Algebra
Basics that we can VISUALIZE
Rigidity with Rules
Cancels Creativity
Not long ago I witnessed a class receiving a review solving equations. Unfortunately the rules were so strict there was little room for students to try their own ideas.
The scenario was to always move the variable to the left side of the equation and numbers to the right. This process was mechanical and void of thought sometimes creating more complicated solutions.
Example: x + 2 = 3x - 3
x - 3x = - 3 - 2
- 2x = - 5
2x = 5
x = 5/2
Why not think of where we move variables and numbers to minimize negatives and fractions if possible (purposeful work).
This time if we move the variables to the right side and constants to the left we keep our variables positive.
x + 2 = 3x - 3
2 + 3 = 3x - x
5 = 2x
5/2 = x
This is the same answer just a slightly different perspective. Encouraging students to try their methods engages them to want to do their work. Presenting your process with purpose is more effective than "this is the way we do it."
Rules of the Game or
Invisible Math
Assumptions are rife in math especially with the simplest concepts. This short video is going to explain some of these assumptions.
What is a TERM, how are they defined/separated? What can I do to a term and not change its value? Once you understand who the "players" are in math you can start playing yourself. The next post I suggest you view is "Get Away from me? - Isolating a Term"
FOIL is a four letter F-word!
Often simple pneumonics are used to memorize a process instead of understanding a concept you can latter synthesize. FOIL=First, Outside, Inside, Last, is only useful in one scenario and fails in every other instance. In mathematical proofs we must find a solution that works in every case not just a unique case. Using FOIL counters this cardinal rule.
This video uses a real world event most students can relate to, and thus visualize to truly understand distribution regardless of number of terms. Enjoy the video so you can realize how enjoyable and easy math is.