Maths at the Manor

Last week I mentioned our foray into living maths using the Domesday survey as our basis for learning about percentages.  We used our handy-dandy papier-mache map (again-this is one of the best investments in time we have made!).  The children built up our very own Manor, complete with a Keep:

I showed them what an average Manor in 1086 consisted of:

This was the girls first introduction to percentages so I asked them to add up all the percentages of the different types of land.  They found it came to 100%  I explained that 100% was all the land included in the Manor.  Having built one they were easily able to visualise it.  I said I wanted to be able to show the different divisions in land using different coloured card and asked them how I could do it.  The girls struggled with this but T11 knew immediately to use a different colour for each land.  However, he was unsure how to partition it out.  There were many elaborate suggestions (completely normal, it seems, during any living maths exercise!), some of which would have worked but were a little convoluted to say the least.  I suggested cutting them into equal parts.  They did so cutting each piece into 20 pieces (no rhyme or reason for that-just how it was!).  I had them decide on a key and wrote in on our board:

C10 thought we could then use each piece of card to represent 1%.  I asked her how many pieces in total she would need.  When she realised it would be 100, she giggled, saying we didn’t have enough room on the map!  L10 suggested each piece of card represent 10% of land.  I want to encourage any participation from L10 as she finds maths so hard.  I told her that was a great idea and asked how she would represent 25% and 35%.  To which she promptly replied ‘cut a card in half!’  Nothing wrong with that mathematically!  T11 suggested each card represented 5%, easily calculating that we could then show 25% and 35% without touching the cards and that in total we would need 20 cards, which would fit on the map without a problem.  We labeled them and I had the girls place them on the map in the proportions required, according to the proportions garnered from the original Domesday Book:

I then told them that their manor was 2 hides (It was a small manor to help L1o be able to join in the maths).  They immediately asked what a hide was.  I replied that each hide was the equivalent to 120 acres.  I asked L10 how she would work out how many acres the manor had in total.  This was well within her capability, and she wrote it on the white board and worked it out to be 240 acres.  I asked how much would be meadow land.  At this point, weary from calculating, L10 gave up the will to live!  T11 knew how to work it out mathematically, C10 had some sensible but ultimately wrong ideas.  I could see L10 glazing over, so I changed what the cards represented.  I moved them all together in a rectangle and told her to pretend they were a tray of chocolate brownies.  Well, I’ve never seen a girl perk up quite so quickly!  I wrote on the board exactly what I needed her to calculate, which she managed VERY easily.  I think brownies are her kind of language!

I had her change her thinking from brownies to acres (as per original investigation).  After she worked out that each card was the equivalent to 12 acres, I asked the other two, who were getting a bit fidgety waiting for L10 to understand, to work out how many acres of arable, pasture land, settlement and wood land the manor had.  They whizzed through it!

This would not have been my most interesting maths lesson, yet I came away so happy.  Why?  Mainly because of the beam on my gorgeous older twin’s face, whilst she (excitedly) worked out her brownie maths.  I had a rare glimpse into the workings of her mathematical mind.  Maybe there is hope for me as her teacher!