The mathematical value of Pieday

Ok, everyone knows how to do maths with pie.
Cut the value of Pi into the top before you bake it, make an open-topped pie chart with different fillings, measure the diameter, circumference, radius and depth: pie-based maths is fairly intuitive really.

Today, however is not about maths with pie pie, or even maths with Pi-pie.
In fact, it wasn't originally going to be about any kind of mathematical pie.
It was going to be about an ancient Roman cake-pie thing called placenta* which we were going to make for the Roman feast we had intended to make tonight, however a change of plans and an untimely stomach bug** later, here we are.


This isn't a recipe, I won't be listing ingredients or going into the method, or anything like that.
This is just a rough approximation of how, and why we make mathematical muffins***.



Start by convincing yourself that muffins count as pie****.
This may seem an unnecessary step but, just like salting and draining aubergines or adding that pinch of turmeric to a curry, it will have a huge, if unnoticed impact on the final result.
Remember that pie is a filling surrounded by some sort of crust.
Note that the glossy top of a muffin is somewhat crust-like and that, while a muffin may not be glossy and crusty all over it is still made from the same muffin mix and therefore, spiritually, all crust.
You have only to add a filling to achieve pie.

Concede that, while filled muffins are an oozy nuisance*****, if you want to call this Pieday then filled muffins you must make.

Get out the emergency box of muffin mix.
Assuming your mix is blueberry, go and get the jar of blueberry conserve from the cupboard.
Make up the muffin mix.
Add a little lemon zest****** because it's there, and because lemon and blueberry go so well together.
Consider swapping the blueberry conserve for lemon curd.
Determine that no, these are blueberry-pie muffins, so blueberry it must be.

Feel a moment's sympathy for the writers of those so-called recipes which list cake-mixture and packaged icing on their ingredients.
Quash this ruthlessly.

Note that at least the blueberries in the package are tinned and not dried because otherwise these would be dried-blueberry muffins not blueberry muffins: it's not as though you call scones******* with raisins in grape scones.
Not that that matters here.
Because these are pies.

Sort out the oven, muffin pie cases and so on.

Now spoon half the muffin mixture into the cases.
Add a teaspoon of the fancy jam in the middle of each splodge of mixture.
Top with the rest of the muffin mix.

Put the pies into the oven, set the timer and have a cup of tea.
Get distracted contemplating apple-pie muffins made with a really good plain muffin mixture with lots of melted butter, and a proper, non-gloopy, apple-pie filling with two kinds of apple, and a crumbly topping made of soft brown sugar and cinnamon*******.
Ok, so not all filled muffins are an abomination

Once the muffins are done take them out, let them cool a little and get on with the maths.

The thing about mathematical muffins is that it's not how they're made********* that makes them mathematical, it's what you do with them.
So count them.
Do addition and subtraction, cut them into halves, quarters and thirds, talk about the number of cuts needed for each and how many times you would need to cut them for each.
Talk about why that isn't the same.
Do most of the things you could do with a normal pie.
Measure them.
Figure out the height of an average muffin, then work out the height of six average muffins balanced on top of one another.
Balance them, giggling madly, and measure them to see if it's the same.
See how many times you can cut a muffin into equal-sized pieces before it crumbles.
Eat them.
Time yourselves cleaning up.

Make some more so you can check your results.





*Ew.
There, now that's out of the way we can get on with the blog.

**Apparently contracted by text.
I suppose it's a natural evolution of the computer virus.

***Which are still American Muffins, but also still get away with murder due to the awesome power of alliteration.

****Because this is Pieday.

*****And, frankly, just rather disappointing cupcakes.
Which are themselves just overblown fairy cakes.

******But not juice, as this would throw off the acidity of the mixture and mess with the raising agents.
Resolve to experiment with lemon muffins another day.

*******And I hope you mentally pronounced that correctly.

********Because cheese on a sweet muffin would be a thousand kinds of wrong.

*********Although obviously weights and measures are all sorts of fun.

Fun with Maths

It's fairly easy to have enjoy reading: even without all the word jigsaws, make-a-word games and so forth available, the very act of reading is in itself fun*.
 In addition there's plenty of material out there to teach reading: even basic workbooks tend to provide twice as much reading support as mathematical, because they treat reading and writing as two different subjects, despite the fact that they support one another.
Science and even maths workbooks still support reading because, well, they're books, you have to read them to use them.
 So home-education-wise reading is not a problem.

Maths, on the other hand, is.
There are workbooks out there, of course, and we can always write out our own problems as well.
We can set sums using handfuls of raisins** or small toys, we can demonstrate on an abacus or on our fingers, we can sing Ten, Twenty or Two Hundred Green Bottles***, there are a lot of things we can do but, in the end it all feels a bit, well, mathematical.
It lacks the enticing air that a good book, or a game of Flag Man**** has without even trying.

 We recently bought a copy of Games for Mathematics, by Peggy Kaye, having found her Games for Reading very enjoyable, but even here the games tended to be of the solve-all-the-sums-to-climb-the-ladder variety, which does little to inspire a reluctant mathematician.

We've found a few things that do work though, so I thought I'd share a few here.

Games

I've said this before, I know, but playing games is wonderful for developing basic maths.
They don't need to be Games for Mathematics, although Orchard Games make some lovely ones, just playing games, counting spaces and spots on dice, developing simple strategies, and following the rules of the game can help to strengthen essential skills.
 Change the number of dice and require players to add them together, or subtract one from the other***** to throw in a few sums without making it too obvious.
 A beetle drive****** is always a good way to practice simple maths, and can be re-themed to suit any project or obsession as needed: house drives, car drives*******, viking longship drives and so on all work very nicely.


Trains and Automobiles

You can play counting and addition games with any small toys, but it can easily turn into just an exercise in bean-counting.
 The advantage of playing with cars or toy trains is that the maths can creep in without being obvious.
Set up a garage with room for a few cars at a time and, as the cars go in an out, ask how many more can go in before it's full, or how many there will be when the next one goes in.
Try racing them across the dining table or down a hill and keep track of which colour car wins most often: do red ones really go faster?
Hopefully the addition, subtraction and basic probability (when you start guessing which car will win this time) will go entirely unnoticed.
 With trains you can add or subtract carriages, compare long and short trains, estimate how many carriages it will take to carry a particular number of things, use carriages as a unit of measurement (how many carriages is it from that bend in the track to the tunnel?) and do just about anything you could with the cars.
 The trick with all of these is not to stress the maths: if the child doesn't want to add up all the blue cars on the track, don't worry about it, just add them up yourself and move on.


World Building

Blocks are great things for basic maths.
Again you can just count or add them, but it's more fun to play around with it.
Build a tower, then without counting, try to estimate the number of blocks needed to make another one the same size.
Or build two and try to guess how tall they'll be when you put one on top of the other.
Or add the two towers together, or see how many you'd need to remove from one tower to make it the same height as another.
 The maths is more overt here, the trick is just to have fun, and build an amazing city, while you do it.
A good idea is to separate the blocks into their various colours and try to guess how many are in each pile, then build towers as you count them.
Once they're up you can see which tower is tallest, how much bigger it is than the next tallest, what tje difference is between the tallest and shortest towers and so forth.
 If all else fails you can always just try to build a tower to the ceiling.


Colouring by Maths

We got this idea from Nicky, who got it from someone at school.
They're sums, but attractively packaged.
Find a picture or two to colour in on the internet, or use an old colouring book.
Then decide what colours you want to use to colour it in, and assign a number to each colour.
Then label each section with the appropriate colour but, instead of just writing in the number, use a suitable sum.
So to colour a duck green, the child would first need to decode 8-3 or 2x2 to get 4, then look up the number four on their list of colours to find green.
It's far more appealing than it sounds, and again you can choose pictures to suit your current project, or a child's particular interests.
Alternating colours on flags, rows of flowers, or other repetitive images is a good way to introduce some simple pattern-recognition as well.


We've also learned that the people who produced Reading Eggs are in the process of bringing out a new offering: called Mathseeds.
They seem to be offering free trials, so once it's up and running we'll give that a go too.
 I'll let you know whether the sound effects have improved********.



*Unless you're reading Mein Kampf or something.

**Subtraction, obviously.

***Or the multiplication version: Ten Green Tribbles

****Apparently we shouldn't hang people because it isn't very nice.
Running them through with pirate swords is A OK though.

*****If you want to avoid minus numbers try buying dice from a specialist games shop: you can get ten, twelve, or even twenty sided dice, which make subtracting a standard six-sider far less likely to cause problems.
You can even get dice numbered in tens, although using these might mean that you finish your game of Snakes and Ladders a little sooner than you intended.

******You know: roll one (or make ten) to draw the body, roll two (or make eight) to draw the head and so forth.

*******Yes, it does.

********Surely they can't be worse?

Use the tools you have to hand

(Originally posted by Amelia)

Ok, so perhaps we can’t really teach Phoebe: the difference between food and not-food is probably something she’ll have to learn for herself, all we can do is keep hazardous materials out of her reach and gently direct her attention towards her Mummy’s bosom and away from her own digits.

Ellie, however, is a whole different kettle of phonetics.

Sticker fun

She has work-books which she fills out with a healthy devotion, if not to the acquisition of knowledge then at least to the shiny gold stickers that come with the books, she has big foam letters for the bath and magnetic ones for the fridge, she has educational games (scrabble is particularly popular) both board and computer, she has an abacus, an overflowing bookcase and a much-used library card.

But probably the most effective learning tool she possesses is a Tinkerbell Sticker album.

It’s sparkly, it’s quite offensively girly (I blame Richard for the Tinkerbell obsession) and it’s utterly brilliant.

As far as Ellie’s concerned she gets to put shiny stickers with Disneyfied fairies on into a big glittery book, meanwhile she’s picking up quite a few skills without even noticing:

• Number recognition: to put the stickers in the right place she has to find the right page, to do that she has to read the numbers on the sticker. Then once we’ve found the right page she has to find the numbers she’s just read. It’s simple, but it works.
• Manual dexterity: stickers are fiddly, sticking stickers in their ordained places is surprisingly tricky for little fingers, the more she sticks the better she gets.
• Comprehension: she reads the words*, she looks at the pictures; she tells us what it’s all about. One page even has a quiz.
• Patience: sparkly fairy stickers come to those who wait.

I was tempted to add:

• Acting: also to those who make big sad eyes at Daddy

But the truth is that even if he was such a soft touch I still wouldn’t let her get away with it.

There’s even a set of character biographies (with accompanying character stickers) that’s convinced her she needs to write her own: My Book About Me sounds like a pretty good way to practise her writing and composition skills.

So, while the big twinkly book of tweeness might irritate me beyond belief, I fear it’s here to stay.

*Ok, some of the words, I don’t think this book was actually aimed at the under-threes.