Misconceptions |
Examples for Preventing or Correcting |
---|---|
Some students do not understand multiplying by a scale factor. |
Reinforce the idea that multiplying by (a fraction equivalent to 1) is the same as multiplying by a scale factor of 3. Use illustrations if necessary. |
Some students confuse proportion vocabulary. |
Explicitly reinforce and use the pertinent vocabulary for this module: “proportion,” “proportional,” “proportional relationship,” and “proportionality.” |
Some students do not know that they are working with ratios in fraction form and that some of the same rules apply. |
Explain that a fraction can represent a ratio. Then, tell students to use what they already know about fractions to determine proportionality. Consider revisiting the Rates and Ratios module. |
Some students do not have a solid foundation with multiplication and division facts. |
Consider revisiting the Multiplication and Division Facts module. This problem will become evident when students attempt to simplify and find missing values. |
Some students have not been exposed to or have difficulty solving equations algebraically. |
For the example equation 6x = 30, use the following language: “6x means 6 times a number, so 6 times what number is 30?” Eventually, transition students to doing the algebraic step of dividing by 6, but using the aforementioned language first will help form students’ conceptual knowledge. |
Some students use cross products but do not understand the mathematical reasoning behind it. |
Clarify that the use of cross products is derived from using common denominators. Also, mention that cross products may not always be the most efficient method. |