Mathematical christmas cake

This cake contains algebraic sequences, inequalities, and geometric sequences, a sum, a square root and a 3D shape you have never heard of before. If you loved the Da Vinci Code, you will love this…. and if it is almost Christmas, then this is great. You can make it from start to finish on Christmas Eve, if you like. It will keep fine for up to 10 days.

And, it is easy, and vegan.

Shopping List:

  • Self Raising Flour
  • Golden Caster Sugar
  • Mixed Spice
  • Ground Ginger
  • Bicaronate of Soda
  • Plain Flour
  • Teabags
  • Dried Mixed Fruit
  • a pack of marzipan
  • some plain jam without pips (apricot is best)
  • Pack of ready made white icing
  • A Mixing Bowl and another bowl
  • Wooden Spoon
  • Sieve
  • Teaspoon measure
  • Weighing Scales
  • Loaf tin
  • Silicone tin liner or greaseproof paper
  • rolling pin (or clean glass bottle) and clean flat surface
  • Oven
  • the number “200”

Arithmetic Sequence

An arithmetic sequence is a list of numbers that goes up (or down) the same amount, all the way through.

The first sequence for this recipe starts with the number 200, like this:

  1. Weigh 200g of dried mixed fruit into a bowl
  2. Make a nice strong mug of tea with the teabag (or use leftover tea without milk)
  3. Put the bowl of mixed fruit on the scales and weigh in 180g of the tea.
  4. Mix together and leave to soak for at least 160 minutes. (you are going to need the number 160 again, so don’t forget it).
  5. When the fruit has soaked, turn on the oven at 160 degrees (fan), and weigh 160g of plain flour into a sieve that is sitting on top of a mixing bowl.

Geometric Sequence using a teaspoon

A geaometric sequence is made, by repeatedly multiplying by the same number. In this sequence, the multiplier is 0.5 which means that every number is half the size of the previous number.

The cake is very spicy, a little bit gingery, and not very light. So measure into the sieve:

  1. Two teaspoons of Mixed Spice
  2. One teaspoon of Ground Ginger
  3. Half a teaspoon of Bicarbonate of Soda

Tap the sieve carefully until all these dry ingredients have fallen into the mixing bowl.

A Sum

40+50 = …

… 90g of golden caster sugar, mixed in with the dry ingredients.

Square Root and a Prismoid

You have 90g of sugar… what is the square root of 9?…

THREE teaspoons of rapeseed oil (often labelled “vegetable oil”). Add this to the mixed fruit and tea, stir in, then stirthe wet mixture into the flour and put it all, carefully, into the loaf tin.

A loaf tin is an example of a prismoid. This is such an obscure word that it does not even have its own Wiki page! Poor little prismoid! It just gets a measly mention on the page for prsimatoids. A psimoid is a bit like a cuboid, except that it has sloping sides. A loaf tin has sloping sides, because if they were straight, it would be really difficult to get the loaf out!!!

Upper and Lower Bounds of Cooking Times

Put the tin in the oven and set the timer. Rememeber the sum 40+50=90? You have used the 90, for the sugar. The 40 and 50 are the upper and lower bounds of the cooking time t.

40 <= t <= 50

If you take a look after 40 minutes, it might be cooked. If it sinks as you look at it, it isn;t cooked. If you slide a knife into it, and the knife comes out smeary with mixture, it isn’t cooked. If it isn’t cooked, give it another 10 minutes.

Cool it in the tin for 5 minutes, then turn it out onto a rack to completely cool.

Sprinkle some icing sugar (about a heaped teaspoon) onto the clean surface and roll out enough marzipan to drape right over the cake.

Brush the top and sides of the cake with jam

Drape the marzipan over the jammy cake and press it gently to stick. Trim off any extra.

Roll out the ready made icing and drape over the marzipan.

Voila. Ready to eat. No fuss.

And next year, will you still remember the recipe?

… 200, 180, 160 …. (160 160)

… 2, 1, 1/2

… 40+50=90 … square root of 9 is 3

marzipan and icing and munch.

Happy Christmas

More interesting Maths Papers (Spire Maths)

I have downloaded some of the Excel Spreadsheets onto my computer and it has not exploded (yet!!) – can’t wait to teach some lessons using this gorgeous set of papers! Some pdfs of examples to download below, if you don’t want to generate your own from EXCEL:

Circles with 24 dots



Dear H,

We have just spent 2 lessons on Trigonometry and here is the writeup as promised. You were getting everything right but these notes are in case you forget a small step and need to revise.

Sorry you couldn’t remember SOH CAH TOA, but it’s really quite complicated, what with labelling the triangle, writing out SOH CAH TOA, remembering which way round they go, what they mean and how to use them…

So anyway we were just using the SINE RULE and CROSS SUMS to find the missing side or the missing angle.

Before you start, make sure you have revised

  • Cross Sums
  • Pythagoras’ Theorem

Finding an unknown side, given a right angled triangle, with one known side and one known angle.

      1. Work out the value of the missing angle and write it into the correct corner. (For example, the 3rd angle in a 90/42/? triangle would be found by doing 180-90-42=)
      2. Draw a cross sum. In the top line, write the KNOWN SIDE and an x (or ?, or whatever the exam is calling the side you are looking for. In the images below we labelled it “?”)
      3. Underneath the KNOWN SIDE write down the sin of its opposite angle
      4. Underneath the “?” side, write the sine of its angle. That’s sin(?)
      5. Write down the sum you plan to type into your calculator
      6. And do it!
      7. Write the answer back on the diagram and check it looks sensible

Finding an unknown angle given a right angled triangle, with two known sides.

  1. If the Hypotenuse is unknown you will have to use PYTHAGORAS’ Theorem to find it, first.
  2. Draw a cross sum. In the top line, write the KNOWN SIDES and an x (or ?, or whatever the exam is calling the side you are looking for. In the images below we labelled it “?”)
  3. underneath the known sides, write sin(of their opposite angle), one should be sin(90), the other will be sin(?)
  4. Write down the sum you plan to type into your calculator
  5. This time the cross sum’s answer will be weird (0.67834 in the example below) and you need to write sin(?)= 0.67834 or whatever.
  6. You found the sine of the angle – to find the angle itself, press Shift, Sin, ANS, =
  7. Write the answer onto the diagram and check it looks reasonable.

If the hypotenuse and one other side is given, then you wont need Pythagoras. So its easier.

Understanding Plans and Elevations

Looking for a website that helps you to learn about Plans and Elevations? And you would like to have some fun as well? Oh, and have to work out new approaches to problems which look easy at first but aren’t?

You will need:

Be patient loading up the last 2 links – it takes a few moments.