LP+solve+equations

1. Knowing that “to solve an equation” means to find values for which the equation is true.
 * The “learning progression” for solving linear equations includes: **

2. Various methods can be used to find values that solve the equation: guess and check, graphing, analytic methods. (These are also alternative representations that can be used for differentiating "process" based on learning profile.)

3. The rules for manipulating equations analytically to get solutions involve using the properties of numbers such as inverses, identities, the commutative, associative and distributive properties, and the idea that since the equation sign means that what’s on one side has an equal value to what’s on the other side – so that adding, subtracting, multiplying or dividing both sides of an equation by the same amount does nothing to change the equality of the two sides. (Students eventually need to be able to justify their analytic solutions by naming the properties they used to solve the equation, but they don't need to start there. Most students should become proficient with symbol manipulation and be able to give an informal justification before they learn the names of these properties.)

4. Alternative representations like balancing games (free one at the National Library of Virtual Manipulatives) or the equations game may be important alternative mental representations for some students.

5. Checking solutions for reasonableness.

6. Knowing the units of the answer as related to the original real-world situation.


 * In addition, if the equation involves fractions or decimals, students need to be proficient with operations with fractions and decimals, including finding common denominators, scaling up/down, understanding why 3 times x/3 produces x (for example), etc.**