Numbed by numeracy? Jaded with geometry? Then why not try this mathematical meander for inspiration.
Take the Docklands Light Railway from Bank station in the City to Island Gardens in what used to be the heart of the capital's docks. En route you can calculate the train's average speed (the trip is 12.4 kilometres - 7.7 miles), or speeds between stations (Bank-Shadwell, 3.8km - 2.4 miles; South Quay-Cross Harbour, 1.28km - 0.8 miles).
Alighting at Island Gardens, follow the signs for the Greenwich Foot Tunnel. Before entering, walk slightly downstream to enjoy the view of Greenwich immortalised by the painter Canaletto in 1750. Stand directly opposite Water Gate which is immediately in front of Wren's Royal Naval College: you are in the right place when the gate (with steps from river to shore), the statue of George II just beyond, Queen's House and the statue on the hill of Greenwich Park are in a perfectly straight line. A splendid opportunity to explain axes.
Use the fact panel to help with calculations in the Foot Tunnel, built when imperial England reigned supreme - and don't forget conversion exercises. What is the angle between the shaft's roof panels at its apex? Count the steps down the shafts. What is their average depth? Measure the tiles lining the tunnel, and the flagstones on the floor. How many tiles are required to connect both ends? The tremendous echoes may also inspire you to calculate how long it takes for the sound of your voice to travel from one end to the other.
Emerging at Greenwich, turn left and walk in front of the Royal Naval College. Count the railings: how many per foot? How tall? The path between shore and college is narrow. Measure its width. Guess why it's called the Five Foot Walk.
Retrace your tracks for the Cutty Sark and Sir Francis Chichester's Gypsy Moth IV. Compare the number of masts and rigging; an information board on Gypsy Moth will help you calculate average and fastest speeds on its round-the-world voyage. Now walk a few yards along King William Walk for the grounds of the Royal Naval College and some serious window counting. What shape? How many? How many panes of glass?
Next stop is Queen's House, a geometric utopia designed by Inigo Jones for Anne of Denmark, mother of Charles I (she died before its completion). The galleried Great Hall is a perfect 40ft (about 12 metres) cube. Count the shapes within the amazingly patterned floor: circles, triangles, rectangles, squares, then check the ceiling, a mirror image of the floor. Before leaving Queen's House, try telling the time by the 18th-century 24-hour astronomical clock. It also tells the day of the year, the Moon's phases, sunrise and sunset.
Enter Greenwich Park by the King William Walk entrance. Turn left until, by the Regatta Cafe, you find the dolphin sundials, which offer a good opportunity to explore angles. The shadows cast by the leaping dolphins'
tails tell the time to an accuracy of one minute.
Walk up the hill to the Royal Observatory. On the wall is another 24-hour analogue clock, and marks for public standards of length - a good place to calibrate rulers and tape measures. A plate indicates you are 152ft - around 46m above mean sea level. General Wolfe's statue - the one you could see from Island Gardens - is adjacent. That perfect axis is still there. You can also count and measure the slabs forming the statue's base.
Facing south, fork left from the main path for some eye-poppingly gigantic chestnut trees. Measure their girth - some exceed 11 adult paces. Return to the main, tree-lined Blackheath Avenue and continue south to its end. Count the trees as you walk, calculating actual and average distance between them.
Return to the observatory and the 17th-century Flamsteed House, also by Wren, and named after the first Astronomer Royal. Don't forget to straddle the line of zero degrees longitude and be sure to find the Octagon Room. It originally housed both telescopes and the exceptionally tall clocks of the day. Practise time-telling skills in the exhibition of occasionally bizarre timepieces - not as easy as it sounds. The walk concludes by returning either via the tunnel or taking the Docklands Railway from Cutty Sark Station.
Recommended for Years 5 and 6, progress will be quicker with groups of about 12. Allow four hours from Bank as the walk is about 2.5 miles. The Royal Observatory and Queen's House are part of the National Maritime Museum - admission is free but advance booking is essential.
Tel: 020 8312 6608www.nmm.ac.uk Royal Naval College grounds, free Tel: 020 8269 4793www.greenwichfoundation.org.uk Greenwich Visitor Information Tel: 0870 608 2000www.greenwich.gov.uk
GREENWICH FOOT TUNNEL
Opened in 1902 to replace a ferry, the tunnel enabled workers south of the river to reach the docks opposite. Designed by Sir Alexander Binnie, it is made of concrete-lined cast iron rings and is 371m (1,217ft) long with an internal diameter of 3.3m (11ft). The floor is York stone, some 200,000 tiles line the walls and it is 16m (53ft) below high water. From ground to shaft floor level is approximately 13m (43ft), with 88 stairs at Island Gardens and 100 at Greenwich. A dramatic narrowing at Island Gardens marks where the tunnel was reinforced after a wartime bomb fell in the river in 1941, causing it to crack slightly.