I put together the following as an activity for a low-attaining year 8 class coming to grips with area. They’ve done area of rectangles and triangles last lesson and so I’m trying to link it to real world contexts this lesson.

The idea is they cut out the shape for which they need to find the area, they then choose a covering for it from the second sheet and cut that out too. They stick both next to each other in their book and then calculate the area and then the total cost of the covering required. I’ve kept it all per sq m to begin with. With the cans of paint they’ll need to calculate how many cans to buy given the coverage of each can. The final slabs choice requires more thought as they are a bulk-buy and not in sq m units. It’s also a compound shape.

# Triangle constructions tangram

Tangram Wolf (Photo credit: Evelyn Saenz)

A colleague of mine, Claire Nealon wanted to adapt a resource I made a while ago of a triangle constructions tangram (see previous post). She wanted to make it more accessible for lower attaining students. Claire simplified the constructions so that the triangles are all right angled with side lengths that are Pythagorean Triples. This made the activity more accessible for her pupils who struggle reading and measuring lengths that are decimal numbers.

The idea is that pupils accurately construct a collection of triangles and then have to fit them together, like a Tangram to form a rectangle.

Claire is working wonders with some level 2/3 pupils this year, adapting and creating resources like these that makes the maths accessible to them. I’m learning a lot from her myself! Thanks Claire!

# The Chaos Game- a very surprising result

Created by Michael Barnsley, The Chaos Game is a deceptively simple idea, but the results are astonishing.

Start with an equilateral triangle, a pencil, a ruler and a die. Label one vertex of the triangle “1 and 2”, the next “3 and 4” and the final one “5 and 6”. Mark a dot on one of the vertices of the equilateral triangle. Now roll the die. This tells you which corner of the triangle to move towards. Mark your next dot half way between your last dot and the corner of the triangle your die identified. Then roll the die again and mark your next dot half way between your last dot and the corner of the triangle your die identified. Repeat this until you discover the beautiful result!

You may like to write a spreadsheet to do this for you rather than constructing it by hand. I wrote a spreadsheet that did 10 000 trials and look at the result:

You get the famous fractal, Sierpinski’s Triangle!

If you extend the idea into three-dimensions, adding a fourth vertex directly above the centre of the equilateral triangle, the points form a Sierpinski Tetrahedron!

Sierpinski Tetrahedron- image from Wikipedia

Who would have thought such ordered, detailed beauty could come from purely random processes?!!!

If you have never seen www.mrbartonmaths.com then you are seriously missing out! Mr B’s website is packed full of great maths teaching resources. These include some excellent ‘follow me cards’ for area and perimeter of squares, rectangles and triangles. I took this resource and slightly changed it so that the question and answers are not adjacent to each other on the worksheets which would otherwise have given the game away before they have even started!

If you don’t know what ‘follow me’ cards are, they are simple. They are like dominoes where you have to match them together. On each card you get a question and an answer (to a question on a different card). The idea is that you match the question and answers up so that the cards form a continuous line.

# The Area Song…

How do you teach kids to remember how to calculate areas of shapes? Here’s one method…

Sing the following song to the tune of Pop Goes The Weasel:

Verse 1:

Multiply the length by the width

Gives the area of a rectangle.

Base times height divided by two

Now gives a triangle.

Verse 2:

Half the sum of the parallel sides

Times the distance between them.

That’s the way to calculate

The area of a trapezium.

If you start them off in year 7 regularly singing the first verse, then move them onto singing the second verse regularly in year 9 by the time they get to their exam in year 11 they’ll never forget how to calculate areas!

Here is a link to a pdf file with the song lyrics on that you can show on the interactive white board.

I can’t remember who told us of this one but a big thank you to you!