
</td>
<td style="height: 18px;">
<p>Various</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Inverses</p>
</td>
<td style="height: 18px;">
<p>Various</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Quadratic functions</p>
</td>
<td style="height: 18px;">
<p>Modelling</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Linear functions</p>
</td>
<td style="height: 18px;">
<p>Modelling, data handling</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Transformation of functions</p>
</td>
<td style="height: 18px;">
<p>Modelling, linearisation</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Asymptotes</p>
</td>
<td style="height: 18px;">
<p>Modelling</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Indices</p>
</td>
<td style="height: 18px;">
<p>Modelling, data handling</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Algebraic fractions</p>
</td>
<td style="height: 18px;">
<p>Modelling, data handling</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Solving equations graphically</p>
</td>
<td style="height: 18px;">
<p>Modelling, data handling</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Other equations</p>
</td>
<td style="height: 18px;">
<p>Modelling, data handling</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Quadratic</p>
</td>
<td style="height: 18px;">
<p>Modelling, data handling</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Simultaneous equations</p>
</td>
<td style="height: 18px;">
<p>Modelling, data handling</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Linear equations</p>
</td>
<td style="height: 18px;">
<p>Modelling, data handling</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Factorisation</p>
</td>
<td style="height: 18px;">
<p>Modelling, data handling</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Expanding brackets</p>
</td>
<td style="height: 18px;">
<p>Modelling, data handling</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Manipulation</p>
</td>
<td style="height: 18px;">
<p>Modelling, data handling</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Creating expressions</p>
</td>
<td style="height: 18px;">
<p>Modelling, data handling</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Introducing algebra</p>
</td>
<td style="height: 18px;">
<p>Modelling, data handling</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Using symbols</p>
</td>
<td style="height: 18px;">
<p>Modelling, data handling</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Formulae</p>
</td>
<td style="height: 18px;">
<p>Modelling, data handling</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Generally</p>
</td>
<td style="height: 18px;">
<p>Modelling, data handling</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Estimating and approximating</p>
</td>
<td style="height: 18px;">
<p>Data handling</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Multiplication + division</p>
</td>
<td style="height: 18px;">
<p>Data handling</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Addition + subtraction</p>
</td>
<td style="height: 18px;">
<p>Data handling</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Approximate solution</p>
</td>
<td style="height: 18px;">
<p>Useful when doing an experiment</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Direct and inverse proportion</p>
</td>
<td style="height: 18px;">
<p>Data handling, modelling</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Ratio</p>
</td>
<td style="height: 18px;">
<p>Data handling</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Equivalent fractions, decimals and percentages</p>
</td>
<td style="height: 18px;">
<p>Data handling</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Mixed fractions, decimals and percentages</p>
</td>
<td style="height: 18px;">
<p>Data handling</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Calculating with percentages</p>
</td>
<td style="height: 18px;">
<p>Data handling</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Calculating with decimals</p>
</td>
<td style="height: 18px;">
<p>Data handling</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Calculating with fractions</p>
</td>
<td style="height: 18px;">
<p>Data handling</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Percentages</p>
</td>
<td style="height: 18px;">
<p>Data handling</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Decimals</p>
</td>
<td style="height: 18px;">
<p>Data handling</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Fractions</p>
</td>
<td style="height: 18px;">
<p>Data handling</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Standard index form</p>
</td>
<td style="height: 18px;">
<p>Data handling</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Powers and roots</p>
</td>
<td style="height: 18px;">
<p>Data handling, experiment</p>
</td>
</tr>
<tr>
<td style="height: 26px;">
<p>Rounding</p>
</td>
<td style="height: 26px;">
<p>Data handling</p>
</td>
</tr>
<tr>
<td colspan="2" style="height: 18px;">
<p> </p>
<h3>Used occasionally</h3>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Optimisation</p>
</td>
<td style="height: 18px;">
<p>More advanced topics</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Chi squared tests</p>
</td>
<td style="height: 18px;">
<p>Usually population-related</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Statistics generally</p>
</td>
<td style="height: 18px;">
<p>ANOVA testing, understanding how reliable a result is</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>3D</p>
</td>
<td style="height: 18px;">
<p>Chemistry - orbital geometry, shapes of molecules</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Max/min/optimise</p>
</td>
<td style="height: 18px;">
<p>Chemical reactions, optimisation</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Curve fitting</p>
</td>
<td style="height: 18px;">
<p>Data handling, modelling</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Matrices</p>
</td>
<td style="height: 18px;">
<p>Game theory: payoff matrices</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Making and proving conjectures</p>
</td>
<td style="height: 18px;">
<p>Experiment</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Mathematical modelling</p>
</td>
<td style="height: 18px;">
<p>Making predictions</p>
</td>
</tr>
<tr>
<td style="height: 18px;">
<p>Complex numbers</p>
</td>
<td style="height: 18px;">
<p>Wave and diffusion equations</p>
</td>
</tr>
</tbody>
</table>
</div>
</li>
<li><a href="#" id="hideShow10">Get started on cross curricular planning</a>
<div id="hidden10" style="display: none;">
<p>To get started on STEM in your school it can be useful simply to get the views of interested parties. These simple questions can be a good focus for discussion.</p>
<div>
<ul>
<li>What do you think might be key elements of good STEM practice?</li>
<li>What do you think might be key obstacles hindering cross-curricular teaching?</li>
<li>What curriculum areas do you think might offer rich opportunities for collaboration?</li>
<li>Can you suggest any practical ways for the departments to work together/to support teachers?</li>
<li>Do you have any general ideas for lessons and learning?</li>
<li>Do you see any potential sources of confusion between departments?</li>
</ul>
</div>
</div>
</li>
<li><a href="#" id="hideShow12">Acknowledgements</a><br></br>
<br></br>
<div id="hidden12" style="display: none;">
<p>We are indebted to the following teachers for contributing to the initial development of the KS3/4 STEM pages:</p>
<p style="margin-left: 1cm;">Samantha Armsby, Sawston Village College</p>
<p style="margin-left: 1cm;">Alissa Baldwin, PGCE Trainee, Cambridge University</p>
<p style="margin-left: 1cm;">Mark Dawes, Comberton Village College</p>
<p style="margin-left: 1cm;">Rachel Dixon, Tudhoe Grange school</p>
<p style="margin-left: 1cm;">Cecilia Freer, Swavesey Village College,</p>
<p style="margin-left: 1cm;">Tabitha George, Swavesey Village College</p>
<p style="margin-left: 1cm;">Sarah Glover, Tudhoe Grange school</p>
<p style="margin-left: 1cm;">Luke Pendlebury, St. Faith's School</p>
<p style="margin-left: 1cm;">Euan Willder, Comberton Village College</p>
<p> </p>
<p>We are also grateful to the many students who have worked with us thus far on developing these scientific mathematics materials.</p>
<p>We thank the Cambridge University Faculty of education for inviting us to speak to their science and maths PGCE students about stemNRICH, from which many developments have followed.</p>
<p>We are also very grateful to the Clothworkers' Foundation for funding this significant and important project at KS3/4.</p>
<p>Finally we are grateful to the Cambridge University Transkills project which provided funding for the development of the KS5 stemNRICH pages where the concepts around which the STEM: secondary pages are to be created were invented, tested and refined; many of the resources in STEM: secondary will form a direct link with these more advanced resources leading to coherent links from years 11 to
18</p>
<p> </p>
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<div class="framework">BACKGROUND<br></br>
<p>This resource is being developed to extend the more advanced <a href="http://nrich.maths.org/stemNRICH">stemNRICH</a> pages to KS3 and 4 level.</p>
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<p>It is being developed by Dr. Jenny Gage (jag55@cam.ac.uk) in collaboration with practising science, mathematics and technology teachers, students and the NRICH community.</p>
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<p>The resources will be designed to fit around meaningful links between subjects and will be accompanied by teacher support material.</p>
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Dev STEM Teachers