maths outdoors primary handout part 2 - creative...

©Creative STAR Learning Company, 2014 www.creativestarlearning.co.uk 1

MEASUREMENT Measurement covers size (length, height and width), weight, volume and capacity. It helps children learn about spatial concepts such as near and far and the amount of space an object takes up. Measurement is also a natural route into discovering bases and place value. When children use metric systems, they are working in base 10. When using imperial systems, they are learning about a multitude of bases. Once children get older the conversions between millimetres and centimetre and centimetres and metres adds to their understanding of place value. When undertaking measurement children are having to count, compare and order numbers. It can be helpful to consider:

The use of standard units (centimetres, metres, etc.) and non-‐standard units (hand span, footprints, skipping ropes, string, natural materials, etc.). Have both available.

Equipment needed: it depends very much on what is being measured! But a range of items is best, carefully presented and accessible by children so that they can compare sizes, shapes and weights of different objects.

The need for things to be measured accurately. This takes time and practice! However children also need to begin to understand that no measurement can ever by 100% accurate – there is always a degree of rounding up or down. The equipment used also affects the accuracy of each measurement.

Developing the language of measurement is important, so undertaking activities with younger children to ensure children understand the terminology is needed. Scavenger hunts Create simple scavenger hunts based upon measurement vocabulary. For example:

A stick smaller than your hand An object that is very light, etc. A twig exactly 20 cm long 3 pebbles weighing 250g Find two trees exactly 4m apart A pine cone less than 6cm long.

Outdoor master chefs in a mud kitchen


You need: pots, pans, jars, kitchen utensils, measuring utensils and weighing machines. Bread crates, old tables, camping tables and boxes are good for creating the kitchen area. Put the outdoor kitchen near: mud and shrubs and trees where children can help themselves to natural materials. You may wish to have some water on hand in an outdoor sink or in canisters. Put weighing scales, measuring jugs and cups, funky bits of paper, balancing scales into the area. Set up challenges such as:

How many grams of petals are needed to make 100ml of perfume? Design the perfect potion. Write down the quantities. Explain the impact of smelling this potion.

Hold a master chef competition. Participants are observed by others and noted for their ability to demonstrate their cookery methods which include weighing out “ingredients”, measuring water required, timing length of mixing, etc. This can be part of the competition – demonstrating knowledge of measurement

Which class can reach the furthest in the school? Each teacher takes their class outside. The class has to predict how far the class can reach from a starting point, by taking hold of each others’ hands. The distance can be measured with a trundle wheel. From here the children can predict how far other classes will spread. This can make a topic of discussion for an assembly. Straight and Squiggly Lines If you are in a playground, children can use chalk. In a woodland or other natural habitat, children can use sticks to draw lines, or put down string or rope, if it’s not too windy. Either in pairs or on their own, each child should draw some long straight lines outside. How can the children work out the longest line? How can they measure this? Have tape measures on hand, but it’s also possible to use footsteps, whole bodies, arm span, sticks, stones and other natural material as non-‐standardised counting methods. The activity can be repeated using squiggly lines. A further challenge can be to find the longest line in the school grounds, on the school building or inside! Developing the concept of one metre Using stones, shells, sticks, conkers or other natural materials children have to make 1 metre, by estimating the length. This is great for discussions: who was the most accurate, how many objects were used, etc. Let children have a metre stick or measure out 1 metre using chalk and a trundle wheel. Then try the activity again. It can be interesting to explore why everyone has a slightly different number of object that make one metre, the accuracy of children’s work, the concept of the mean number, etc. Comparing measurements Sticks of specific lengths, e.g. 1m can be used in simple measuring activities, such as seeing how many are needed to measure the width of a playground. This can be compared with results


from trundle wheels, tape measures and rules. The challenge can be increased by using 30cm or 60cm sticks which involve more complex calculations to obtain the results. Aeroplanes The children each need their own paper aeroplane and a ruler. Standing along a line in the playground, e.g. the edge of a basketball court, the children guess how far they can throw their aeroplane. Next they throw their plane and wait until it has landed. Then using their ruler they can measure the distance it flies. To make this activity more challenging for older children, as well as using a ruler, they can use a tape measure, trundle wheel and metre stick. See if there are differences between the results obtain and discuss why. This is a useful way of discussing margins of error when undertaking fieldwork. It also works well when children work in groups and share the equipment. How many shoe lengths does it take to cover the width of the playground? Children can estimate how many lengths of their shoe will cover the playground from one side to the other. Then they need to decide how this can be worked out and experiment with their ideas. Show the children the importance of being accurate and need to have the shoes touching each other. Much discussion can be had around why everyone might have a different answer. For older children work can be done on using everyone’s shoes and working out the mean. Children can make their own suggestions for what to measure with shoes -‐ length/area. Again, discussion can be had about the accuracy of the experiment and ways of completing the challenge. This activity can be varied using different body parts, e.g. arm span, body length (!) or using specific objects. Measuring the perimeter of irregular shapes When children create shapes with sticks of a specific length, they can make approximate calculation of the perimeter. For example if 10 x30cm sticks were used to make an outline, then the perimeter is 3m. How far do your trees spread? This is a good winter activity. The spread of the branches gives a good indication of how far the roots spread underground. Identify the 4 points of a compass and measure the distance you walk under the branch until you reach the tips. Do trees spread evenly in all directions? Is their growth symmetrical? If not, why not? For example, the growth of branches often favours the sunnier and more sheltered side. What is the average girth (circumference) of the trees in a designated area? Measuring trees can be a complex process. Normally measurements are taken at “breast height” which varies slightly according to each person. It is a good idea to let children measure


a tree at different heights so that they can see the differences on just the one tree. If there are not enough tape measures, use string and have a measuring tape laid out nearby. Prior to using a measuring tape, children can learn to estimate the girth through hugging a tree! For very big trees this may require more than one child! Look and see if there is wide variation within species as between species. If there is, think about why this could be so? The trees might be different ages or in different growing conditions. Some species grow faster than others. How can we measure the height of a school building or the tallest tree in the school grounds? There are several ways of doing this, but it can be interesting for children to try out their own ideas.

Shadow ratios. When your shadow is the same height as you are, then the shadow of the building will be at its actual height. It is also worth investigating ratios and whether a shadow half your height, is the same for other objects, e.g. a litter bin.

Look through your legs. This is for agile people with a good sense of balance! Have your back to the tree and walk out the approximate distance from the tree. Bend over and look at the tree through your legs. If you can see the top of the tree – just, then this is where you stop and stand still so that your partner can measure the distance from the foot of the tree to where you are standing. Add on your own height to this measurement and the sum will be the approximate height of the tree. Let people of different heights try this out and see if there is much variation.

Use a stick. Hold a stick vertically and move back until the stick fits the height of the tree from its base to its crown. Carefully turn the stick horizontally so it “lies” along the ground. Get another person to walk out from the tree to the top of the stick. This is the height of the tree. Mark it and then measure the length back to the base of the tree.

Use a friend. Have your friend stand at the foot of the tree and measure his or her height. Walk back then estimate how many times your friend will fit into the height of the tree. Multiply this number by the height of your friend to calculate the approximate height.

Does the height of a tree correlate with its girth (circumference)? This is an interesting challenge. It is important to know the type of tree measured as this might be a contributing factor. The heights of the trees can be plotted on a graph against the measures of the girth of a tree, to see if there is a correlation i.e. do taller the tree tend to be wider in girth (circumference)? Investigate crowns


Think about different species of tree -‐ for example, do oak trees generally have larger crowns than birch trees of the same age? It is also worth discussing why there is variety between trees and their canopy sizes. How can this be investigated? Google Earth Comparisons This activity can be as simple or a difficult as needed. It works well as a mapping project that involves numeracy. Using the measuring tool on Google Earth children can use this to calculate the perimeter and convert the results from kilometres into metres. Let the children decide which measuring equipment they would like to use outside depending upon what’s available in school. This may include: trundle wheels, measuring tapes, metre sticks, mobile phone apps, etc. Next, children measure the actual perimeter of the school grounds. Remind the children about the need for accuracy. Back inside compare results. It is also possible to annotate a Google Earth map and print it out. So the results of each device can be recorded and displayed in this format. For some groups, non-‐standard units of measure may be used. For example:

If children hold hands in a circle then it is possible to measure the perimeter quickly if the group circle “rolls” around without breaking hands. It is best done in groups of around 10 pupils.

A child can measure the length of his footprint and measure part of the perimeter this way.

Look on Google Earth and see if there are other features that can be easily measured and compared in the local area.

Sand and snow sculptures Sand can be a useful medium for investigating volume, area, perimeter and shapes. It can be moulded in so many ways. Putting sand on blue tarp means that children can only build up rather than dig down which can be an interesting way of working. Use snow as a substitute!

What is the biggest shape that can be made with one litre of sand? How would you define “big”? Is this perimeter, area, or both?

What is the tallest unsupported structure that can be created with 1 litre of sand? What engineering principles have been applied to ensure the structure is tall. Let the class research the structure of some of the world’s tallest free standing structures to gain some ideas here.

The capacity of a puddle On a flat piece of tarmac ask children to estimate how big a puddle will be created from ¼ litre. Draw this on the ground with chalk. Then pour this amount of water on the ground and compare. Draw a chalk mark around the size of the puddle and encourage children to think about how they can measure its perimeter.


From here, children can estimate and explore the sizes of puddles made by other quantities of water. On a hot day, it can also be interesting to see if the puddles disappear at the same or differing rates.

TIME Time is a very environmental aspect of numeracy. The seasonal and daily changes in the natural world combined with the changes in our lives and through history as time passes means that concepts around time can be taught as an ongoing part of a class or nursery’s routine. There are a lot of skills involved in understanding time. It involves children:

Knowing and being able to use vocabulary associated with time Counting time as it moves forward or backwards Comparing digital and analogue time Sequencing events in time. Remember to allow plenty of time to celebrate traditional customs, festivals and events in your community and any extra special celebrations

Being able to measure time with a variety of different equipment Being aware of seasonal changes taking place and learning how to address appropriately

Vocabulary Long time, short time, season, date, day, month, year, hour, minute, second, now, then, soon, early, later, forever, never, quickly, fast, slow, slowly, almost, nearly, morning, afternoon, evening, night, midnight, midday, noon, etc. Routines and resources to develop understanding of time as a concept

Have a range of timers, stopwatches and clocks which can be used outside on a regular basis in all sorts of structured and free play activities. A clock facing outwards into the outdoor area can be helpful for staff and children! Sand timers are often portable, robust and waterproof. They are useful for turn taking outside

Use mobile phones and show children where to find and read the time when they ask how long they have before going home, etc.

Time Lapse Photos and Videos On YouTube there are many examples of time lapse videos such as “A year in a forest in 40 seconds” which provide good examples of changing seasons and events. Many children do not realise or readily see the changes happening in nature. By doing a time lapse activity, this can help children look and see. It involves taking a photo within a set time period, e.g. once a day or once an hour, etc. Good examples include:

A dandelion changing into a dandelion clock A prepared wormery getting mixed up by earthworm activity


A fast-‐growing plant beginning to bloom A snowball melting, or a patch of grass

There are time lapse apps available for tablets and smartphones which can be set to automatically take photos every few seconds. Rear animals Watching animals grow and change helps children understand life cycles and develop another sense of what time means. Even if your nursery does not have hens, fertile chicken eggs can be bought and hatched from the Happy Chicken Company and other firms. If possible keep the chickens afterwards but they can be returned with the egg station. Frogs spawn is also exciting to keep. With any animal based activity, care of the animals is of paramount importance and routines to ensure their well-‐being as well as the children in your care. It is also important that such activities are highlighted and children know what is happening and why. It is a time-‐based celebration of life! Human Clocks Start by getting the children to rock from foot to foot and chanting slowly, “Tick, tock, tick, tock. I’m a ticking human clock. What time is it?” The adult calls out a time, e.g. 5 o’clock or 6.30. The children make the time with their hands. Remember it will look back-‐to-‐front if you are standing in front of the children. This also works as an activity undertaken in pairs with one child moving the hands of her partner to the correct place. Have a clock face on hand so that children can check and correct their answers. Repeat the chant before calling out each time. Time Line Up Put clock faces and/or digital clock times on laminated cards. Give one card to each child in the group and ask them to line up in order of the times stated. Alternatively, give children a post-‐it note and ask them to write down their favourite time of the day and use this to order the class. “What time is it Mr Wolf?” One child is the wolf who stands at the opposite end of the playground to the rest of the group. The group chants, “What time is it Mr Wolf?”. The wolf turns around and says a time, e.g. 3.15pm. The group takes three steps towards the wolf. The chant is repeated and the wolf turns around and calls out another time. When someone gets close to the wolf, the wolf can shout “Dinner Time” and chase the group back to the line. Then another child becomes the wolf and the game begins again. Decide the language you wish to use in advance to reinforce the current concept, e.g. digital, analogue, 12-‐hour or 24-‐hour time. Hoop Clocks Each child or pair needs a hoop, chalk and two sticks (one short one for the hour hand and one long one for the minute hand). The hoop is put on the ground and the numbers drawn around


the outside of the hoop. Numbered bean bags are helpful for children who prefer this to writing the numerals. The adult can then ask the children to make different times, e.g.

Show me 2 o’clock, 5 o’clock. 7 o’clock, etc. Show me 3pm, 5am, 7am, etc. Show me one hour later than 4 o’clock, 9 o’clock, midday, etc Show me one hour before 4 o’clock, 9 o’clock, midday, etc Move on to half past the hour, then quarter past, quarter to, etc.

The children use the sticks to make the time. Have a clock face ready to show children the time and allow children to correct their mistakes. Alternatively set out a range of materials such as bean bags, cards, chalk, number stones, number confetti and ask the children to create their own clock. This is a great activity for Primary 1 and 2 where you can see how much children understand about a clock. Class-‐sized clocks Brainstorm with your class ways of making a huge clock that is big enough for all the class to use for games. What games can everyone invent and what skills and concepts will be developed or reinforced? Calendars and seasonal concepts relating to time

Spend time outside throughout the year undertaking seasonal activities such as gardening where plants grow at different rates and at different times of the year.

If your class has a garden or area of the school grounds to look after, create a maintenance plan based on what needs to be done on a monthly basis. Set up a rota of duties such as watering, weeding, pruning and planting.

Play hopscotch but write the days of the week or months of the year on grid instead of numbers

Cross-‐sections of trees can be counted to determine the age of a tree. This can be transferred onto a time line and marked with key dates which the tree has witnessed. Generally conifer trees grow faster than broadleaved trees. The weather and climatic conditions affect the growth of a tree each year. The closer together the tree rings, the slower the tree has grown. In windy places, the trees are likely to have narrow rings on the side facing the prevailing wind. The rings become further spaced on the sheltered side. These rings can be traced and then used to create a contour graph.

Measuring time

Snow or ice melting can be timed – at any time of the year! (Freeze snow to bring out at other times of the year)

Create a sand timer that accurately measures 1-‐minute from different household and unwanted items in the sandpit. Alternatively try building a water clock.

Estimate how long it takes for a bottle of water to travel through guttering. Put on a stick or ping-‐pong ball to watch it float on the water. Is it possible to adjust the flow to ensure that a ping-‐pong ball takes exactly one-‐minute to move through the guttering.


Does the size of the snowball affect the volume of water that melts within a certain length of time? Does the weigh of snow affect the volume of water that melts within a given time period?

Create a sand timer that accurately measures 1-‐minute from different household and unwanted items in the sandpit. Alternatively try building a water clock.

Speed, distance and time activities

If there is a suitable river or stream, that is safely accessed, children can measure the speed at which an orange floats down a measured length of stream.

Is it possible to measure the speed of passing cars safely? If so, how could this be undertaken?

How could we set up a speed, distance, time experiment on our playing field or school ground? Do we have to always run or walk? What equipment is needed? How can we make the investigation a fair test?

Time and handling data With the children, plan a series of tasks outside that will take time to complete, e.g.:

How long they can hula hoop? Do 20 star jumps Get 5 children through a hoop Run round the playground Bounce a ball 50 times Etc.

Once the list is compiled, let the children estimate how long each task will take. Then it is time for the fun to begin. Make sure the children know how to use a stopwatch to measure time. The children should write down the actual time it takes to complete each activity. Afterwards compare the estimates with the actual times and discuss the differences. What estimates were close and why? Which ones were harder to guess? Etc. Timetables

Use bus and train timetables and travel by public transport if possible on school trips, ensuring that a school trip can be planned within the school day.

Create timetables for the school such as a daily schedule, weekly planner and yearly overview.

Measure the age of fallen or cut trees by looking at the number of rings and their spacing. The better the growing conditions, the greater the spacing between the rings. Once the age of the tree has been worked out, create a timeline of events that the trees will have witnessed or lived through.


PATTERNS AND RELATIONSHIPS Patterns are all around us outside in both the natural and built environments. They come in many guises:

Number patterns are part of the joy and wonder of maths. Forms such as the Fibonacci sequence are link numbers with shape and form in nature. Patterns help us understand order both of numbers and objects, e.g. 1st, 2nd, 3rd, etc.

Logic patterns made different attributes including shapes, colours, sizes and lines. Logic patterns naturally work as part of different art activities

Word patterns because all languages have patterns within them based upon their lettering or symbols. Rhymes are lovely examples of word patterns. There are intrinsic links between mark making and pattern work. Patterns also provide many ideas for developing descriptive vocabulary

Patterns which are heard or felt such as music and dance activities Within some curricula, the focus is primarily on number patterns and relationships which in many ways limits possibilities. What is a pattern? Children explore pattern in different ways, from the casual arranging of shapes, toys and artefacts to making large complicated patterns. Allow children time to create and re-‐create simple patterns before moving onto more complex ones. Let them comment, question and enjoy the simplicity and complexity of patterns. Making patterns Let children make patterns for each other to continue using natural materials found outside. Another option is to get children to copy each other’s pattern. This can be surprisingly challenging if you request that size and similarity matters. Snow is a wonderful medium for making patterns. Use this as a creative opportunity where children make patterns that tell a story, a bit like how trackers follow trails. Leaf Logic http://creativestarlearning.co.uk/maths-‐outdoors/leaf-‐logic/


Doing this logic activity with leaves adds an additional level of challenge in the leaves are not homogenous in size, shape or colour so a continuous discussion is needed as to how to make decisions as to what makes a leaf big or small or a particular colour. Ask each child to gather a few leaves from under a tree. It works best if the leaves have several different colours. Maple trees are especially good for this. Everyone needs to be sitting in a circle around a large sheet. The challenge of the group is to see if everyone can contribute a leaf to the logic line. If you are playing this in a windy place then put stones on top of the leaves to stop them blowing away. This is how it works:

The first person puts a leaf down in the middle of the sheet. The next person puts a leaf beside it. One attribute is changed. The leaf is still a big, maple leaf only this time the colour has changed to green.

The third person puts a leaf down. This time the leaf is still a green, maple. The attribute that has been changed is size. This leaf is small.

The fourth person puts down another leaf. Here the one attribute that has changed is the colour. We've gone back to yellow.

The activity continues until no more leaves can be placed in a line. Like with dominoes you can work either end of the line.

Once children have got the hang of this activity, it is easy to introduce Carroll Diagrams, which involve sorting objects according to defined attributes. Strategy Games In the majority world countries, many cultural activities take place outdoors. Thus a strategy game is more likely to be played outside using stones and holes or circles drawn in the ground. This is a tradition which has happened for thousands of years. Strategy games have a universal appeal. They are often known by different names and have slightly different rules in different countries. When creating a base on which to play, chalk can be used or stones to scratch a board pattern onto a paving slab. It's worth remembering that time is needed to develop competency in any of these games. Thus by introducing them at the start of the year, they can be used as an interesting alternative to indoor board games. In terms of extending children’s strategic thinking, use questions such as:

From which positions on the board is it possible to make two / three/ four moves? Sketch a diagram of the board and record your findings.

Where are the best places to put your pieces on the board in order to make a good start? Why?

Is it an advantage to start? Explain. Please refer to the separate maths strategy handout. Alternatively email Juliet for a copy.


The Game of Nim -‐ An ancient game for 2 players With your partner collect 20 stones, cones or other small objects to use as counters. Taking turns, each player chooses to pick up 1, 2 or 3 counters. The player who picks up the last counter loses the game. There is a trick you can use to ensure that you do not lose. See if you can discover it! Make number sequences with gathered objects from outside The children can be challenged to create a number sequence each and then have to swap with a friend and work out each other’s pattern. These can get quite sophisticated over time. Secret Codes Children enjoy making up numerical codes and sequences for others to crack. This blog post explains how this can be taken a step further when outdoors: http://creativestarlearning.co.uk/nature-play-learning/nature-detectives/ Cows and Bulls This game is the predecessor to Mastermind. It can be played as a whole class prior to children working in smaller groups of pairs. This version uses natural materials whereas the traditional approach was to use numbers which is also a useful alternative. The aim is to break the code -‐ that is to work out the pattern of the hidden natural materials Materials • White cloth or long box • At least 6 different types of natural materials in groups of 6, e.g. 6 stones, 6 sticks, 6 leaves,

6 shells, 6 bark chips, 6 conkers Create a line of 4 stones or shells. Do not let the children see this pattern. Put the pattern in a box or hide it somehow. On top of the white cloth, the children take turns or work in small groups to take turns to put a line of 4 stones or shells onto the cloth facing you and the hidden pattern. For every object correctly placed, then you say it is a “bull”. For every correct object but in the wrong place, then this is a “cow.” The games continues until a group or individual has worked out the code. You may want painted pebbles or similar to help children remember the bulls and cows in each line of objects. The game is played in a line of 4 with 6 different types of natural materials – can the children work out the number of possibilities? There are 6x6x6x6 = 1296 possible combinations if one allows for duplicate use of natural materials, e.g. stones are used more than once in a line. The other challenge is to try and crack the code in six turns or less. For younger children or when starting out, begin with a line of 3 objects.


Fibonacci in Woodlands – A Mathematical Investigation Fibonacci lived from 1180-‐1250. He was the son of an Italian merchant. He developed a passion for numbers and discovered the following sequence that can be observed in leaf arrangements, flower segments, pine cones, etc.: 1, 1, 2, 3, 5, 8, 13, 21… If you look at a pine cone you can see that the scales of the cone form regular spirals – some go to the left and some to the right. If you count the numbers of scales at each level, you will find that they follow the Fibonacci sequence. Many plants produce new branches in quantities that are based upon Fibonacci numbers. Introducing Fibonacci to young children Get the children to gather some loose material – whatever is readily available in the wood, e.g. cones or sticks. As a group, layout the material in the Fibonacci sequence on a light coloured cloth so that the children can see the pattern and write down the numbers beside this, e.g. with sticks: 1 I 1 I 2 II 3 III 5 IIIII 8 IIIIIIII 13 IIIIIIIIIIIIII It’s unlikely that the children will understand the pattern. However, you can demonstrate how it is created by moving the sticks. Finish up with the story of Mr Fibonacci and how he used pine cones to practise counting… 1,1,2,3,5,8,13,21,34, etc (demonstrate this with a pine cone). This was a problem for him. For example when he went to buy food in a shop he always counted out the wrong amounts. If his lemons cost 10 lire, he couldn’t count the number 10 so he always gave 13 coins. Everybody laughed at him and thought he was very silly. Over time, he grew more and more unhappy. One day a little girl who had just learned to count realised his problem. When she saw Fibonacci using a pine cone to count, she gave him a daisy and showed him how to pull the petals off and count like everybody else. So Mr Fibonacci was very happy…but to this day we are very pleased about the way he counted because he showed the world one of the cleverest number patterns of all!


Make your own Fibonacci pattern Collect cones, flowers, stones, leaves or other loose material and try and arrange to create a Fibonacci pattern of your own. Which materials work best for this? Does it depend upon shape, size, weight or another factor? Think about how this can be followed up with an art activity (indoors or out) that uses the Fibonacci pattern as an inspiration. Flower petal challenge Do the number of petals on a flower match the numbers in the Fibonacci sequence? Decide as a class how you will work this out. Fibonacci woodland poems The beginning of the Fibonacci sequence can be used to create Haiku-‐like poetry or stories based upon syllables in each line: 1 Trees 1 in 2 the woods 3 standing tall 5 waving their green leaves 8 catching and filtering sunlight Fibonacci Rabbits – Population control! The original problem that Fibonacci investigated (in the year 1202) was about how fast rabbits could breed in ideal circumstances. Suppose a newly-‐born pair of rabbits, one male, one female, are put in a field. Rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits. Suppose that our rabbits never die and that the female always produces one new pair (one male, one female) every month from the second month on. The puzzle that Fibonacci posed was... How many pairs will there be in one year?

• At the end of the first month, they mate, but there is still one only 1 pair. • At the end of the second month the female produces a new pair, so now there are 2

pairs of rabbits in the field. • At the end of the third month, the original female produces a second pair, making 3

pairs in all in the field. At the end of the fourth month, the original female has produced yet another new pair, the female born two months ago produces her first pair also, making 5 pairs.


Fibonacci and the Golden Ratio The golden ratio is another story for another day. It is hugely significant in nature (e.g. spirals), artwork, building design and is inextricably linked to the Fibonacci sequence: 1/1 = 1,

2/1 = 2, 3/2 = 1·∙5,

5/3 = 1·∙666..., 8/5 = 1·∙6,

13/8 = 1·∙625, 21/13 = 1·∙61538...

34/21 = 1·∙61905 If you continue, eventually the pattern settles into the Golden Number of approximately 1.618034. This is a great extension into an investigative project around the Golden Ratio. Have a look at this YouTube video and be inspired http://www.youtube.com/watch?v=fmaVqkR0ZXg The Tower of Hanoi http://creativestarlearning.co.uk/maths-‐outdoors/a-‐leafy-‐tower-‐of-‐hanoi/ The Tower of Hanoi is a maths puzzle that is traditionally completed on rods with wooden discs. However, it is possible to do this using different sizes and colours of leaves. The first job is to create a "base". This can be drawn in forest litter with a stick. Alternatively, sticks, stones, cones or any other material to hand can be used to make the three squares. Next find three leaves of different sizes. These go in the left hand square. The aim of the puzzle is to move all the leaves into another square so they end up in the same order with the largest leaf on the bottom and the smallest leaf on top. There are some rules to follow:

Firstly only one leaf may be moved at a time. You may only move the top leaf on a pile. It must be moved to one of the other squares. No leaf may be placed on top of a smaller leaf.

With just three leaves this puzzle is straightforward. The more leaves in your pile, the more challenging the problem becomes. With three leaves, it takes seven moves to complete the puzzle. With four leaves, it takes fifteen moves. With five leaves it takes thirty-‐one moves. Can you work out the pattern? For getting into the deep maths, have a look at the Wiki page http://en.wikipedia.org/wiki/Tower_of_Hanoi Children can use leaves on the ground by themselves or in pairs. However using tyres or large blocks of different sizes, spaced further apart, turns this into a much larger group problem solver especially if the team is timed to see how quickly they can complete the puzzle. Fractals in Nature Fractals also work well and can be introduced through using sticks to explain the rules of self-‐similarity in patterns. These blog posts explain fractals in more detail: http://creativestarlearning.co.uk/maths-‐outdoors/outdoor-‐maths-‐fractals-‐in-‐nature/ http://creativestarlearning.co.uk/maths-‐outdoors/how-‐to-‐make-‐a-‐fractal-‐dragon-‐with-‐sticks/


SHAPE, POSITION AND MOVEMENT Opportunities to investigate and explore 2D and 3D shapes outside are popular with children. The practical tasks are key to understanding the potential and purpose of shapes in a way that paper and pencil activities are unlikely to achieve. Often children who struggle with number work find they can identify with shape and the need for spatial awareness. It is a different form of mathematical thinking. For this reason, do not feel that you have to differentiate through providing lots of different activities outdoors in the one session. Whole class activities with differentiation happening through questioning and open-‐ended outcomes tend to be more effective as well as a lot less stressful to manage. The relationship between 3D objects and their 2D representation is an important component of understanding maps. The 2D symbols on maps represent 3D or real life features. Have a collection of household objects and robust 2D and 3D shapes for outdoor use. Often there are used and worn collections of shapes in schools which work well serving their final days outside. Shape searching Go around your school grounds and try and complete the challenge of finding all the different objects which demonstrate properties of shapes. Take a photo of each one or write down where you found it:

• A right angle • Lots of angles • Vertical line • Horizontal line

• A right-‐angled triangle • A shape within a shape • Diagonal line • Examples of 2D shapes

• A vertex or an object with 3 vertices

• Curved line • Examples of 3D objects.

Shape Basket Each child needs a piece of chalk. In the playground each child draws a shape of his or her choosing, e.g. square, rectangle, triangle, circle, etc. Demonstrate how to do this: they need to make the shape big enough to stand inside and clear enough for others to see. Some Swedish schools have shapes painted on the ground for this activity!


The children stand inside their shape. Then the fun begins. The adult calls out instructions such as: • If you are standing in a circle, change places • If your shape has a curved side, change places • If you are in a polygon, change places. The children move from shape to shape as per instructions. Once the children know what to do, they can write up instructions to call out for subsequent games. The instructions can become more complex for older children. Compile a list of shape vocabulary and concepts you wish to cover for each session. The children quickly build up their knowledge. Shapes within Shapes What is the biggest number of shapes within shapes that can be found at your school? Window panes and buildings are particularly good for this. The children have to find examples of shapes within shapes and count up the possibilities. For example, how many shapes exist in the array below:

Hunt the shape Knowledge of 2D and 3D shape names and properties. Great fun. Hide lots of shapes in the school grounds or one part of it. The children have to find the shapes and then put them into the correct place on a Venn Diagram or Carroll Diagram, e.g.

Shapes with… Regular sides Irregular sides

A right angle

No right angle

Triangles made from sticks Many variations can happen from one activity. It works best with sticks that are all the same length. Each pair of children needs nine sticks. Investigate how many triangles can be made with nine sticks of equal length. What happens when • The number of sticks is changed? Is there a pattern between the number of sticks used and

the number of triangles which can be made? • Sticks of assorted lengths are used? How does this affect the numbers of triangles made? • The shape changes but the numbers of sticks used remain constant. So how does this

challenge apply to making hexagons or squares?


• What other similar investigations can the children come up with? Creating shapes This blog post looks at group challenges around shapes and pictures which have key properties that reinforce children’s understanding of 2D shapes and their properties: http://creativestarlearning.co.uk/maths-‐outdoors/an-‐outdoor-‐shape-‐activity-‐with-‐sticks/ Under the Sheet This activity is similar to Shape Basket in that it is about understanding and following directions. The language associated with maths is reinforced. It can be demonstrated as a whole class game but works well once this has happened as an activity when a group finishes a task early. Using up to 10 sticks, the teacher makes a 2D shape out of sight of the children. This can be covered with a small sheet. He or she then tells the class how to make the shape. The children can work in pairs or alone to follow the instructions. With younger classes, use a smaller number of sticks to begin with. For added challenge each child has a cloth and hides their work. Everyone reveals their results at the end! Encourage the children to ask questions as part of this activity and the teacher should answer these in as helpful way as possible. Tiling Look for repeating patterns in buildings and natural objects. Look at the shapes within the patterns. A good example of the different between a tessellation and a repeating pattern is a ladybird. There are often 7 spots laid out in a symmetrical fashion on the ladybird’s shell. Because the spots are not touching each other and do not fit together, the pattern is not a tessellation. Let children look at brick walls, fence patterns, paving slabs, curtain and carpet designs, and other man-‐made examples of tiling patterns. Then let the children have a go with big objects such as building blocks to copy the pattern. An interesting strategy game has been devised by Eduard de Bono using L-‐shaped tiles, called the L-‐Game. This is a good follow up activity. Instructions and the board can be found at http://www.edwdebono.com/debono/lgame.htm

Making Nets from Sticks


Sticks can be lashed together to create simple 3D structures – which can lead on to some interesting den work! Use 1m sticks. Bamboo canes can also be used but with care as they are on the whippy side.

5. ANGLES, SYMMETRY AND TRANSFORMATION Scale Activities The term “scale” has several meanings in maths:

It can be used for measuring such as the Beaufort Scale which measures windspeed It can also be used for grading and other comparisons such as the Mohs scale of hardness to grade rocks

Rulers and other measuring tools have scales which enable a person to quickly work out the length of an object

There are scales in music, which are patterns of notes played in a particular ascending or descending order.

Make time to discuss these different meanings when introducing the term “scale”. What do children understand when it comes to thinking about scale? It could be:

Scales on animals such as fish or dinosaur scales Weighing scales in a bathroom or kitchen Superheroes scaling walls and climbing high

For the purposes of this section, activities relating to ratios of size are covered which have close links to measurement activities. This leads into looking at maps, models, drawings and plans. As children’s understanding grows, the language of size can be more accurately determined by numerical scales. Before embarking on any scale work, children need to have a good concept of size and its relativity. Photograph objects in the school grounds or designated outdoor area from different angles. Laminate the photos and let the children see if they can match them accurately. Next let the children take photos and repeat the activity. Play hide’n’seek. Encourage children to hide in different places where they get a different view, e.g. on top of a slide or on the ground peeking out from under a den. This can also be linked to taking photos from different places and angles. Use comparative vocabulary Comparative vocabulary needs reinforced. This can be done by giving the children the key words and phrases such as: smaller than, biggest, heavier than, lighter than, higher than, lower than, almost as big as, nearly as small as, etc. The children have to go round the school grounds and find comparative objects and write them down, e.g:


The main entrance door is the biggest door in the school The litter bin is smaller than the picnic bench

Set up a scavenger hunt where children have to find objects of certain sizes, e.g. a stick smaller than my hand, a blade of grass longer than my thumb, etc. When the class gathers together, the challenge is to group the objects everyone has collected by comparable size. You may need a few rulers or tape measures to do this. Introducing ratios and specific scale Children need opportunities to simple scale drawings and models e.g. 1:2. A simple activity is for children to find 2 sticks, one of which is twice as long as the other. If you have a pack of sticks cut to specific lengths, e.g. 30cm and 60cm, then children can make a small picture while a partner copies it with big sticks. To make the small picture as big, twice the number of sticks will need to be used. This can begin to help with the concept of ratios. Next, each child finds a leaf and draws around it on squared paper. Count the number of squares which is the approximate area of the leaf. The challenge now, is to find a leaf that has twice the area! This works best using the same species of leaf. After this, the challenge is to work out a system for measuring the area of a football pitch or netball court and then making a scale drawing of this. The children should aim to make a scale drawing with a reasonable degree of accuracy and proportion. When children use Ordinance Survey maps or a digital mapping tool such as Google Earth, always encourage them to find and work out the scale. Let the children estimate distance on a map using scale line and aid such as paper strip or string. This can be compared with the ruler tool on Google Earth for measuring distance. If this can be done, using maps of the school grounds and measuring the boundary, children can then decide how they can practically measure the boundary. Bing maps also come in different scales on the Internet. Children can jump between 1:25000 and 1:50000 and compare the differences. As the children’s skills increase, children can calculate approximate area progressing from regular to irregular shapes and make scale drawings of larger areas. Another example of scale work can be seen in this blog post: http://creativestarlearning.co.uk/maths-outdoors/scale-and-geometric-patterns-with-sticks/ Shadow ratios. When your shadow is the same height as you are, then perhaps the shadow of the building will be at its actual height. It is also worth investigating ratios and whether a shadow half your height, is the same for other objects, e.g. a litter bin so that there is a fair test carried out.


Using the human body It is important that children know, understand and explain the relative size of objects. This can be taught by children standing in the playground and having their height measured by a partner. The child can then move halfway across the playground and the partner measures his height from the original position. The child then moves to the other side of the playground, and his height is measured again from the original position. How does the apparent height decrease with distance from the original point? Silly trousers Let children find a pair of trousers to cut out from a magazine or let them design their own trousers. These should also be cut out. In pairs, the children work on a flat piece of ground. One child holds out their trousers in front of their partner. The partner has to walk backwards carefully until they “fit” the pair of trousers. Does the size or shape of the trousers affects the distance a person must walk to “fit” the trousers? How can the children design a fair test for this investigation? Sketching and art activities This can be followed up with an art activity that focuses on scale, e.g. a road going into the distance. Another option is to undertake a landscape sketch outdoors where children can draw features that are large and in the foreground and smaller features in the background. Children also need to understand that things in picture form can be shown larger and smaller than they are in real life. In groups the children have to pick three objects or features within the school grounds. Using a digital camera, the children take a close up shot of the object, that shows only part of it. Then the children take a distant shot, where the whole object is shown in the frame. Back in the classroom, the photos are printed out and a matching game is created where children have to match up the near and far shots of each object.

POSITION When beginning work on position, it is important that children learn to orientate themselves and develop an awareness of space and location of key features. These are key mapping skills. Begin by calling out the names of key features and common plants that children can see outside. The children should quickly point to these from a stationary spot. This can be extended to indicate the direction of notable features within the immediate neighbourhood Use simple vocabulary to describe position, e.g. near to, above, far, distant, overseas, abroad, local, surroundings, close, vicinity, neighbourhood, district, area. Introduce the cardinal points of the compass too. Shadow Positions


Get a child to stand in a specific spot at the start of the session. Ask another child to chalk round her shadow. Every hour repeat this activity using different colour chalk each time. The children will be able to see how the shadow moves and changes through the day. This is particularly interesting on sunny days in the winter when the shadows are longer Use compass bearings Have the compass bearings painted or chalked on the ground and refer to the directions when describing the location of different objects and discussing where seeds and plants should be positioned. Find north without a compass It is perfectly possible to find north without having a compass, providing it is a bright sunny day.

1) Put a stick upright in sand or on the ground. Place a mark (A) exactly at the end of the shadow.

2) Wait half an hour or even longer as this increases the accuracy of your experiment. Go and do some other activities.

3) Come back to the shadow stick and mark the new position of the end of the shadow (B). 4) Draw a straight line between marks A and B. A is West and B is East. 5) Draw a bisecting line (this is the half way point between A and B) perpendicular to the

line AB. This is the North-‐South line. 6) If you really want to double check, compare your result with a compass.

Near Far Game (for KS1) On a playing field or space outdoors, play the “Near Far” Game to emphasise the distance. Laminated labels or signs can be put to indicate position. When the teacher calls out:

Near: children run and sit down or crouch at the teacher’s feet Quite near: children walk around (to represent places within walking distance) Further away: children run around making a car or bus noise (to represent places that require a journey by transport)

A long way: children make plane wings and run about as if they are aeroplanes(to represent travelling abroad or overseas)

Very, very far away: children crouch down and listen to the teacher count backwards for blastoff into outer space. Then they jump as high as they can into the air and shout “Blast Off!”

Use simple positional vocabulary, e.g. left of, right of, up, down, on, over, under, above, below, next to, behind, in front of, in between. Play the following games in the school grounds or local park:

“Where’s the object?” The children have to guess which feature you are thinking about by asking positional yes/no questions, e.g. “Is it near the gate?” or “Is it on the fence?”


Put a collection of Lego people, soft toys or other objects in different places within part of the school grounds. For example, put a toy on a wall, under a bench, between two goal posts, beside a flower, next to the tree, in front a door, in a crevice, etc. In pairs the children have to go around

In groups get children to design an obstacle course outdoors with simple gym equipment. Next the children draw the course as a simple plan showing the direction of movement. Alternatively the children could record the directions to completing the course on a digital voice recorder, e.g. “Jump over the hurdle. Walk along the bench. Jump in and out of the hoops. Crawl through the tunnel. Climb up the steps. Slide down the slide.” The accuracy of the instructions can be tested by other groups completing the obstacle course successfully or by building it from scratch!

Direction games If there is a grid painted on the playground (e.g. for chess or snakes and ladders or other number games), this can be used for children to guide each other from one square to another, e.g. move from number 1 to number 20, the shortest possible way. Children should be encourage to use positional language such as forward 3 squares, turn right, forward 5 squares, etc. This activity can be made more challenging by placing obstacles (e.g. plastic toy animals) on different squares so children must avoid them. If there are no grids outside, this can be done on paving stones or rubberised squares. Alternatively duck tape can be used by older children to make a grid for the younger ones to use. A challenging extension of this game is to have child blindfolded who has move through an area with various objects. For a Second World War theme, this might be bombs in a minefield. The other children in the group have to give instructions. This works especially well if each child can only state one instruction, e.g.

Left 90 degrees Right 90 degrees Forward Back

Children can describe their journeys to school using such directions. Play “Hunt the Thimble” outdoors. For example, describe where an object is located by its position outside within a given area. Alternatively peg some objects or laminated pictures onto a washing line and give clues such as “This object is beside the blue train. It is almost at the end of the line. It is to the left of the red circle, etc.” Compass treasure hunts Before undertaking this activity, place some treasure in a few hidden spots around the area where you are working. Then mark these with crosses on a map of the area. The children begin by all sitting in the same direction. Get the children to use a compass and chalk on the grounds the compass points. This can be done on a large scale for all the class to see.


Next, one child has to find some treasure. He will be guided by the others who are the navigators. They take turns to look at the treasure map – where the treasure is hidden and shout out directions such as “10 steps north” or “3 steps east. After each instruction, another navigator has a go.

As the children become more proficient at this game, they can aim to reduce the number of instructions given (use a tally chart to monitor this). Also NE, SE, NW and SW can also be introduced. Amazing -‐ A team based problem solving activity to online maze creations Lay out 25 hoops in a square, e.g. (Sorry I’ve used squares as I’m useless with drawing – even on a computer!)

You may want to decrease the number of hoops for younger children. Have a map of the hoops with a path going through it. Do not share this with the children, e.g.

x X X

X

X x

X

x x x x

The whole class works as a team. They should make a circle around the hoop square so that they can see what is happening. Explain that the children may step forwards, backwards, left or right but not diagonally. As a team they have to work out their way across the hoops. The first child steps on the starting hoop. She then steps onto another hoop. It this is not on your secret map, so tell her that she is “out” and the next child has a go. The activity continues until the class have worked their way through your “maze”. Back inside the children can look at online maze creating programmes. Again the level depends upon the age and ability of the children. Secondary school pupils who are doing programming might enjoy http://www.mazeworks.com/mazegen/mazetut/index.htm Younger pupils will find this advice helpful http://www.wikihow.com/Make-‐a-‐Picture-‐Maze This site has some


great advice: http://gwydir.demon.co.uk/jo/maze/ . This website also has some useful information https://www.ncetm.org.uk/resources/10769 Consider building a maze outside. Look at mazes on line and see what would work well. Simple small mazes can be made with chalk. But 3D mazes are a lot of fun and can be made with boxes, play tunnels, etc. It’s also possible to create mazes through planting daffodil bulbs or other quick growing plants. Street names Use Google maps to download accurate street maps and when undertaking project work in the local area. Use the opportunity to describe and discuss routes. If you live in a very urban area, see if you can mark a route that spells out the name of your school. Then go for the walk along the streets to spell the name and take photos. Introducing simple grids, e.g. plotting by means of ordered pairs – A6, B5, etc. Begin by teaching the children how to use simple grids by reading the letters or numbers along the bottom first (the eastings). Then the numbers on the side are read (the northings). “Along the corridor and up the stairs” is an old saying which some children may find helpful. Using a painted blank grid on the playground (or chalk one on, if needed) let the children plan and create simple activities to practise reading the ordered pairs. This might be making a treasure island or creating a game. Orientate oneself to a plan of the school grounds Give the children a map of the school grounds that has a simple grid placed over it. Create simple activities which involve locating objects around the grounds and marking them on the map. For example mark several objects, each in a different square with an X. The children have to locate this object and write down what it is on the map. N.B. Ensure children are aware of, and able to use, the four cardinal points of the compass in the playground and on local maps. For older children, the above activities can also be used and differentiated by:

Using more sophisticated symbols, e.g. ordinance survey symbols on grids and maps Being aware of and able to use the eight points of the compass to show direction and then the sixteen points

Use four-‐figure grid references, then move onto use of six-‐figure grid references Indicate direction from one place to another on an OS. Map using the grid lines


Possible activities also include:

Islands chalked onto a grid square and used as a map. The children can identify features of the island and give their grid reference. This can be extended into treasure hunts and trails within the school grounds by giving children a map of the school grounds with a grid reference system. This can be used for a wide variety of project work by posting signs, symbols or artefacts in different places. The children have to locate the object, mark it on the map and list on the back what the object is.

The activities can become increasing complex in accordance with the age and ability of the children. For example, rather than grid referencing squares with a letter on the x axis, have a number so that 2 figure coordinates are given. Move from numbering the squares to the lines of latitude and longitude. Maps of the local area can be used, with key features indicated.

Work up to children using large scale Ordinance Survey maps and being able to locate features on the ground by using the map. Orienteering is also useful for developing map reading skills.

Have the compass bearing painted or chalked on the ground and refer to the directions when describing the location of different objects and discussing where seeds and plants should be positioned.

Shadow Angles On a sunny day, children can investigate angles in shadows. Before going outside, ask children to hypothesise about the angles they are likely to find in shadows. For example, it could be a statement such as “Shadow angles are more acute than the actual angle within an object.” This is a great opportunity to design a fair test and to think about how the activity will be undertaken by each group. The next step here is to investigate how the movement of shadows can be used to create a sun dial and to ascertain the compass directions. For more information have a look at the Shadow Play blog post: http://creativestarlearning.co.uk/science-outdoors/shadow-play/ Create right angle detectors! Take an acetate sheet and cut into palm sized squares. Using a permanent marker pen and a ruler draw along two edges so they meet in one corner and put a square to symbolise a right angle. This see-‐through detector allows children to place it on any object and check whether it is a right angle, acute or greater than a right angle. After demonstrating indoors, children can go outside and see what objects have right angles. This can lead to all sorts of problem solving including working out how many right angles are in a wall of bricks (or even on the whole school building). The detectors can also be used to see whether angles are obtuse or acute. An interesting investigation is to find out whether it is just buildings that have right angles or whether right angles exist in nature. What about curved and straight lines?


Introduce clinometers for measuring the height of buildings, trees and other landscape features, following on the activity described above. Angles in nature Investigating right angles through the use of sticks is covered by this blog post: http://creativestarlearning.co.uk/maths-‐outdoors/outdoor-‐maths-‐investigating-‐right-‐angles-‐with-‐sticks/ As well as angles in man-‐made structures, searching for different angles in nature works well. It can be surprisingly challenging to measure the angles of branches – figuring out ways of doing this accurately can be a good challenge for older children: http://creativestarlearning.co.uk/digital-‐technology/outdoor-‐maths-‐looking-‐at-‐different-‐angles-‐in-‐nature/ Angle trails This is a form of orienteering. The children will need to be taught how to use a Silva compass or the equivalent on a smartphone or tablet. Put up a series of signs or numbers or QR codes around the school grounds. Plot these on a map. Children have to use the map to locate the signs, write down the symbol, QR reference or number and work out the angles between each sign, from north. C Do right angles matter? Is it possible to create a right angle using two sticks? Can you make 2 right angles with two sticks? What about 3 or 4 right angles with two sticks? See if you can find a relationship between the number of sticks and the number of right angles that can be made. When might this matter in your life? Investigating right angles Investigating right angles through the use of sticks is covered by this blog post: http://creativestarlearning.co.uk/maths-outdoors/outdoor-maths-investigating-right-angles-with-sticks/ The challenge is for children to work in a small group. Using six large and six small sticks, what is the most number of right angles which can be made by one group? This challenge can be extended to include other criteria too, such as perpendicular lines, obtuse and acute angles, parallel lines, etc. Sticky Numbers Challenge a group of children to make the numbers from 1 to 9 with sticks. But there is a new angle on this!


• Number 1 must have only one angle less than 180 degrees. • Number 2 must have exactly 2 angles less than 180 degrees. • Number 3 must have exactly 3 angles less than 180 degrees. • Etc. As 0 has zero angles, this need not be made with sticks. Can the children find a zero in another object to complete the numerals? Frisbee golf This is a fun way of putting angles into a game. Set up a course of cone markers on a playing field and create a very simple map. In small groups, children have to take turns to throw the Frisbee from cone to cone, aiming for a throw-‐in-‐one. At each cone, the children take turns to align their compass to north and work out the angle from north to the next cone (reflex angles can be used here too). The distance in metres can also be measured between each cone and this can give rise to some good discussions especially if different measuring markers are used, e.g. one group uses a metre stick, another a trundle wheel and another a tape measure. If there is a GPS system in school, this can be used to accurately measure all angles and distances quickly. Orienteering is an excellent way of developing these skills and putting them into practice. The TOP Outdoors pack from Sport Scotland has many good ideas about introducing this sport, beginning in the school grounds.

SYMMETRY It is helpful if the children have had some experience of symmetry. This can include investigating reflections, folding “butterfly” paintings, looking at capital letters of the alphabet and drawing in the lines of symmetry, etc. Outdoor Art Symmetry Include shape and symmetry work as part of outdoor art activities, e.g.

Have mirrors and natural materials available. Children can create pictures or place natural materials on mirrors and look at the reflection that is made

Undertaking large scale printing activities. The children can compare the print with the object used for printing. For example it can be fun to compare a foot dipped in paint with the footprint that has been created

Encourage children to try symmetrical weaving patterns on fences. This can lead on to geometrical shape explorations. Look at apps such as Geoboard, Geodraw and Grid Drawing for Kids. Many fences are just life-‐size grids and geoboards…

Bookmark environmental art images that have clear lines of symmetry or symmetrical patterns and use these as inspiration for creating symmetrical patterns outside


Happa Zome is a Japanese printing technique. It involves placing freshly picked weeds between two sheets of calico. The calico is then beaten with a hammer or mallet. When the weeds are removed, their imprint is left on the material.

Same and Different Get children to find a natural object. Then ask them to find another one exactly the same. Discuss similarities and differences between the two objects. This can be recorded in big books and added to throughout the year. Extend this activity by placing the objects down a line in a symmetrical pattern so that the object on one side of the line reflects the same object on the other side. Once children understand this, they can work with a partner to create symmetrical pattern pictures using found objects. This can be extended if undertaken on a blank grid outside or place where the position of an object can be determined more precisely. Symmetry is part of nature This activity is designed to help children to identify the symmetrical properties of leaves. It is an ideal activity for a woodland walk, but if you have access to a number of different trees and plants around your school, then it will be possible to undertake this task on the school grounds. Invite the children to work in small groups to collect leaves. They are then encouraged to discuss some of the properties of the leaves. Direct them to think about the symmetrical properties and 'challenge' them to answer a number of questions about each leaf in their collection.

Is it symmetrical? How do you know it is symmetrical? How many lines of symmetry does it have?

Encourage the children to collect at least 6 leaves that display some of these properties. They could take digital photographs of the leaves, make leaf rubbings and/or complete a chart as a way of recording their data. Closely monitor their use of mathematical language (whether oral or written) and encourage the accurate use of vocabulary throughout their discussions. Clay faces The investigation is to find out whether symmetrical or asymmetrical faces are the most scary. The children can decide as a class how to carry this out. Demonstrate the difference between symmetrical and asymmetrical features. If there are no trees, then this can be done on the sides of buildings. The clay is used to make the features. Add tiny berries, stones, leaves and other natural materials to hand. Symmetry hunt


Using plastic mirrors and building upon previous outdoor symmetry work, undertake a symmetry walk outside. Start with small objects until children develop an eye for what they are looking for:

Look for leaves and flowers with symmetrical patterns. Check using the mirror Look for symmetrical shapes on buildings, e.g. doors, windows, bridges Look at symmetrical patterns of planting flowers and beds in local parks Look at patterns of bricks, pavements, cobbles.

Take photos and use for follow up display or artwork on pattern and symmetry. Think about different objects outdoors and encourage the children to observe and answers questions such as:

Is this object symmetrical and how do you know this? How many lines of symmetry does it have? (talk about horizontal, vertical, diagonal lines of symmetry)

What sort of symmetry does the object have – reflective or rotational? Are windows and doors placed in symmetrical patterns? If not, why not.

With the activities below, create a chart to record the results, e.g.

Object Number of lines of symmetry

Rotational symmetry Comment

Extending symmetry outside Again, building upon the outdoor symmetry work undertaken previously, consider a visit to a town or part of a city where further building designs can be observed and a great range of patterns. Using Google Earth prior to going out can be a useful introduction to looking at symmetry, shapes and angles from a bird’s eye view and for illustrating what is symmetrical and what isn’t. Get the children to take photos with a digital camera when on an outing or walk and draw on the lines of symmetry which have been observed outside. Kite making and flying This links nicely with a science project about flight. Children can make their own kite which is dependent on symmetrical accuracy in order to fly. For more information and video clips, have a look at https://www.ncetm.org.uk/resources/13529

Symmetrical Sketches A useful assessment for upper primary school involves enjoying art work. Have a look at how artists interpret the landscape around them. Very often they draw things slightly differently to


help people view the world in different ways. In this activity encourage children to sketch a symmetrical landscape. This could be in your school grounds or off-‐site. Challenge the class to ensure that every aspect of symmetry is represented in their interpretation. For example, features with:

Infinite lines of symmetry (a circular window or a football) One (a tree or a roof)), two (a door) and three axis of symmetry (equilateral triangles for leaves)

Rotational symmetry (rotation of 2, 3, 4 or more) Tessellating patterns – a pavement, etc.

HANDLING DATA Information handling is a dynamic area of maths which allows for creativity and innovation both in the approaches taken and possible developments of ideas, discussions and activities across all subject areas. According to Rhydderch-‐Evans (1993) there are four critical questions that children should learn to answer:

What do I want or need to know? How am I going to get the information I need? How am I going to organise and represent the information? What did I find out?

The links between indoor and outdoor activities can be close. In inclement weather, the preparation, introduction and review of activities may well happen inside when children need to discuss or listen to each other as part of a group or class. Digital technologies are useful tools for enhancing and adding breadth and depth to information handling before, during and after an activity. There are an ever-‐growing variety of apps, software and programmes that enable data to be collected, stored and presented in many interesting ways. Have a look at Visualise Everything1 blog post for ideas. Nevertheless, the skill of being able to create a neat, accurate table, graph and other representations still needs to be encouraged and taught. Expect rigour and consistency in terms of format and layout from learners. Look at examples in mathematics schemes and textbooks or online for guidance here if needed. Working outdoors enables learners to experience a broader range of information handling opportunities including:

Developing practical field study skills

1 http://www.1stwebdesigner.com/freebies/free-‐online-‐tools-‐create-‐diagrams/


Collecting real world data about the immediate environment Presenting information in different ways e.g. through the use of natural materials in situ Creating bigger representations outside beyond the use of pencil and paper activities

Idea 1: Only learners create the worksheet Worksheets are unnecessary for most outdoor activities. However, if children are developing their own information handling challenge then part of this may include designing and creating a worksheet for use outside. Microsoft Word has many charts, graphs and diagrams which children may enjoy experimenting with. Excel spreadsheets are great for creating databases and allow children to develop practical skills for use beyond school.

Idea 2: Collecting, discussing and sorting materials Many simple information handling activities can be undertaken through collecting objects and bringing them back to a gathering circle for sorting and comparative activities. Objects could include:

Something interesting (you may wish to set parameters with your group here, e.g. no jaggy things, non-‐living materials, natural materials only, etc.

An item connected to the class project A leaf, stone or other specific item

Ask the class or group to think about how the materials could be sorted, e.g. by colour. Each person is to find other people with the same colour and stand together or make a group display of themselves and their objects. Within a circle, the objects can be placed on a light-‐coloured sheet. The children can demonstrate different ways of sorting objects. In pairs, children find a selection of 10 objects in the vicinity. Then together they must decide how the objects can be categorised according to criteria called out by the adult or other children, e.g. “living and non-‐living” or “natural and man-‐made” or “big and small” or “rough and smooth”. This can lead to some interesting discussions depending upon what objects are in everyone’s collections.


Idea 3: Line up activities Challenging children to create line ups is a useful way to encourage children to think about specific properties or fields within information handling. For example if every child picks a leaf, then ask the children to line up in different ways. After one example, encourage children to think of other ways. Possibilities include:

Leaf length or width Lightest to darkest Prickly to smooth, etc.

Idea 4: Venn Diagrams Venn Diagrams are handy introduction to the use of sets and the relationship between objects. Remember that objects that fit into both sets should be placed in the overlap Use hoops, string, ropes, tubing or simply draw circles into earth, sand, snow or other surfaces. Circles made from birdseed provide a nice treat for wildlife visitors afterwards and look effective in the snow! Encourage children to think about and create Venn Diagrams for relationships that they can see in the world around them, e.g.

This is a good exercise for thinking about connections and relationships within the environment. Initially the children will need some support to come up with ideas, but once they get going, a new perspective on the environment or community can happen. Remember to have writing equipment and card or paper to explain the sets. Big class-‐sized Venn Diagrams can be created for a whole class to stand in! A simple whole class exercise is to have children number off in accordance with the 5 and 10 times tables. This can be done whilst standing in a circle and learners saying their number in turn. After that, the children have to move themselves into the correct part of a Venn Diagram:

Plants that grow on the playing 1ield

Plants that grow in our wildlife garden


It is also possible to add in a 3rd hoop with another multiple, e.g 2 and look for how this changes the Venn Diagram.

Idea 5: Carroll Diagrams Carroll Diagrams involve sorting objects according to defined attributes based upon what objects are and are not. For example, if children have gathered stones as part of a rock project then a possible Carroll Diagram may look like this:

Grey Not Grey

Bigger than my fist

Not bigger than my fist

Carroll diagrams can also be used for number problems, e.g. multiple of 3, not a multiple of 3.

Idea 6: Mud Pie Charts Pie charts and information handling go together like toast and Marmite. Children need to know and have experience of making and using pie charts before undertaking this activity which requires a number of practical skills to make. Ask groups of children to create simple mud pie charts using mud and other natural materials to present the results of a survey, e.g. What is your favourite activity at Forest School? Encourage the groups to think about the materials they will use and how they will label their mud pie chart. In particular, the challenge is to create the circle and divide it up accurately. You may need to show the children how to do this, e.g. with a stick and string for a radius. Children can compare this activity to completing a pie chart using a computer programme.

Multiple of 5

Multiple of 10


Idea 7: Simple Pictograms Pictograms have photos or graphics to help children identify and record information. For example, beside a minibeast home, create a pictogram for children to record the minibeasts found, e.g. Pictograms work well outside as a big display, if the materials are ready for the children to use. The pictogram can be:

Displayed on a white board, using laminated cards Drawn on the ground. Let the children paint stones to represent the symbols Magnetic board and pieces. It is possible to buy magnetic squares relating to project or outdoor themes

Simple charts such as weather charts can also be displayed in picture form:

This week’s weather

Monday Tuesday Wednesday Thursday Friday

Sun

Rain

Wind

Clouds

Other

Idea 8: Tick charts and tally marks with sticks Tick charts tend to precede tally charts for measuring the frequency of an event or the numbers of an item being recorded. One tick represents each item recorded:

Mode of transport Tick Total

Bicycle √ √√√√ 5

Car √√√ 3

Walking √√√√√√√√√√ 10

Other √ 1

Children need practice at making tally marks before using them in the context of recording information. Use sticks to introduce the concept:

Demonstrate how to make different numbers Let the children decide what number they are going to make (it may be wise to limit this to numbers smaller than 20)

The children then need to find their sticks and create a tally


Next, let the children walk round in pairs and see if they can accurately work out everyone else’s number

Idea 9: Line reviews A simple, reflective activity is to draw a line or have a rope and number it from 0 to 10, e.g.

0 1 2 3 4 5 6 7 8 9 10

Ask children questions such as:

How tricky did you find …? How successful were your group at …? How kind were you to other people in your group?

The children have to rate themselves on a scale of 0 to 10 by going and standing at the number on the line. Once a group or class have done this, whilst still in line talk briefly with the children about why they chose to place themselves where. An interesting extension can be for a child to evaluate where others are and if they give a good reason, moving a child or two do a different place on the line, e.g. “Fred helped Mary stay in the hoop, so I think he was kinder than 2 out of 10. I’m moving Fred to 5.”

Idea 10: Use a thinking skills approach outside Edward De Bono is famous for his strategies for developing thinking, reason and argument. In his book, De Bono’s Thinking Course, he discusses the framework “Pluses, Minuses and Interesting” (PMI). This is a good review tool. Chalk out or write down on mini whiteboards, the terms “Plus”, “Minus” and “Interesting”. Create a large chart in the playground using tape, sticks, string or chalk:

X

Y

Plus Minus Interesting


When reviewing an outdoor activity, the class should stand facing the PMI words. One at a time, the children come forward and stand behind the sign. For example, the first child will stand at position X, facing her classmates and will tell them what she thought was a plus about the activity. Another child might choose to stand at position Y and state something he found interesting. The graph is built up as children add to the PMI comments. Every time a new person enters the graph, the line of children should shuffle backwards so that the new person stands just behind the word. Not every child has to contribute. Part of the experience is simply hearing what others have to say!

Idea 11: Line graphs with ropes Line graphs are popular at upper primary levels for demonstrating air temperatures over a number of days as part of a weather project. Simple line graphs can be demonstrated outside using skipping ropes tied together or a large piece of rope. It works well as a whole class or large group activity if sufficient data exists. First, the children need to decide how each axis needs to be labelled and the range needed. A blank grid square can be helpful for more accurate representation of the data. Using chalk or a child, plot the data on the graph. Use the rope to join the points plotted – each child can either stand on the rope laid on the ground or hold the rope at waist height at each of the plotted points. Look at the data presented this way and ask the children to think of questions to ask for others to answer about the weather recorded. twigs. Instead of joining the points with a rope, the children have to find sticks that fit neatly between the plotted points.

Idea 12: Introducing the mean, median, mode and range of data Looking at mean, median, mode and the range of data are activities that need to be explicitly taught with frequent opportunities for practice. There are many outdoor activities that can help reinforce these concepts with whole class, group or individual activities. This is one possible introduction: Give children ten seconds to gather as many items of a common object as possible, e.g. daisies, or clover, or pebbles. Each child should count the number of objects (known as values) they have collected.

Ask children to line up with the objects from the person with the most to the person with the least. To find range of data, show children that this is found by subtracting the lowest value from the highest one.


The mode is the most popular value. Find the mean or average number of objects gathered. To do this everyone’s data needs to be added up and divided by the number of children in the group.

The median is the middle value. If the children are lined up correctly then the person in the middle of the range has the median value. If there are two people in the middle, then obtain the mean of these two values.

The mode is the most popular value and appears most often in the data. . Sometimes there may be more than one answer if two values have the same result.

It is a good idea to practice this activity a couple more times. Let children decide what objects to gather and to take turns at leading each mini activity.

Idea 13: Sampling the variety of flowers on the playing field Which is the most common flower that grows on your school playing field? Using a hoop as a sampling technique, can each group undertake to collect and record information to determine the mean, median and mode of each plant? It is worthwhile creating or ensuring there are identification cards readily available for each group to access. For example, common summer plants on UK playing fields include: speedwell, buttercup, daisy, dandelion, clover, plantain and thistle. Having these identified and labelled will enable each group to complete the task independently. This activity builds on Idea 23.

Idea 14: Create a diagram Using materials found outside, such as shells on a beach or leaves in a woodland area, check how many varieties there are. This links nicely to work on biodiversity. Create a diagram using the actual materials to represent the distribution of the materials. This activity works well as a precedent to looking at the variety of charts available in Microsoft Word and other software. It can also be useful as a next step to print out these charts and “smart art” ideas and to take them outside to recreate. The 3D charts are especially interesting to recreate!

Idea 15: Scattergraphs Scattergraphs are useful for plotting the relationship between two variables on a graph. The results are usually scattered and a line of best fit is drawn. At the primary school level, experience of creating a human scattergraph should be kept simple. Focus on whether a correlation can be found between two variables. For example, after completing a team problem solving challenge, ask children to undertake a line review (Idea 17). Let them stand on a line ranging from 0 to 10 to rate how challenging the activity was, e.g.


x x

x

x x

x

x

x

x

Next ask the children to consider how much they enjoyed the activity, on a scale of 0 to 10. Only this time, the children (x) move into a scattergraph formation, e.g.

Relationship between the challenge and enjoyment of the team problem solving activity

With opinions, the results are likely to show no clear correlation as indicated above. Comparing leaf width with leaf length in millimetres may give a more definite correlation.

Idea 16: Databases Databases are worthwhile compiling for science work outside such as ongoing work monitoring biodiversity within a habitat or the school grounds. Over several years, useful information can be gathered about the distribution and numbers of animals, plants and fungi within an area. This can be used to monitor population trends. Go for a “Top Trumps” approach. Encourage children to look at the information that is written on these cards and use them to decide useful fields for developing online records. Examples can be found on the Nature Detectives website: http://www.naturedetectives.org.uk/download/trumps_minibeasts However it may be worth adapting these to increase the level of rigour. Databases can be created using Microsoft Excel spread sheets or similar software. However, the information can be presented like “Top Trump” cards for children to use outside or in to play the game and develop their knowledge about the subject. Possible databases include:

Weather recordings: temperature, humidity, wind speed, atmospheric pressure, cloud cover, etc.

Plants growing on the playing field Items on sale in a local shop or menu items in a café

0 10

10

y

x

Challenge

Enjoyment


Creating databases within school grounds can be an ideal way to work with a ranger, scientist, natural history enthusiast or other professional to identify the variety of wildlife.

Idea 17: Information diagrams This is an alternative way of displaying information gathered. For example, if the class were collecting information about the numbers of children and where they were playing at break time, then the results can be displayed in a diagram rather than a chart of a graph. If 100 children were playing then the diagram may look like this:

Activity Colour Number of children

Skipping 8

Chatting with friends 20

Scrapstore Play Pod 40

Football 20

Other 12

Be flexible about the colours, layout and style! If the numbers don’t fit into a neat table, there may be additional challenge by converting the numbers to fit a table, e.g. percentages, etc. If the graph is completed in a word document then cells can also be merged to remove the individual cells!


With children all choosing their own interpretation of the results, it is possible to demonstrate that variation in presentation can be an art form.

Idea 18: Sports day Planning and participating in sports day is an ideal mini project for a class especially if potted sports are involved. It’s fun if there is a theme such as an Eco-‐friendly sports day or the Royal Family. Alternatively link this to a whole school project or plan as a shared activity with a school in a different country. The children will have all sorts of data handling activities to undertake including:

Creating activities which are easy to set up and record The creation of recording sheets for each activity Instructions required for each activity and recording of the results How the information is to be collated Creating a summary sheet of Sports Day to share with parents. This can be an opportunity to show off different ways of presenting information!

Idea 19: Angles in the environment Which type of angle is most commonly found in school grounds? How will you investigate this? Think about:

The equipment you will need Where you will go to find, collect and record your data Your method of presenting the data for others to interpret Useful questions to help your audience interpret the data How your group can organise the work efficiently to meet the deadline

Is there are greater variety of angles observed in nature or on buildings?

Idea 20: How many bricks were used to build the school (or just one wall)?


If your school building has a wall with visible bricks, this is good practice for estimation. For example, one method is to count the number of bricks in one line and then count the number of lines. Children can discuss how they are going to work this out as a class. Which group is going to do what job? How will the data be recorded and presented?

Idea 21: How many shoes cover the width of the playground? Children can estimate how many lengths of their shoe will cover the playground from one side to the other. Then they need to decide how this can be worked out and experiment with their ideas. Show the children the importance of being accurate and need to have the shoes touching each other. Much discussion can be had around why everyone might have a different answer. For older children work can be done on using everyone’s shoes and working out the mean. Children can make their own suggestions for what to measure with shoes -‐ length/area. Again, discussion can be had about the accuracy of the experiment and ways of completing the challenge. This activity can be varied using different body parts, e.g. arm span, body length (!) or using specific objects. How can children record and present their results?

Idea 22: Introducing chance and uncertainty Chance and uncertainty activities work well with children of all ages. Informal opportunities for developing knowledge and understanding of concepts such as fairness, predicting outcomes in games and activities and whether we can be certain of an event happening in the future all build children’s capacity for tackling more challenging work as they go through primary school. Make time for discussions with children around questions such as:

Do you think it will snow today? What about rain? How do you know? What’s the chance of someone getting wet if Fred jumps in the puddle? Will the dog chase the cat? What are the chances of getting sunburnt if you don’t apply suncream?

This helps children realise that probability, chance and uncertainty are concepts that can be discussed and analysed. Note the vocabulary used and model this yourself, e.g. fair, unfair, certain, uncertain, never, definitely, maybe, chance, etc. Another important step is to encourage children to justify their suggestions:


What makes you so sure about this? How do we know this for certain? Is there anything about today’s weather which we can say is very likely or unlikely. How do we know?

How can we be more certain about this? Tell me your thoughts

Idea 23: A random walk “Walking round in circles” is a phrase associated with being lost outside. According to bushcraft law it is highly likely that unless a compass or other way of telling direction is used, someone who is lost will always end up back where they started. It can be fun to test this theory in the playground or on open space. It is a good opportunity for children to discuss concepts such as random, chance and uncertainty whilst revising the points on a compass. Ideally each pair of children needs a compass but one drawn on the ground works fine. Each direction is allocated a number, e.g. N-‐1, NE-‐2, E-‐3, etc. Give each pair a set of numbers from 1-‐8. On the ground, the pair marks the starting point with a symbol, e.g. chalk mark or stick. One person keeps the numbers, the other moves around. A number is picked at random. The children may need to decide how this can be done accurately. This is the direction, the walker must face. Next, the number is reinserted back into the rest and, for the second time, a number is picked at random. This time the walk has to take that number of steps in the direction he or she is facing. Then the process is repeated until the walker ends up back at the symbol… or not! It is really important to review progress with this activity. Some pairs will meet dead ends, others will be far away from their symbol. Others will make it back in an instant. This is the time to consider:

Average number of moves it is likely to take Whether varying step size makes a difference and if so, does this affect the random nature of this activity?

An online version of a random walk has been created by 11-‐yr old Jake Irvine who was inspired after reading about the concept in Alex’s Adventures in Numberland by Alex Bellos

http://scratch.mit.edu/projects/16070026/

Idea 24: The probability game


Ask each pair of children to find 3 of 3 different objects outside that can fit inside a bag. All 9 objects should be put inside the bag. The aim of the game is to withdraw 2 objects. You win if they are the same. How likely are you to get 2 the same?

What are the possible outcomes? How do you know you have found them all? Can you find a systematic way of writing them down? What is the probability of winning this game? How could you change this game? What is the chance of you winning your new game?

Finally, I hope this booklet is a springboard to many other creative and interesting mathematical explorations with your class. Please get in touch if you have any queries or to book me to work or provide training your school. Juliet Robertson

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“I’m a teacher, get me OUTSIDE here!” http://creativestarlearning.co.uk/blog

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FURTHER INFORMATION Contact Juliet Robertson via email is best: [email protected]

Telephone: 07802 800167

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