## MSTAR Interventions

### Common Misconceptions and How to Prevent Them

#### 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.