MATHS TRAILS What is a maths trail? - A way of using the environment to explore some mathematics Why do a maths trail? - Fun and enjoyment - To see some mathematics in the environment - To encourage observation and problem solving - As starting points for classroom activities - For its cross curricular possibilities - Reference to maths in real contexts in the framework for teaching mathematics Where can a maths trail be set up? - School (classroom, hall, gym, library, corridor, school grounds ) - Local vicinity - Village, part of town or city, shopping centre.. - Park, countryside, playground. - Church, cathedral.. - Museums, stately homes. In considering the venue for your trail you may need to think about How busy will the area be at times when children will be on the trail? Are the features you want the children to look for easily seen at these times? Is it safe for your children? Is there sufficient space for all your children? Does it need to be traffic free? Could the number of children in such an area cause a nuisance to other people? How can it be organised? - Is it going to be a trail suitable for various year groups and ability ranges? If so you may need to choose objects or places where different levels of questioning would be possible. - Will the whole class do the trail at the same time or not? - Will the children work individually or in pairs or in groups or.? - Is it going to be a trail which is completed in one 'go' or one which could be split into several sections? - Are you going to use other teachers, parents, helpers? How can it be presented? - A series of questions in the order in which they must be done? - Direct instructions of where to go to next? - Clues about where to go next? - A map or plan? Path drawn in, or areas marked in some way? - Questions which can be attempted in any order? - Answers written on the sheet/booklet or on a separate piece of paper?
What types of questions are you going to ask? - All of which can be answered "on trail"? - Some questions or ideas taken back to be developed further? - Some starting points for activities? - Closed questions, open questions or a mixture? - Questions which deal with various aspects of mathematics? (It is important to have a variety?) - Would you like the children to think of some questions themselves? When are you going to ask them to do this? - Questions which ask the children to 'collect' things whilst on the trail? How do you organise helpers? - What will you expect of them? - Will they work alongside the children, will they support the children or will they 'merely' act as adult supervisors? - Will you meet with them beforehand? Other considerations - Transport arrangements - The things children will need on the trail eg writing materials, a bag in which to collect items - parental consent Children (and teachers) need to be aware of the purpose of the trail. Look round a possible site noting things that are interesting and seem to have some mathematical possibilities. Don't worry too much about the actual questions on the first visit. Get the children to find further questions of their own. More ideas for you for next time! What do they think makes a good question? Conjecture: Shape activities are easy to find whereas good number activities are harder to find. What to look for in a school setting or in the vicinity: Playground Climbing frames, painted floor patterns, paving slabs Car park Vehicles Rooms Hall Layout, size of spaces, number of spaces Registration numbers, age by registration letter, tax discs, hub cap designs, frequency, vehicle types, colours, manufacturers Bicycles, wheels, spokes, gears, combination padlocks Number, sizes, how many children in each classroom, routes for messengers, lunch boxes, coat pegs Size, seating/standing capacity, wall bars, jumping horses
Library Estimate number of books, sorting, cataloguing Furniture Shapes, fitting together, heights, standard sizes, stacking Windows Floors Walls Ceilings Pillars Doors Stairs Shapes, proportion of wall area, skylights Paving slabs, tiles, floor tiles, carpet tiles, parquet flooring, floor plan, floor area Brick designs, concrete panels, tiles, decoration, display boards, window patterns, mirrors, glass, dates, name plaques Ceiling tiles (shapes, number), height, lights, shapes, number (sufficient?) Cross-section, shape, height, tapering Shape, standard door size, door handles, letter boxes, pediments, fire exits, time to evacuate, usual rate of entering and leaving Number, number of flights Fire extinguishers Weights, date inspected, capacity Railings Fencing Playing field Shape, spacing Shapes, lengths of fencing, length of wire, weaved fencing (wood or wire), area enclosed Size of pitches, proportion of sides, size of goals, nets, height of tennis nets Heights, girth, age, most common, leaf shapes, pine cones, fruit What to look for in a countryside setting: Fencing Gates Shapes, lengths of fencing, length of wire, weaved fencing (wood or wire), area enclosed Heights, girth, most common, leaf shapes, pine conces, fruit, ring count for age of fallen trees Shapes, construction, hinges, angle of turn
What to look for in a town setting: Logos Timetables Clocks Banks Shops, posters, vehicles, symmetry Bus, posting times, church service times, opening times, closing times, meeting times, exhibitions, cinema/theatre performances Town clocks, church clocks, clocks in shop windows, different clock faces, digital display, roman numerals, some hours shown only, 24 hour clocks, no hours shown, geared clocks, sundials Exchange rates, interest rates, types of account, PIN numbers, Tower blocks Shops Queuing Car-parks Vehicles Signs Notice-boards Estimating heights, lifts Prices (in window, on signs, posters, or hoardings), discounts, sales, best buys between shops, economy/family/giant sizes, change, ways of paying, credit, displays, stacking, packing Entrance and exits, flow of people/cars, lifts, does everyone always back the wrong queue? Prices, layout, size of space, number of spaces, multi-storey, times open Registration numbers, age by registration letter, tax discs, hub cap designs, frequency, vehicle types, colours, manufacturers Bicycle/motor-bike wheels Street names, road signs, signposts, symbols (phone, toilets), parking restrictions Dates, times, frequency, town plans (coordinates) Shadows Routes Floors Walls Windows Pillars Length, time of day, shapes Bus, delivery, how to get from/to, instructions for blindfolded person Paving slabs, tiles, floor tiles, carpet tiles Brick designs, concrete panels, tiles, mosaics, mirrors, glass, dates, name plaques, balconies Shape, window patterns, proportion of wall area, skylights, leaded lights, window displays Cross-section, shape, height
Doors Stairs Flower beds Shapes, door handles, letter boxes, pediments, door numbers, standard door heights, knobs and knockers (!), do people prefer automatic doors? Number, number of flights, gradient, spiral staircases, escalators, number of steps visible, lifts Shape, planting patterns, spacing, volume, weight Dates Phone boxes Lamp posts Traffic lights Statues Memorials Seats Buildings, statues, memorials Telephone numbers, codes, costs of calls (local, national, international, services) Heights, girth, age, most common, leaf shapes, pine cones, fruits Designs, heights, numbers, shape of glass Sequence, sequence on more complicated junctions with/without pedestrian lights, is there enough time to cross the road? Dates, heights, scale War memorials, dates, numbers, frequent names, foundation stones, commemorative plaques Designs, dates, dedications, number, heights If you post a letter at 4 pm on Friday, when will it be collected? How many postal collections are there from Saturday to the following Friday Look out for. vertical objects taller than two metres and find 3 things that are a bit taller than you. How many different road sign shapes can you see? Look at the floor. Dow you think there are more black tiles than white tiles? Look at one shape is often repeated. Why do you think this is so? Look at the seating area. Why has this shape been chosen? (For later - design a seating area for somewhere in your school)