outlook • MAY 2007

LEARNING THROUGH LANDSCAPES

groundnotes January 2008

Why teach maths outdoors?Evidence is growing that outdoor

lessons help pupil motivation andunderstanding and encourage anatmosphere of collaboration betweenpupils and teachers, which helps childrendevelop their interpersonal skills. Movingoutside the confines of the classroomrequires that pupils are given responsibility,this increases levels of trust and pupils’sense of ownership.

Lessons outdoors also offer moreopportunities to use different teaching andlearning styles, particularly problem solvingand group work, which enhance pupils’self-esteem and self-confidence. Childrenreport that outdoor lessons are generallymore interesting, varied and relaxed, thatpractical lessons are easier to understand,and that teachers are friendlier outdoors.Even a simple blast of fresh air, comparedto a hot and stuffy classroom, can make awelcome difference.

Outdoors maths

Schoolgrounds-UK

While any outdoor environment canpromote learning, use of the schoolgrounds offers specific benefits. Becausethey are on your doorstep school groundscan make outdoor learning a daily event.Staff new to outdoor learning can taketheir first outdoor lessons alongside moreexperienced colleagues in a familiarenvironment, building confidence in theirabilities to assess and manage risk outsidethe classroom. In this way, you can lay thefoundations for learning beyond theschool site and ensure that off siteeducational visits run smoothly.

The way that learning outside theclassroom can motivate children and helpthem apply their knowledge has particularimportance for a subject which manychildren find difficult. By providing realexamples of how mathematical conceptscan be developed and applied, teachingmaths outdoors can prevent the subjectbeing seen as too abstract.

Where can you teach mathsin your school grounds?

Every part of your school grounds can beused as a learning resource but in thisGroundnotes we will look at some specific,common features. The suggested activitiesare most relevant for the primarycurriculum, but hopefully will provide someideas for extending them for older or moreable pupils. The challenge provided byeach activity can be varied according tohow detailed your instructions are. Formore able pupils set them a challenge ofanswering a question, but let them workout how.

BoundariesBoundaries offer an ideal opportunity for

practising the estimation and measurementof distance, whether they are walls, fencesor hedges.

Choose a section with a clear start andfinish mark that pupils can walk alongsidesafely. Mark a set distance, perhaps 100metres, and ask children to walk thedistance, counting their paces. It is easier tocount double paces (i.e. always on thesame foot) particularly once you reach

© Ian Jackson

groundnotes • JANUARY 2008

OUTDOORS MATHS

Then measure the distance to each pointby pacing. A scale map can be drawn up byusing a protractor to mark the bearings,and marking the distance along eachbearing to the edges of the field using asuitable scale. The area of an irregular fieldcan be estimated by dividing it intorectangles and triangles whose areas canbe more easily calculated, or by drawing itonto squared paper and counting thesquares.

Hard surfaced areas can be enhancedwith mathematical playground markings ormazes. Even a simple game of hopscotchinvolves counting skills, but you couldinvent your own games that practise morecomplex mathematical skills. Paving stonesoffer a ready-made grid for chalking innumber patterns or for creating giantversions of board games, such as snakesand ladders (you’ll need to buy some giantdice). You also have more opportunities forpractising area calculations, as well asdemonstrations of tessellations.

If you have a large area of grass, linkscience and maths by carrying out a daisysurvey. A good tip for keeping track ofdaisies is to use counting cubes, as well as aquadrat or hoop to define an area. Throwthe quadrat onto the grass, and then covereach daisy with a counting cube. Once allthe daisies are covered, the cubes can betaken away and built into columns of ten tohelp with the counting. Test hypothesesabout where daisies grow best bycomparing the numbers in different areasof the field: shady or sunny, where they aretrampled or where they are not.

Play and sport areasApply maths to sports to practise

timings, draw graphs and calculate averagesor percentages. Time how long each childtakes to complete a set challenge on a trimtrail or time races across the playground.Who is the fastest and who the slowest?What is the average time? Create a graphto show different times. If you have footballor netball goals, ask each child to take 5shots, and then calculate their percentagesuccess rate, which can be also be shownon a graph.

above twenty. Set children off individuallyat intervals of about 20 seconds to avoidthem falling into step with each other,though they may need some practise towalk at a steady, comfortable rate. Get thechildren to repeat the exercise until they are sure they have a consistent number of paces.

Once pupils have practised measuringone length, ask them to estimate differentdistances – e.g. 5 metres or 20 metres –either by eye or by pacing, standing wherethey think that distance reaches. Use a longmeasure to find out who’s closest to theright distance. Pupils can then trymeasuring the whole grounds by pacing.

Paces are one ancient way of measuringdistances, but you might be able to thinkup more, for example lying on the groundto see how many body lengths a path is.You can link this into old methods ofmeasuring such as those used by theRomans, which included pes (foot = 29.6cm), digitus (thumbnail = 1.85 cm) orpalmus (palm = 7.4 cm).

Brick walls provide an opportunity forestimating quantities which can be checkedby counting. Measure the area of anindividual brick then multiply by thenumber of bricks, to estimate the area ofthe whole wall. Compare your answer tothe area you get by multiplying the widthand length of the wall – you might need toestimate the height if the wall is very tall.

If your boundaries are old hedgerowsyou can estimate their age by countinghow many species of trees and shrubs thereare in a 30 metre length. Large stumps inthe hedge will prove that it is old and notrecently planted with lots of differentspecies. As a rough guide, there is onespecies of hedgerow plant for every 100years of a hedge’s life.

SpacesSchool grounds provide large spaces for

applying calculations such as areas andperimeters on a giant scale. Choose a clearlydefined hard surface area, such as a gamescourt, and measure the length and widthwith a long measuring tape, a trundlewheel or by pacing. Calculate the area andperimeter of the space – you could chalkyour calculations onto the ground. If youhave two suitable areas, pupils couldestimate which is larger before theymeasure, or calculate how many times onespace would fit into the other.

More challenge is provided by anirregularly shaped field. From a centralpoint, use a compass to measure thebearing (angle of turn away from north) tovarious points around the edge of the field.

groundnotes • JANUARY 2008

OUTDOORS MATHS

measurements all round the pond cancreate an accurate scale drawing.

Times tables can be illustrated withnatural features. Easy ones include legs oninsects for the 6x table or wings on birdsfor the 2x table. Different flowers havedifferent numbers of petals, use abuttercup for the 5x table. Woodlice have7 segments to their bodies. How manyother times tables can pupils find in the grounds?

CreaturesAs with many mathematical

investigations, activities involving livingcreatures can link with other subjects such as ICT, geography, environmental studiesand science.

A minibeast hunt will uncover creatureswith different numbers of legs, with orwithout wings, and with other physicaldifferences. Putting minibeasts into setsaccording to these differences helps withidentification. Children could create theirown identification charts according tothese sets, drawing pictures of eachminibeast. Got a vegetable garden plaguedwith snails? Look upon them as an easy-to-handle minibeast for your lessons. Closeobservation of the shells providesopportunities for sorting according todifferences, comparative language, andlooking at spirals.

Feeding birds can help your mathslessons as well as the local featheredpopulation. There are lots of observationsand experiments that can be carried out, aspart of hypothesis testing or learning aboutgraphical presentation of data. Carry outobservations of your bird feeders at settimes to see how the numbers of visitorsvary across the day, week or year? Placefeeders in different parts of the grounds tofind out if some are more popular thanothers? Experiment with different types offood on different tables and work out whatfood attracts which birds? Observing birdsacross your grounds can also revealinteresting patterns like those schools witha peak in gull numbers after lunchtime, asthey come to scavenge.

Trim trail equipment includesinteresting shapes and angles for namingand measurement. Ask children to searchfor triangles, squares or circles, or measureangles between different parts of theequipment.

Natural areasTrees, gardens, ponds or wildlife areas

offer a wealth of opportunities forapplying maths to real contexts. Differentleaves and flowers can provide exercises incounting, multiplying, sorting, comparativelanguage (more / fewer petals) andsymmetry.

A famous numerical phenomenonoccurring in plants is the Fibonacci Series,named after an Italian mathematicianborn in 1175. The series begins: 1, 1, 2, 3,5, 8, 13, 21, 34, 55, 89, 144, 233 . . . andso on, forever. Each number is the sum ofthe preceding two. Look closely at seedand flower heads (sunflowers or daisies aregood examples) and you can see spirals,curving both to the left and to the right.The number of spirals will nearly always beconsecutive numbers in the Fibonacciseries. This arrangement seems to form anoptimal packing of the seeds so that, nomatter how large the seed head, they areuniformly packed at any stage, all theseeds being the same size, no crowding in the centre and not too sparse at the edges.

Pine cones also show Fibonacci spiralsclearly, and many plants show theFibonacci series in the arrangements of theleaves around their stems. Look down on

a plant and see that the leaves are oftenarranged so that those above do not hidethe leaves below. This means that eachgets a good share of the sunlight andcatches the most rain to channel down to the roots as it runs down the leaf to the stem. How many spirals and Fibonacci sequences can be found in your school grounds?

If you have several trees in yourgrounds you could set the challenge offinding which is tallest or which has thebiggest girth or widest canopy, perhapsfirst by estimation and then by measuring.Children could also measure anglesbetween two twigs. See the Groundnotes*Teaching with Trees for more ideas.

Ponds of different shapes providediffering levels of difficulty in calculatingsurface areas. Rectangular ponds aresimple but irregular natural ponds offer achallenging task to work out how tosketch a scale diagram and estimate thearea. One method is: choose two fixedpoints near the pond or put two sticks inthe ground; mark the two fixed points onsquared paper, making sure that they arethe right distance apart according to yourscale; measure to different points of thepond’s perimeter from each fixed point(e.g. one point might be 2 metres fromone stick and 3.5 metres from the other);use a pair of compasses to mark thosedistances to scale on your diagram (e.g.draw an arc 2 cm from one point and anarc 3.5 cm from the other); where the twoarcs intersect will be a point on the edgeon the pond. Repeating these

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groundnotes • JANUARY 2008

OUTDOORS MATHS

the confines of the classroom. In fact,children are usually better behaved inoutdoor lessons as they are moremotivated and interested, but there aresome general planning tips in theGroundnotes* on Managing behaviour inthe outdoor classroom.

Of course, maths is not the only subjectto teach outdoors. You might want to buildin a rolling programme of curriculumreview and gradually take more lessons inall subjects into the school grounds.Creating a timetable for school groundslessons will ensure that there are no clashesover the use of this valuable space.

*These Groundnotes are available from the MemberServices area of our website.

Planning maths in yourschool grounds

To make the most of your schoolgrounds for teaching maths, outdoorlessons should be written into yourcurriculum planning, so that it is anexpectation that lessons are taken outsideon a regular basis. When lessons in theschool grounds are regular and frequent,children can quickly learn the expectedbehaviour.

At a maths curriculum planning session,work through your scheme of work,highlighting opportunities for schoolgrounds lessons. You could start with the

ideas included in this Groundnotes. Lookfor gaps, either throughout the year or inareas of the curriculum, and talk aboutwhat other learning opportunities thereare. When you review your lessons, includeopportunities for staff to feedback on howtheir school grounds lessons wentincluding what worked, and what needschanging?

Some teachers will be more confidentthan others in teaching outdoors. Considerhow you can share this expertise, forexample through team teaching, orspending staff meeting or training timesharing good practice. A particular concern can be pupil behaviour beyond

© This resource was originally created as part of the Schoolgrounds-UKmembership scheme from the national school grounds charityLearning through Landscapesoperating in Scotland as Grounds for LearningA registered charity (No. 803270)

To find out more about membership call 01962 845811 or visit www.ltl.org.uk

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© Ian Jackson