Learning Maths outside the Classroom in a Special Educational Needs (SEN) Environment
The hall or playground is a great place for People graphs
- Many schools have markings painted on the ground for children to enjoy games at break and lunchtime. In one school there is a 6 by 6 square grid marked out in 1 metre squares.
- Pupils chose a token [coloured cube, football team, favourite sweet or crisps, etc]. They will then line up on the grid in rows according to that token. The teacher might place a similar token on the floor for them to line up behind.. This will give a living bar graph.
- One teacher followed this by using lengths of coloured ribbon. She gave each line of pupils a length of a different colour, allowing 1 metre of ribbon for each pupil in that line. Using the ribbons the children formed themselves into a circle, each group holding their length with ones at either end joining with other groups. This gave the idea of a pie chart.
- Older [and more-able] children acted out a pupil spreadsheet on the grid with formulas set for each line and numbers set for the front row. All other in the line worked out their number and held this up on a mini-whiteboard.
- Other games on the grid included a version of FROGS where the grid [2 by 2, 3 by 3, etc] was filled with children except for one corner. The opposite corner contained a child with a hat on. The aim was to get the child in the hat to the empty square by forward, back, left & right moves.....in the fewest number of moves!!
Being part of graphs and movement games like this will build a stronger feel for the concept.
The athletics track with already-measured lengths can support work around speed & time. Older children can use stopwatches to time a 100m race and scale this up to time for a kilometre or distance for 1 minute or 1 hour. Similarly working with the times for a 400 metre race will produce a slower speed and questions can be posed about this. Exact calculations are not needed and ample opportunity will be there to estimate and approximate.
There is lots of scope for using the grounds and buildings to reinforce simple ideas about shape and angle.
- School buildings have frequent examples of right angles [walls, doors, window frames]. Estimating heights of buildings using non-standard units such children or measuring door heights using standard units.
- Some building designs use circles and semi-circles for windows and arches.
- The school field offers opportunities to measure perimeter and area; comparing other areas with the field or yard enables estimation. "How many classrooms will fill the yard space?", etc. The football pitch will offer work on angles and degrees with older pupils, 360º centre circle, 180º semi circle. 90º corner quadrants.
- Think also of other sports [hockey field, tennis court, cricket pitch, rugby field, etc]. Each will present opportunities to explore symmetry, locus, area, etc in a practical way. There are a lot of "mysterious" circles, semi-circles, arcs and parallel lines on sports fields which are superb for getting across the concept of locus.[this will be very useful in the non-SEN classroom as well!!]
- Brickwork patterns offer challenges around tessellations. Pavement areas will give the same. Some shopping malls will have hexagonal or octagonal paving. Visits are useful but photographs of these can equally well provide that stimulus.
A special school in a semi-rural area of Cumbria is able to enjoy many nature walks in a woodland area next to school. Children experience sounds and tactile stimulation linked to simple mathematical activities e.g. to collect five leaves, measure 10ml of soil, feel different bark surfaces, compare photographs of a large flower and a smaller flower.
- One teacher has designed and made a set of attractive laminated cards for children to use.
- These might show a picture of a leaf and invite the child to find a similar leaf and match it. There are several different leaf types to try as each activity is completed. Sometimes the card will ask for a specific number of leaves.
- Another card asks the child to collect 3 twigs and make a triangle; another asks for 4 twigs and to make a square, etc. Pupils will place their sticks on top of the picture to match the shape; more-able children will make the shape without a prompt.
- Other cards will show small creatures, insects, etc and ask how many legs.
- Teaching assistants will prompt further questions and photograph children’s work.
There are lots of commercial Treasure hunts around but it is always nice to design your own to fit local surroundings. Holly Mount RC Primary School in Bury arranges trails regularly around the building or using the grounds. A number of "stations" [rooms or landmarks in the grounds] are selected and at each one there is a maths problem to solve. At times the subject leader / SENCO will invite other schools to join in.
- Trails will often be connected to something nearby but not always. The answer to a problem might be a number and children are given a grid which matches a letter of the alphabet to that number. In this way the trail will "lead" to a word or phrase. They will also be told which station / which problem is next.
- Sometimes the trail will have cards with a variety of things on them. [e.g. how many chair legs in the school hall?] Others might involve shape vocabulary around the school. At other times the trail will reflect the school focus for the term.
The use of a washing line between trees or posts provides many activities for pinning up and ordering of all sorts of things.
- Sorting and ranking numbers [single digit or larger]
- Sorting and ranking directed numbers [positive, negative....and zero!!]
- Sorting probability statements [impossible, likely, certain]
Built Environment & Heritage
There is ample opportunity to use mathematics around cars.
- A school’s grounds, close to a busy road junction [with 4 roads converging on a round-about], gave excellent facilities for safe observation of traffic movements. Pupils were tasked with specific roles.
- One pair tracked and recorded the directions from which the vehicles came; another recorded where the traffic went to.
- Another pair recorded the types of vehicle. Other pairs looked just for cars; some recorded colour, others makes.
- Back in class there was much activity around different sorts of diagram to represent the data. The usual bar charts and pie charts and sometimes "home-made" attempts to represent the traffic flows through the junction. Perhaps children will build a model.
- The work provided chance to think about other areas of mathematics; the probability of a vehicle turning right, the most frequent vehicle movement, etc.
- Questions arose about whether the movements would be the same at other times [evening, middle of the night, weekends, etc] and this allowed the pupils to speculate and ask if the could test their hypotheses at a later time.
- Visits to car showrooms and second hand car sales will prompt a lot of work back in school perhaps to set up a database with groups simulating their own showroom. Some children will use car magazines to simulate their own "used car dealership" of perhaps 20 cars, classifying these by colour, make, price, mileage, etc and then respond to the teacher’s and other pupils’ questions and enquiries about the stock they had.
- Other development of this type of work will be with similar work on pet shops, dog sellers and horse sales.........perhaps a football agent with different players on his books!! Much will depend upon children’s interest but the activities will allow rich and practical work around data handling.
Sport & Adventurous Activities
Mathematics at the match, Great Arley School, Lancashire
A favourite activity for secondary pupils at this special school is the trip to their local Championship team’s home matches at Preston North End. A few matches during the season are chosen as school activities to give the class chance to use real maths in a purposeful way.
- First they had to work out the distance to travel and estimate the time it will take to get to the ground. They needed to build in time for delays and allow time to queue, buy a drink and food as well as leaving time to get comfortably to their seat. All this presented a good opportunity to use a time line. With everything included in the time-line, the young people can then work out what time to leave school and when they expect to get home. Some will even extend the line to allow them to work out what time to leave their home to go to school to meet up.
- A big part of the match experience is cost. As well as the entrance charge, they needed to include cost of travel and food. Some include the cost of match programme and a few will call at the club shop before matches to buy merchandise.
- Inside the ground and during the game presented many more opportunities to use mathematics.
- Among the more common activities was estimation of the number of seats in a stand. Different pairs did this for all 4 sides of the ground and shared answers to give ground capacity. More able pupils estimated the number of empty seats and worked out the proportion of capacity taken up.
- One thing which fascinated one group was the amount of added time the referee gives at the end and how does this relate to the actual time lost. Using stopwatches, they timed how long the ball was out of play [at throw-ins, corners, free-kicks, etc]. They checked time lost through injury stoppages. One group even decided to check time lost for goal celebrations. At some games the club used a "multi-ball" system where the ball boys have several balls and can throw a new one in as soon as one is kicked out. At other games the same ball had to be recovered and thrown back. Groups checked whether less time was really lost with multi-ball.
- The field of play presents many opportunities to explore maths. Measurement [and estimation] of the length and width of the playing area [including penalty box, 6-yard box, centre circle, corner quadrants], the height and width of goals. Some children tried to estimate how far an assistant referee would run up and down the line in a game; they found this too difficult for a player or the referee.
- Back in school, much work is possible on the financial aspects of the game. With attendance figures, the pupils attempted to work out the receipts for the game. Lots of discussion took place about the different ticket prices, how many paid which price [and who did not pay at all!]. Talk went on to other receipts [food, programmes, etc].
- Inevitably the other side of the finance issue was players’ wages. There was lot of estimating who earned what. This led to the whole field of transfer fees and other club costs.
- Finding all possibilities offers activities around combinations of shirts shorts and socks for different teams. This can be as complex or simple as needed for the level of ability of the children. Best results are when children physically manipulate paper [laminated] shirts, shorts and socks.
- All in all, there are lots of opportunities to explore Maths Outside the Classroom through a trip to the local football team at whatever level they play. Indeed it might be easier if the team is a lower league or even non-league, local football
Mathematics, science and technology events activity Several schools use the hall and playground for children to make and test their own wheeled vehicles as part of adventure theme days. Some models were powered by elastic bands while others used sails and were powered by hairdryers. As well as the creativity in design and construction, a lot of mathematical ideas were accessible to the children in a relevant context. As well as the obvious competition, great fun and lots of measurement of time and distance went on.
At Ravenshall School in Dewsbury, Key Stage 3 pupils were given the challenge of setting up and running a juice bar. They decided to call it ‘Strictly Come Juicy’ and promoted interest around the school by offering free samples.
Through this activity, pupils had different jobs to do on a daily basis, which focused on different areas of the mathematics curriculum.
- They worked out the cost of different types of fruit (including which fruits were in season)
- They decided how much to add on to the cost of the fruit to make some profit
- They gathered together resources and tools
- They cut fruit into different fractions in order for them to fit into the juicer. This was an excellent way to address different fractions in context.
- They measured juice out into equal quantities for customers.
- They handled money at the counter and counted up to work out how much money had been taken each day. Some were able to keep simple accounts and the balance so far
- They would decide how much money they needed to spend on fruit for the next order
- The juice bar served fresh fruit juice at break times to pupils from different classes [and staff!!] They were encouraged to buy a cup as one of their ‘five a day’ and meet their healthy schools target.
This activity was a lot of fun, which meant that they fully engaged in the tasks without noticing that they were learning key numeracy skills at the same time. It also equipped the pupils with real life skills that they can use in their everyday lives, which is important to motivate the pupils; if they see a real use for a skill then they are encouraged and motivated to develop that skill.
Finally, the pupils learnt about money in a real sense and not in a theoretical sense. They learnt the value of money along with other key skills that encompassed team working and, in some cases leadership.
Since November 2009, the pupils have been running a school juice bar each morning as an enterprise in addition to a toast club which also takes place each morning. They have been able to self fund their own business and make enough profit to pay for a school trips.
An excellent way to give pupils the chance to engage with and use maths is through mini-enterprise activities.
- Some secondary special schools use the hot summer days to let groups of Y9’s set up iced lolly companies. Each is responsible for its whole operation. The plan the advertising and marketing, source and cost materials and decide price for different flavours and sizes. Valuable practice is offered in counting money as well as drawing up accounts and working out profits. There are many opportunities for teachers to pose additional questions around the project, knowing that pupils’ ownership of their work will remove any barriers which may have been present in a less practical setting.
- A few schools used the idea of a car wash. While the initial intention was purely fund-raising, there was a lot of mathematics that teachers exploited. Groups worked in pairs and so a rota was arranged which allowed time off for rest periods without stopping the work. Different price tariffs were set. Costs of materials were calculated after a trip to buy buckets, leathers, sponges and soap. Pupils got practice at counting money and giving change. At the end a set of accounts showed how much profit was made.
- Many schools do a regular shopping trip. Part of the preparation is be about what we plan to buy and what will this cost. There is also a lot of work around local bus times if public transport is used. Pupils needed to decide when to leave school to catch the bus and what time they had to leave the store to get the bus back; a good use of the time-line and strong links with social skills.
Great Arley School in Lancashire regularly uses the idea of a theme day across the school. Themes have included Dinosaur Days, French Cafe, Volcanoes and Air travel.
Dinosaurs provide rich ideas for maths.
- Comparing lengths of different dinosaurs will lead to how many T-Rex will be as long as a brontosaurus. Working with cut-out and laminated scaled figures of the dinosaurs, children will compare and estimate and even judge the size of a person against the creature.
- Other groups measured out and marked the size of different dinosaurs in the playground.
- One task was to plan a theme park in the school playing field. Everything had to be done to scale. They used tape measures to check how big the creatures were and how much space they would need to occupy. They also used a map of the grounds and dinosaur pictures on the same scale to see how many could be included. Some produced a plan of a dinosaur park which gave the teacher more chance to ask questions about how the exhibits were sited [e.g. whether meat eaters should be near the people areas, etc]
- Other problems were related to the size and type of enclosure a dinosaur would need. How much area was required? How many different shapes would provide this area? What is the perimeter for each if these and which requires least perimeter and fencing? All this task was done very practically using scaled pictures and maps and squared paper.
The French Cafe allows many good opportunities to use mathematics.
- Converting Euros [keeping the rate simple].
- Some children tried to do simple mental maths in French
- Using cups of different sizes children estimate capacity and compare capacity by filling and pouring.
- Children used recipes to make a French tart and then scaled up ingredients to make several tarts. They costed the ingredients and so worked out a price to sell slices to school friends, teachers and parents.
- Shopping trips to buy materials provided more opportunities to engage the children with time-tables, handling money, etc.
Vocanoes provided a number of opportunities
- There was strong cross-curricular links with geography, history and science
- Measurements of heights, distances fro home, etc
- Children enjoyed building their own volcanoes and this gave chance to improve art, craft and technology skills
- Several children enjoyed looking for volcano-type features round school
Air Travel was set as the theme of for one day.
- Groups investigated journey times, distances and aircraft speeds.
- Some looked at seating configurations on different aircraft with scale drawings of cabins. Using these they measured leg-room and investigated how many seats could be fitted for different amounts of leg-room. They checked how this might affect takings.
- Others looked a fares and discounts for early booking. They investigated the difference in revenue for various numbers of early bookings.
- Some worked on problems of planes that were not full.
- Some investigated luggage charges set by different airlines.
- Linking with technology, one class designed and made paper aeroplanes. They tested these in the hall to see which flew furthest using tape measures to check distance and stopwatches to check flight times.
Themes like this will allow children to be able access the concepts of ratio & proportion in lots of ways.
- A group in one school offered a stall making "smoothies" to pupils at lunchtime.
- They had to make these to a set ratio of fruit to milk, etc. Teacher was able to probe understanding of ratio with focused questions.
In another school, one teacher shared a story about his mum’s recipe for "perfect custard".
- He said he remembered it as 10 fluid ounces of milk to 4 spoons of custard and so the ratio was 10 to 4. He could remember this easily because this was his mum’s birthday [10th of April or 10/04].
- He then asked how much would be needed for half as much custard....or twice as much? Which birthdays would be good to remember these?
- If you used too much milk to powder the custard was runny and if you used too much powder to milk it was too thick. Children were asked to think whether their birthday would make for "runny" custard or "thick" custard. Children tried to line up from "runniest" to "thickest"
- Finally he posed the question as to which birthday produced the "runniest" custard and which produced the "thickest".
- The children lined themselves up from the "runniest" to the "thickest". The explaining, negotiating and arguing provided some very rich opportunities to develop learning in a practical way and, through eaves-dropping on this dialogue, teachers found good evidence to assess progress.