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outlook • MAY 2007



                 groundnotes                                                                                                              January 2008

                                                                                                                                Schoolgrounds-UK
© Ian Jackson




                Outdoors maths                                                                                 Where can you teach maths
                                                                                                               in your school grounds?
                                                                                                                  Every part of your school grounds can be
                                                                                                               used as a learning resource but in this
                                                                                                               Groundnotes we will look at some specific,
                Why teach maths outdoors?                           While any outdoor environment can          common features. The suggested activities
                    Evidence is growing that outdoor             promote learning, use of the school           are most relevant for the primary
                lessons help pupil motivation and                grounds offers specific benefits. Because       curriculum, but hopefully will provide some
                understanding and encourage an                   they are on your doorstep school grounds      ideas for extending them for older or more
                atmosphere of collaboration between              can make outdoor learning a daily event.      able pupils. The challenge provided by
                pupils and teachers, which helps children        Staff new to outdoor learning can take        each activity can be varied according to
                develop their interpersonal skills. Moving       their first outdoor lessons alongside more     how detailed your instructions are. For
                outside the confines of the classroom             experienced colleagues in a familiar          more able pupils set them a challenge of
                requires that pupils are given responsibility,   environment, building confidence in their      answering a question, but let them work
                this increases levels of trust and pupils’       abilities to assess and manage risk outside   out how.
                sense of ownership.                              the classroom. In this way, you can lay the
                    Lessons outdoors also offer more             foundations for learning beyond the           Boundaries
                opportunities to use different teaching and      school site and ensure that off site              Boundaries offer an ideal opportunity for
                learning styles, particularly problem solving    educational visits run smoothly.              practising the estimation and measurement
                and group work, which enhance pupils’               The way that learning outside the          of distance, whether they are walls, fences
                self-esteem and self-confidence. Children         classroom can motivate children and help      or hedges.
                report that outdoor lessons are generally        them apply their knowledge has particular         Choose a section with a clear start and
                more interesting, varied and relaxed, that       importance for a subject which many           finish mark that pupils can walk alongside
                practical lessons are easier to understand,      children find difficult. By providing real      safely. Mark a set distance, perhaps 100
                and that teachers are friendlier outdoors.       examples of how mathematical concepts         metres, and ask children to walk the
                Even a simple blast of fresh air, compared       can be developed and applied, teaching        distance, counting their paces. It is easier to
                to a hot and stuffy classroom, can make a        maths outdoors can prevent the subject        count double paces (i.e. always on the
                welcome difference.                              being seen as too abstract.                   same foot) particularly once you reach

                                                                                                                          LEARNING THROUGH LANDSCAPES
groundnotes • JANUARY 2008                                                                     Then measure the distance to each point
                                                                                               by pacing. A scale map can be drawn up by
                                                                                               using a protractor to mark the bearings,
                                                                                               and marking the distance along each
                                                                                               bearing to the edges of the field using a
                                                                                               suitable scale. The area of an irregular field
                                                                                               can be estimated by dividing it into
                                                                                               rectangles and triangles whose areas can
                                                                                               be more easily calculated, or by drawing it
                                                                                               onto squared paper and counting the
                                                                                               squares.
                                                                                                   Hard surfaced areas can be enhanced
                                                                                               with mathematical playground markings or
                                                                                               mazes. Even a simple game of hopscotch
                                                                                               involves counting skills, but you could
                                                                                               invent your own games that practise more
                                                                                               complex mathematical skills. Paving stones
                                                                                               offer a ready-made grid for chalking in
                                                                                               number patterns or for creating giant
                                                                                               versions of board games, such as snakes
                                                                                               and ladders (you’ll need to buy some giant
                                                                                               dice). You also have more opportunities for
                                                                                               practising area calculations, as well as
                                                                                               demonstrations of tessellations.
                                                                                                   If you have a large area of grass, link
                                                                                               science and maths by carrying out a daisy
                                                                                               survey. A good tip for keeping track of
                                                                                               daisies is to use counting cubes, as well as a
                                                                                               quadrat or hoop to define an area. Throw
                                                                                               the quadrat onto the grass, and then cover
                                                                                               each daisy with a counting cube. Once all
above twenty. Set children off individually       Brick walls provide an opportunity for       the daisies are covered, the cubes can be
at intervals of about 20 seconds to avoid      estimating quantities which can be checked      taken away and built into columns of ten to
them falling into step with each other,        by counting. Measure the area of an             help with the counting. Test hypotheses
though they may need some practise to          individual brick then multiply by the           about where daisies grow best by
walk at a steady, comfortable rate. Get the    number of bricks, to estimate the area of       comparing the numbers in different areas
children to repeat the exercise until they     the whole wall. Compare your answer to          of the field: shady or sunny, where they are
are sure they have a consistent number         the area you get by multiplying the width       trampled or where they are not.
of paces.                                      and length of the wall – you might need to
    Once pupils have practised measuring       estimate the height if the wall is very tall.
one length, ask them to estimate different        If your boundaries are old hedgerows
distances – e.g. 5 metres or 20 metres –       you can estimate their age by counting
either by eye or by pacing, standing where     how many species of trees and shrubs there
they think that distance reaches. Use a long   are in a 30 metre length. Large stumps in
measure to find out who’s closest to the        the hedge will prove that it is old and not
right distance. Pupils can then try            recently planted with lots of different
measuring the whole grounds by pacing.         species. As a rough guide, there is one
    Paces are one ancient way of measuring     species of hedgerow plant for every 100
distances, but you might be able to think      years of a hedge’s life.
up more, for example lying on the ground
to see how many body lengths a path is.        Spaces
You can link this into old methods of              School grounds provide large spaces for
measuring such as those used by the            applying calculations such as areas and
Romans, which included pes (foot = 29.6        perimeters on a giant scale. Choose a clearly
cm), digitus (thumbnail = 1.85 cm) or          defined hard surface area, such as a games
palmus (palm = 7.4 cm).                        court, and measure the length and width
                                               with a long measuring tape, a trundle           Play and sport areas
                                               wheel or by pacing. Calculate the area and          Apply maths to sports to practise
                                               perimeter of the space – you could chalk        timings, draw graphs and calculate averages
                                               your calculations onto the ground. If you       or percentages. Time how long each child
                                               have two suitable areas, pupils could           takes to complete a set challenge on a trim
                                               estimate which is larger before they            trail or time races across the playground.
                                               measure, or calculate how many times one        Who is the fastest and who the slowest?
                                               space would fit into the other.                  What is the average time? Create a graph
                                                   More challenge is provided by an            to show different times. If you have football
                                               irregularly shaped field. From a central         or netball goals, ask each child to take 5
                                               point, use a compass to measure the             shots, and then calculate their percentage
                                               bearing (angle of turn away from north) to      success rate, which can be also be shown
                                               various points around the edge of the field.     on a graph.

OUTDOORS MATHS
groundnotes • JANUARY 2008

                                                                                               measurements all round the pond can
                                                                                               create an accurate scale drawing.
                                                                                                  Times tables can be illustrated with
                                                                                               natural features. Easy ones include legs on
                                                                                               insects for the 6x table or wings on birds
                                                                                               for the 2x table. Different flowers have
                                                                                               different numbers of petals, use a
                                                                                               buttercup for the 5x table. Woodlice have
                                                                                               7 segments to their bodies. How many
                                                                                               other times tables can pupils find in
                                                                                               the grounds?


                                                                                               Creatures
                                                                                                   As with many mathematical
                                                                                               investigations, activities involving living
                                                                                               creatures can link with other subjects such
                                                                                               as ICT, geography, environmental studies
                                                                                               and science.
                                                                                                   A minibeast hunt will uncover creatures
                                                                                               with different numbers of legs, with or
                                                                                               without wings, and with other physical
                                                                                               differences. Putting minibeasts into sets
                                                                                               according to these differences helps with
                                                                                               identification. Children could create their
                                                                                               own identification charts according to
                                                                                               these sets, drawing pictures of each
                                                                                               minibeast. Got a vegetable garden plagued
                                                                                               with snails? Look upon them as an easy-to-
    Trim trail equipment includes               a plant and see that the leaves are often      handle minibeast for your lessons. Close
interesting shapes and angles for naming        arranged so that those above do not hide       observation of the shells provides
and measurement. Ask children to search         the leaves below. This means that each         opportunities for sorting according to
for triangles, squares or circles, or measure   gets a good share of the sunlight and          differences, comparative language, and
angles between different parts of the           catches the most rain to channel down          looking at spirals.
equipment.                                      to the roots as it runs down the leaf to
                                                the stem. How many spirals and
Natural areas                                   Fibonacci sequences can be found in
    Trees, gardens, ponds or wildlife areas     your school grounds?
offer a wealth of opportunities for                If you have several trees in your
applying maths to real contexts. Different      grounds you could set the challenge of
leaves and flowers can provide exercises in      finding which is tallest or which has the
counting, multiplying, sorting, comparative     biggest girth or widest canopy, perhaps
language (more / fewer petals) and              first by estimation and then by measuring.
symmetry.                                       Children could also measure angles
    A famous numerical phenomenon               between two twigs. See the Groundnotes*
occurring in plants is the Fibonacci Series,    Teaching with Trees for more ideas.
named after an Italian mathematician               Ponds of different shapes provide
born in 1175. The series begins: 1, 1, 2, 3,    differing levels of difficulty in calculating
5, 8, 13, 21, 34, 55, 89, 144, 233 . . . and    surface areas. Rectangular ponds are
so on, forever. Each number is the sum of       simple but irregular natural ponds offer a         Feeding birds can help your maths
the preceding two. Look closely at seed         challenging task to work out how to            lessons as well as the local feathered
and flower heads (sunflowers or daisies are       sketch a scale diagram and estimate the        population. There are lots of observations
good examples) and you can see spirals,         area. One method is: choose two fixed           and experiments that can be carried out, as
curving both to the left and to the right.      points near the pond or put two sticks in      part of hypothesis testing or learning about
The number of spirals will nearly always be     the ground; mark the two fixed points on        graphical presentation of data. Carry out
consecutive numbers in the Fibonacci            squared paper, making sure that they are       observations of your bird feeders at set
series. This arrangement seems to form an       the right distance apart according to your     times to see how the numbers of visitors
optimal packing of the seeds so that, no        scale; measure to different points of the      vary across the day, week or year? Place
matter how large the seed head, they are        pond’s perimeter from each fixed point          feeders in different parts of the grounds to
uniformly packed at any stage, all the          (e.g. one point might be 2 metres from         find out if some are more popular than
seeds being the same size, no crowding          one stick and 3.5 metres from the other);      others? Experiment with different types of
in the centre and not too sparse at             use a pair of compasses to mark those          food on different tables and work out what
the edges.                                      distances to scale on your diagram (e.g.       food attracts which birds? Observing birds
    Pine cones also show Fibonacci spirals      draw an arc 2 cm from one point and an         across your grounds can also reveal
clearly, and many plants show the               arc 3.5 cm from the other); where the two      interesting patterns like those schools with
Fibonacci series in the arrangements of the     arcs intersect will be a point on the edge     a peak in gull numbers after lunchtime, as
leaves around their stems. Look down on         on the pond. Repeating these                   they come to scavenge.

                                                                                                                        OUTDOORS MATHS
,

groundnotes • JANUARY 2008




                                              ideas included in this Groundnotes. Look                           the confines of the classroom. In fact,
Planning maths in your                        for gaps, either throughout the year or in                         children are usually better behaved in
school grounds                                areas of the curriculum, and talk about                            outdoor lessons as they are more
    To make the most of your school           what other learning opportunities there                            motivated and interested, but there are
grounds for teaching maths, outdoor           are. When you review your lessons, include                         some general planning tips in the
lessons should be written into your           opportunities for staff to feedback on how                         Groundnotes* on Managing behaviour in
curriculum planning, so that it is an         their school grounds lessons went                                  the outdoor classroom.
expectation that lessons are taken outside    including what worked, and what needs                                  Of course, maths is not the only subject
on a regular basis. When lessons in the       changing?                                                          to teach outdoors. You might want to build
school grounds are regular and frequent,          Some teachers will be more confident                            in a rolling programme of curriculum
children can quickly learn the expected       than others in teaching outdoors. Consider                         review and gradually take more lessons in
behaviour.                                    how you can share this expertise, for                              all subjects into the school grounds.
    At a maths curriculum planning session,   example through team teaching, or                                  Creating a timetable for school grounds
work through your scheme of work,             spending staff meeting or training time                            lessons will ensure that there are no clashes
highlighting opportunities for school         sharing good practice. A particular                                over the use of this valuable space.
grounds lessons. You could start with the     concern can be pupil behaviour beyond
                                                                                           © Jim Wileman, Apex




                                                                                                                                                                        © Ian Jackson




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


                                                                                                                 © This resource was originally
                                                                                                                 created as part of the Schoolgrounds-UK
                                                                                                                 membership scheme from the
                                                                                                                 national school grounds charity
                                                                                                                 Learning through Landscapes
                                                                                                                 operating in Scotland as
                                                                                                                 Grounds for Learning
                                                                                                                 A registered charity (No. 803270)

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


OUTDOORS MATHS

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Outdoor Math: Outdoor Learning and Play

  • 1. outlook • MAY 2007 groundnotes January 2008 Schoolgrounds-UK © Ian Jackson Outdoors maths Where can you teach maths in your school grounds? Every part of your school grounds can be used as a learning resource but in this Groundnotes we will look at some specific, Why teach maths outdoors? While any outdoor environment can common features. The suggested activities Evidence is growing that outdoor promote learning, use of the school are most relevant for the primary lessons help pupil motivation and grounds offers specific benefits. Because curriculum, but hopefully will provide some understanding and encourage an they are on your doorstep school grounds ideas for extending them for older or more atmosphere of collaboration between can make outdoor learning a daily event. able pupils. The challenge provided by pupils and teachers, which helps children Staff new to outdoor learning can take each activity can be varied according to develop their interpersonal skills. Moving their first outdoor lessons alongside more how detailed your instructions are. For outside the confines of the classroom experienced colleagues in a familiar more able pupils set them a challenge of requires that pupils are given responsibility, environment, building confidence in their answering a question, but let them work this increases levels of trust and pupils’ abilities to assess and manage risk outside out how. sense of ownership. the classroom. In this way, you can lay the Lessons outdoors also offer more foundations for learning beyond the Boundaries opportunities to use different teaching and school site and ensure that off site Boundaries offer an ideal opportunity for learning styles, particularly problem solving educational visits run smoothly. practising the estimation and measurement and group work, which enhance pupils’ The way that learning outside the of distance, whether they are walls, fences self-esteem and self-confidence. Children classroom can motivate children and help or hedges. report that outdoor lessons are generally them apply their knowledge has particular Choose a section with a clear start and more interesting, varied and relaxed, that importance for a subject which many finish mark that pupils can walk alongside practical lessons are easier to understand, children find difficult. By providing real safely. Mark a set distance, perhaps 100 and that teachers are friendlier outdoors. examples of how mathematical concepts metres, and ask children to walk the Even a simple blast of fresh air, compared can be developed and applied, teaching distance, counting their paces. It is easier to to a hot and stuffy classroom, can make a maths outdoors can prevent the subject count double paces (i.e. always on the welcome difference. being seen as too abstract. same foot) particularly once you reach LEARNING THROUGH LANDSCAPES
  • 2. groundnotes • JANUARY 2008 Then measure the distance to each point by pacing. A scale map can be drawn up by using a protractor to mark the bearings, and marking the distance along each bearing to the edges of the field using a suitable scale. The area of an irregular field can be estimated by dividing it into rectangles and triangles whose areas can be more easily calculated, or by drawing it onto squared paper and counting the squares. Hard surfaced areas can be enhanced with mathematical playground markings or mazes. Even a simple game of hopscotch involves counting skills, but you could invent your own games that practise more complex mathematical skills. Paving stones offer a ready-made grid for chalking in number patterns or for creating giant versions of board games, such as snakes and ladders (you’ll need to buy some giant dice). You also have more opportunities for practising area calculations, as well as demonstrations of tessellations. If you have a large area of grass, link science and maths by carrying out a daisy survey. A good tip for keeping track of daisies is to use counting cubes, as well as a quadrat or hoop to define an area. Throw the quadrat onto the grass, and then cover each daisy with a counting cube. Once all above twenty. Set children off individually Brick walls provide an opportunity for the daisies are covered, the cubes can be at intervals of about 20 seconds to avoid estimating quantities which can be checked taken away and built into columns of ten to them falling into step with each other, by counting. Measure the area of an help with the counting. Test hypotheses though they may need some practise to individual brick then multiply by the about where daisies grow best by walk at a steady, comfortable rate. Get the number of bricks, to estimate the area of comparing the numbers in different areas children to repeat the exercise until they the whole wall. Compare your answer to of the field: shady or sunny, where they are are sure they have a consistent number the area you get by multiplying the width trampled or where they are not. of paces. and length of the wall – you might need to Once pupils have practised measuring estimate the height if the wall is very tall. one length, ask them to estimate different If your boundaries are old hedgerows distances – e.g. 5 metres or 20 metres – you can estimate their age by counting either by eye or by pacing, standing where how many species of trees and shrubs there they think that distance reaches. Use a long are in a 30 metre length. Large stumps in measure to find out who’s closest to the the hedge will prove that it is old and not right distance. Pupils can then try recently planted with lots of different measuring the whole grounds by pacing. species. As a rough guide, there is one Paces are one ancient way of measuring species of hedgerow plant for every 100 distances, but you might be able to think years of a hedge’s life. up more, for example lying on the ground to see how many body lengths a path is. Spaces You can link this into old methods of School grounds provide large spaces for measuring such as those used by the applying calculations such as areas and Romans, which included pes (foot = 29.6 perimeters on a giant scale. Choose a clearly cm), digitus (thumbnail = 1.85 cm) or defined hard surface area, such as a games palmus (palm = 7.4 cm). court, and measure the length and width with a long measuring tape, a trundle Play and sport areas wheel or by pacing. Calculate the area and Apply maths to sports to practise perimeter of the space – you could chalk timings, draw graphs and calculate averages your calculations onto the ground. If you or percentages. Time how long each child have two suitable areas, pupils could takes to complete a set challenge on a trim estimate which is larger before they trail or time races across the playground. measure, or calculate how many times one Who is the fastest and who the slowest? space would fit into the other. What is the average time? Create a graph More challenge is provided by an to show different times. If you have football irregularly shaped field. From a central or netball goals, ask each child to take 5 point, use a compass to measure the shots, and then calculate their percentage bearing (angle of turn away from north) to success rate, which can be also be shown various points around the edge of the field. on a graph. OUTDOORS MATHS
  • 3. groundnotes • JANUARY 2008 measurements all round the pond can create an accurate scale drawing. Times tables can be illustrated with natural features. Easy ones include legs on insects for the 6x table or wings on birds for the 2x table. Different flowers have different numbers of petals, use a buttercup for the 5x table. Woodlice have 7 segments to their bodies. How many other times tables can pupils find in the grounds? Creatures As with many mathematical investigations, activities involving living creatures can link with other subjects such as ICT, geography, environmental studies and science. A minibeast hunt will uncover creatures with different numbers of legs, with or without wings, and with other physical differences. Putting minibeasts into sets according to these differences helps with identification. Children could create their own identification charts according to these sets, drawing pictures of each minibeast. Got a vegetable garden plagued with snails? Look upon them as an easy-to- Trim trail equipment includes a plant and see that the leaves are often handle minibeast for your lessons. Close interesting shapes and angles for naming arranged so that those above do not hide observation of the shells provides and measurement. Ask children to search the leaves below. This means that each opportunities for sorting according to for triangles, squares or circles, or measure gets a good share of the sunlight and differences, comparative language, and angles between different parts of the catches the most rain to channel down looking at spirals. equipment. to the roots as it runs down the leaf to the stem. How many spirals and Natural areas Fibonacci sequences can be found in Trees, gardens, ponds or wildlife areas your school grounds? offer a wealth of opportunities for If you have several trees in your applying maths to real contexts. Different grounds you could set the challenge of leaves and flowers can provide exercises in finding which is tallest or which has the counting, multiplying, sorting, comparative biggest girth or widest canopy, perhaps language (more / fewer petals) and first by estimation and then by measuring. symmetry. Children could also measure angles A famous numerical phenomenon between two twigs. See the Groundnotes* occurring in plants is the Fibonacci Series, Teaching with Trees for more ideas. named after an Italian mathematician Ponds of different shapes provide born in 1175. The series begins: 1, 1, 2, 3, differing levels of difficulty in calculating 5, 8, 13, 21, 34, 55, 89, 144, 233 . . . and surface areas. Rectangular ponds are so on, forever. Each number is the sum of simple but irregular natural ponds offer a Feeding birds can help your maths the preceding two. Look closely at seed challenging task to work out how to lessons as well as the local feathered and flower heads (sunflowers or daisies are sketch a scale diagram and estimate the population. There are lots of observations good examples) and you can see spirals, area. One method is: choose two fixed and experiments that can be carried out, as curving both to the left and to the right. points near the pond or put two sticks in part of hypothesis testing or learning about The number of spirals will nearly always be the ground; mark the two fixed points on graphical presentation of data. Carry out consecutive numbers in the Fibonacci squared paper, making sure that they are observations of your bird feeders at set series. This arrangement seems to form an the right distance apart according to your times to see how the numbers of visitors optimal packing of the seeds so that, no scale; measure to different points of the vary across the day, week or year? Place matter how large the seed head, they are pond’s perimeter from each fixed point feeders in different parts of the grounds to uniformly packed at any stage, all the (e.g. one point might be 2 metres from find out if some are more popular than seeds being the same size, no crowding one stick and 3.5 metres from the other); others? Experiment with different types of in the centre and not too sparse at use a pair of compasses to mark those food on different tables and work out what the edges. distances to scale on your diagram (e.g. food attracts which birds? Observing birds Pine cones also show Fibonacci spirals draw an arc 2 cm from one point and an across your grounds can also reveal clearly, and many plants show the arc 3.5 cm from the other); where the two interesting patterns like those schools with Fibonacci series in the arrangements of the arcs intersect will be a point on the edge a peak in gull numbers after lunchtime, as leaves around their stems. Look down on on the pond. Repeating these they come to scavenge. OUTDOORS MATHS
  • 4. , groundnotes • JANUARY 2008 ideas included in this Groundnotes. Look the confines of the classroom. In fact, Planning maths in your for gaps, either throughout the year or in children are usually better behaved in school grounds areas of the curriculum, and talk about outdoor lessons as they are more To make the most of your school what other learning opportunities there motivated and interested, but there are grounds for teaching maths, outdoor are. When you review your lessons, include some general planning tips in the lessons should be written into your opportunities for staff to feedback on how Groundnotes* on Managing behaviour in curriculum planning, so that it is an their school grounds lessons went the outdoor classroom. expectation that lessons are taken outside including what worked, and what needs Of course, maths is not the only subject on a regular basis. When lessons in the changing? to teach outdoors. You might want to build school grounds are regular and frequent, Some teachers will be more confident in a rolling programme of curriculum children can quickly learn the expected than others in teaching outdoors. Consider review and gradually take more lessons in behaviour. how you can share this expertise, for all subjects into the school grounds. At a maths curriculum planning session, example through team teaching, or Creating a timetable for school grounds work through your scheme of work, spending staff meeting or training time lessons will ensure that there are no clashes highlighting opportunities for school sharing good practice. A particular over the use of this valuable space. grounds lessons. You could start with the concern can be pupil behaviour beyond © Jim Wileman, Apex © Ian Jackson *These Groundnotes are available from the Member Services area of our website. © This resource was originally created as part of the Schoolgrounds-UK membership scheme from the national school grounds charity Learning through Landscapes operating in Scotland as Grounds for Learning A registered charity (No. 803270) To find out more about membership call 01962 845811 or visit www.ltl.org.uk OUTDOORS MATHS