Tag Archives: Area

315. Mancunian Shapes

I’ve been at a meeting in the Manchester Chamber of Commerce today and I was fascinated by how sympathetically the building has been renovated and preserved. The plasterwork, tiling, glasswork and carving demonstrated exquisite use of shapes, symmetry and tessellation. Here are a few images that you could use as discussion starter:

Just think of all the shape related problems you could set from each image!

310. Menseki Meiro Area Maze

Menseki Meiro puzzle books crossed my Twitter feed a few months ago and I took the plunge.

Menseki

Image Credit: Amazon.co.uk

The problem is I couldn’t find an English language version. The Japanese originals were expensive so I bought the Spanish version. I don’t speak Spanish so asked my Spanish first language student who said it wasn’t Spanish – she suspected it was in Catalan!

But back to the Menseki puzzles …

They are ingenious puzzles where you simply use your knowledge of the area of a rectangle to solve the problem. Click on the image to see the cover problem. Puzzle 1 was so straightforward a nine year old could do it, puzzle 99 had Y13 Further Mathematicians befuddled. They make perfect starter or plenary activities for any age or ability.

Solutions are provided and if your copy is in a different language, like mine, you might just expand your mathematical vocabulary.

Whilst looking for a suitable image I also came across Alex Bellos discussing them on The Guardian website. Worth a look!

(By the way – the Menseki book also makes a good birthday present for that special geeky someone)

 

250. Crack the Circle

Here’s a quick resource for consolidating and revising the area and perimeter of circles and semi-circles.

Circles Crack the Safe (pdf)

Pupils complete the worksheet then work out the code. I personally like having a clear glass Kilner-style jar with a combination padlock at the front of the class … with a little treat for the class to aim for securely locked inside!

248. Fair decorations

Here is a quick cake conundrum for you.

image

Two girls are decorating the christmas cake. It is a square fruit cake. They share the icing such that one girl ices the top and one face. The other girl ices the remaining three faces. What possible dimensions of the cake will make the icing areas equal?

245. Fair share

I spotted this ‘Expert Tip’ whilst flicking through a supermarket magazine:

image

Image credit: tesco.com/foodandliving

Question
If this cake has a diameter of 18cm (7in), is this a fair way to split it between guests? Can you prove your result in general terms?

Of course, this assumes that the icing on the side doesn’t count in the diameter or guest preference.

216. Back to the Takeaway

If you like Takeaway homeworks or need a resource for the area and perimeter of circles, including some arc/sector challenges, then my third takeaway homework is for you!

Takeaway Homework 3: Area & circumference of circles

190. Visual Compound interest

So you’ve reached that bit of the Number curriculum at the end of Percentages – Simple and Compound interest. The theory is straight forward enough:

  • Simple interest is calculated on the original balance.
  • Compound interest is calculated fresh every year on the current balance.

This shouldn’t be a tricky concept, yet it is frequently  glossed over or partially taught to lower ability students. This is the maths they’ll need to get their head around at the bank in a few years time. So why not replace the scary calculations and rote learning with diagrams, which embed understanding.

Equipment

  • Coloured pens
  • Whiteboard
  • Squared paper
  • Ruler
  • Calculator (Optional)

Simple Interest: Step 1

Draw a square which has sides which are a multiple of ten (I used 10×10). This area represents the original investment.

image

Step 2

Assume the interest rate is 10%. Calculate 10% of the area and shade it in lightly. Basically one column, since it’s a 10×10 grid.

image

Step 3

Add on 10% by drawing the shaded area again. This is the 1st interest payment.

image

Step 4

Repeat Step 3 for the 2nd and 3rd years.

image

Step 5

In summary, a simple interest (10%) investment over 3 years is the same as adding on 30%.

image

 

Compound Interest: Step 1

Repeat steps 1 -3 of simple interest

image

Step 2

Work out 10% of the height and draw a new row – since the grid is 10 squares high, it’s simply one square high.

image

Notice that the row is wider than the original square – the dotted area indicates the extra interest earned on the previous years interest. This starts the discussion that you are not adding on the same amount each time.

Step 3

Using the same concept as Step 2, work out 10% of the width of the diagram. This time the width is a little more than one square wide.

image

Once again it’s clear to see that you are adding on more than the last year.

 

Comparison: Simple vs Compound interest

Which is the better investment? It’s pretty clear to see:

image

You can compare these two types of interest using area calculations, rather than long lists of percentage calculations and you can actually ‘see’ the different methods.