High School: Algebra
Creating Equations HSA-CED.A.4
4. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's Law V = IR to highlight resistance R.
Students can rearrange formulas until their pencils whittle down to toothpicks, but it won't help them one bit if the formulas they use won't enable them actually solve the problem. That means students should be able to match commonly encountered formulas to context in word problems as well as rearranging them to solve for whatever value they want.
Matching Formulas to Create Equations
In addition to being able to translate word problems into equations, students also need to be able to identify when a common formula is needed for the given context. These are most commonly geometric formulas (like perimeter, area, or volume of various shapes) or physical formulas (such as F = ma, p = mv, V = IR, v = d⁄t, KE = ½mv2, or GPE = mgh).
It is important to note that this assumes that students are already familiar with the relevant formulas from previous learning. Students who are not already familiar with the formulas need to be supported in understanding them before they will be able to match them to contexts. Matching formulas may be treated as a variation from the creating equations process. When attempting to write down the equality or inequality, students will notice that there isn't enough information. A general relationship might be implied, but no specific equality or inequality is described. What ever will they do?
Well, students need to identify the formula that describes that relationship. They can look for clues such as appropriate units (volume, for example, is always in cubic units). Once the correct formula is matched to the contextual relationship, the students can continue solving the problem as usual.
Once a formula is written algebraically, students can manipulate it however they want (within mathematical reason). The process for rearranging it is identical to the process of rearranging any equation or system of equations. It involves simplifying expressions and solving equations, which students should already know how to do.
The best way to rearrange questions when looking for a particular value is to isolate that value. Students should rearrange the equations so that the desired value is on one side of the equal sign, and there's a whole big mess of stuff on the other. That way, they'll be able to plug in the values they know and end up with whatever they want equals some number.
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