Solving Multi-Step Equations

For the past few days we've explored whether there are generic guiding principles that help us in solving 1st degree linear equations. It appears as though the following concepts have worked thus far and may be of use in the future.

1. Balance - this notion that we can use the rules of equality to change the appearance of an equation by performing the same operation on both sides, while preserving the original value of the variable and maintaining the equality that we started with.

2. Isolating the Variable - students seem convinced that getting the variable by itself or finding the value of just one unknown is a dependable pathway for finding its value.

3. Opposite Operations or Applying Math Properties - while some students view opposite operations as 'undoing' an operation, still other view these steps as fundamental math properties. For instance, given the equation x + 3 = 9, adding a -3 to both sides is making use of the additive inverse to achieve a value of 0 on the left side of the equality.

Furthermore, it is becoming clear to students that they have to be in complete control of fraction algorithms if they are to be successful in solving equations. Rather than simply 'go over' these processes for what may be the umpteenth time, we seek to ask, "why do these algorithms work." For instance, the common algorithm for dividing fractions is to invert and multiply. But very few students examine what may have led to such a process.

Themes of notation have been a feature of our discussions as well. Some of these include:

* Where is it appropriate to place a negative sign relative to a fraction? (numerator, denominator or next to the division bar)

* Reporting solutions with the variable on the left side and the numerical value on the right side of the equality and how the symmetric property allows us this liberty.

* The convenience of cross-simplification as a means of simplifying a product ahead of time.

Tonight, students apply all of these concepts as they solve multi-step equations and prepare for equations that will feature variables on both sides of the equation.

Home Nugget #15
Assigned on Thursday Sept 30
Due on Friday Oct 1

In Algebra book,

Page 95 # 17 - 22, 25 - 27

Page 96 # 31 - 32, 34, 35, 39 - 42

Page 97 # 47 - 49