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Math Misconceptions and Considerations HSN-Q.A.1, 2, & 3

Look closely at errors in students’ work (formative assessment) to help you reflect and make instructional decisions to suit all students’ needs.

I set up my proportion, so why can’t I get the right answer? Just setting up a proportion with the correct units doesn’t ensure that you will get the correct answer. Misconception: Many times the student will set up one side of the proportion correctly, but fail to be consistent when writing the other ratio.

What to do: Have students write the units throughout the problem, rather than only in the answer. This will ensure that the answer contains a final unit of measurement because other units should “cancel”. If the final unit is not correct, then the student will know that they set up the proportion incorrectly. Remind students that similar units in the proportion should either line up vertically or horizontally, based on the crossproduct property.

Do I divide or multiply? Once students have begun converting using mental math instead of proportions, they often choose the wrong mathematical operation. Misconception: When converting units of measurement, students often divide when they should multiply (or viceversa).

What to do: When students are determining what have students think about whether mathematical operation to use, the answer should be larger or smaller. Based on what unit they are converting to, students should remember that multiplication will make the answer larger, while division will make it smaller.

I pushed the “graph” button on my calculator, so where is the graph? Graphing calculators are only as smart as the person using them. Misconception: Students assume that by simply inputting the data into the calculator, that the graph will look they way they want it to look.

What to do: Just as we need to choose the appropriate scale when graphing on paper, the same must be done on a graphing calculator. Students need to assess the data to be graphed and determine the proper “window” for their graph.

Bobby’s age was negative 15.3. The calculator is only going to give you an answer for the math you asked it to do, not necessarily the correct answer. Misconception: When using a calculator to find a solution, students assume that whatever answer is given is correct. What to do: Throughout the process of solving a problem, answers should always be discussed in the context of the problem. Students should always assess whether a solution makes sense in a real-life situation.