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
