As I was going to St Ives 1: See the signs

No - not the old riddle, even though it appears in DieHard: with a Vengeance and would link with an earlier blog (and it probably isn’t that St Ives anyway - I was in Cambridgeshire).

[Incidentally, I never quite understood why I couldn’t be going in the same direction as the polygamist - surely all those “kits, cats, sacks, wives” would slow a man down so I could easily catch him up?  2802 seems a perfectly sensible answer to me (although it assumes that I am not carrying sacks, cats, etc too).]

I took these photographs on a bike ride close to St Ives.

What maths can we do with a class with these?  Lots, it turns out.  Let’s start with just the first picture (but before you do you might want to ask pupils what is strange about the way fractions are written on road signs - most of them will never have spotted that they are written without a line):

• How far is St Ives from The River?  
• What problems might there be with that answer?   There might be a more direct route from St Ives to The River that is shorter than 2¼ miles.
• What about the accuracy of the measurements?  Presumably they have been rounded
• What degree of accuracy might have been used?  
• So: what is the maximum distance of The River from St Ives?  From this sign the most precise measurement involves quarters, so maybe everything has been rounded to the nearest quarter.  In this case the biggest River distance would be 5/8 and the biggest St Ives distance would be 1 7/8, giving 2½ miles as the maximum.

Now let’s put picture 2 alongside picture 1:

What can we do with this one?  I would let pupils decide what questions they can answer.  Ideas include:

• How far from St Ives to Fenstanton?
• How far from St Ives to Hilton?
• How far from Hilton to Fenstanton?
• Why might these answers not be accurate?
• What if we consider the rounding that has taken place? 
• What happens if a lorry needs to go to Fenstanton?
• Combining it with the first picture: what is the maximum distance of Hilton from The River? 
• What is the minimum distance?

Finally, let’s add picture 3:

We could repeat similar sorts of questions with this one, including: “How far did I cycle between taking pictures 2 and 3?”. 

But hold on: on this one it says that Fenstanton is 2 1/3 miles away.  Our previous assumption about rounding to the nearest quarter is incorrect! 

So, what is the upper bound of signpost measurement given as ¼ ?

More on this in a future post!