Algebra

Author | View as single page | Feedback/Impact
Algebra
Evidence
Conceptions
Methods
Resources
Introduction – What is algebra?
Two big ideas
Where to start
Manipulatives
What are the barriers
Errors and Misconceptions
Approaches
Websites
Teaching Algebra
The curriculum
Use of technology
Further Reading
Why is Algebra Important?
Timing
References
Cognitive Demands
Strength of Evidence
Transferability
Editors' Comments

The curriculum

 

Investigating alternate approaches to the teaching of algebra such as the use of Algebra Tiles needs to be given serious consideration.

A good reference for further reading is the materials provided by National Centre for the Excellence in teaching Mathematics as is the audio extract.

I particular like to introduce algebra to a group of learners, and more importantly the need for algebra, by using polygons. This is a very limited version of the conversation with a class along the lines of (and I tend to use the word shape rather than polygon at this point).

I have been given this shape, holding up the triangle.

 

 

 

 

 

 

What is the shape called and what do we know about it (asking about it’s properties), ie recalling previously learnt facts.

 

 

 

 

 

What shall we call the area of shape

Eventually after lots of suggestions we settle on “t”

 

 

 

 

Right Hand

 

 

Left Hand

Then I show the follow in two hands. What is the area of this shape (right hand and this one (left hand) before putting them together t+t … ie 2t

 

 

 

 

We then investigate the areas of other shapes such as the ones opposite and showing that the area of the parallelogram “p” is 2t

Forming expression and simplifying

 

 

 

Then we move into exploring other shapes and combining shapes to get expressions such as p + t.

 

This process can go on for a while getting ever more complex.

Forming expression and simplifying where appropriate

 

 

 

 

Each pair (group) of learners would be given a set of card cut outs of the polygons and asked to make 6 shapes (drawings) with their associated expressions.

 

The expressions are then passed to a different group for them to make the shapes – this results in some discussion as there can be different interpretations.

 

 

 

 

Eventually, I show them the shape opposite and say the area is “h”, but get from them that h = 6t (sometimes having to overlay some triangles to demonstrate- depends on the class).

 

 

At this point I say the area of the hexagon is 60 cm2, so what is the are o the triangle, the parallelogram etc.

 

As a final step (again depending on the class), I might say I made a mistake with the area of the hexagon it was actually 120 cm2 and get the class to tell me the areas of the other shapes.

This begins the process of forming and solving equations

 

 

 

Plastic polygons can be purchased relatively cheaply – for example from

 

https://www.didax.com/plastic-polygons-26-shapes-800-pcs.html?srsltid=AfmBOoobUyF7TX9mpZfaHrugge2VnEG9tJgpdoFPQF41Jkpp5ljLoVZV

 

Or

 

https://www.learningresources.co.uk/power-polygonstm-set-of-450

 

Tags: