Math Misconceptions and Considerations HSG-SRT.C.6
Look closely at errors in students’ work (formative assessment) to help you reflect and make instructional decisions to suit all students’ needs.
The hypotenuse can be an adjacent side. It is very important that students understand that identifying the three sides in a right triangle (opposite, adjacent, hypotenuse) is associated with an identified acute angle. Misconception:
Often times, students will mistakenly identify the hypotenuse as the adjacent side; after all it is next to angle C in the diagram. What to do:
The hypotenuse will always be the side opposite the right angle. Have students identify the hypotenuse first, before even looking at the angles. Locating the side that is opposite of the right angle will prevent students from mistakenly labeling it as the adjacent side. Students get the trigonometric ratios mixed up. When learning this new concept, it is important that students are remembering the correct ratios. Once a student memorizes a ratio incorrectly, it is hard for them to relearn the correct ratio. Misconception:
Students may have memorized the trigonometric ratios incorrectly and therefore can’t apply them to right triangles correctly. What to do:
In the past, students have been taught the trigonometric ratios in three completely different lessons. If all three ratios are built at the same time, then students begin the decision making process about which ratio to use based on what is provided. Teachers should also utilize mnemonic devices, such as SOHCAHTOA, to help students remember the ratios. Students easily forget the formulas for special right triangles In mathematics, students acquire a multitude of formulas over their educational careers. This may make it difficult for them to recall the formulas at any given time.
Misconception:
Due to the fact that students were just given a sheet with the 45-45-90 and 3060-90 formulas on them, they cannot make a connection between the formula and what it means mathematically. This makes is difficult for students to retrieve the appropriate formula for a given situation. What to do:
Using a discovery activity to derive the patterns for special right triangles, allows students to recreate the patterns if they forget, or can’t memorize the pattern.