Algebra Tiles

In Anne's Algebra sessions we were introduced to Algebra Tiles.

Using algebra tiles to express (a+b)(a+b)

The templates for these can be found here. Acadia list a number of ways that they can be used, which can be accessed here. A few applications are found below:

COLLECTING LIKE TERMS

EXPANDING BRACKETS

X	2R	3
R	2R2	3R
2	4R	6

UPDATE: 22/05/2013 Having used these with a Year 9 class where the general teaching style is less exploratory and more methodical, I received the following feedback (food for thought!)

• confusing because they weren't labelled
• didn't need them
• gave me one more thing to remember
• distracting for some students
• helped me a little but confused me compared to the way I already knew it
• they helped me solve equations
• I could literally see the equation and understood it better
• gave me a visual way of doing the sum
• interactive and helpful to get started with the grid method
• easier to understand the method we were using

New Year Algebra

We were advised to look at Anne's paper on Algebraic Reasoning.

The key ideas of algebra were decided to be:

• relationships
• representation
• generalising
• communication
• mathematical objects

"If you always do what you always did, then you'll always get what you always did"

In defining a variable (for Barry!):
2y + 1
Get students to put in values for y and see what happens when something is a variable.

Begin algebra by using it to express things they already know, and use "non-calculation arithmetic", e.g.
2 + 8 = 8 + 2
therefore ....
a + b = b + a

A dance routine was used to see how like terms could be found, or more importantly, what like terms actually were!
[dance routine]



We were advised to be careful with tables when asking students to create them in order to find a formula - rather checking that the formula that they had fitted the structure of the problem.

e.g.  matchsticks

The formula:

3n + 1

Only makes sense because you are adding 3 matchsticks on each time, however a quadratic or sinusoidal curve could equally fit the results if only these situations are considered.

The activity involving ordering algebraic expressions with each person choosing an appropriate value for x was also very interesting.

Dan Meyer has some interesting ideas about algebra in mathematics:

We were also advised to read

The Equation, The Whole Equation and Nothing but the Equation