By now, students are aware that a relationship between two or more quantities can be expressed in multiple ways by writing equivalent equations. In this lesson, they see that depending on the quantity in which we are interested, one form of equation might be more useful than others. To pin down a quantity of interest may mean manipulating or rearranging a given equation. The rearrangement may involve solving for a variable—isolating it and defining it in terms of the other variables. Students notice that solving for a variable can be an efficient way to solve problems and to avoid cumbersome calculations.
Throughout the lesson, students reason repeatedly and look for regularity as they manipulate equations and solve for a variable (MP8).
- Comprehend that “to solve for a variable” is to rearrange an equation to isolate a variable of interest.
- Rearrange multi-variable equations to highlight a particular quantity.
- Let’s rearrange equations to pin down a certain quantity.
- Given an equation, I can solve for a particular variable (like height, time, or length) when the equation would be more useful in that form.
- I know the meaning of the phrase “to solve for a variable.”
Equations that have the exact same solutions are equivalent equations.
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