## MSTAR Interventions

### Instructional Background

#### Preskills Knowledge and Skills for Students

• Solve basic multiplication facts through 12 x 12.
• Simplify a ratio in fractional form to the lowest terms.
• Describe a relationship with a ratio.
• Generate equivalent ratios.
• Identify the greatest common factor of 2 numbers.

#### Mathematics Content Knowledge for Teachers

• A multiplicative relationship is characteristic of proportional scenarios. Nonproportional scenarios have an additive component.
• A simplified ratio, or unit rate, is the foundation of 2 equivalent ratios. 1 way to determine whether 2 ratios are equivalent is to simplify the ratios to a unit rate.
• A constant called a scale factor can describe the relationship between the numerators and denominators of equivalent ratios. A scale factor can be a whole or fractional number.
• Using cross products is a valuable strategy for determining whether 2 ratios are proportional or to find the missing value in a proportion, but do not introduce the strategy until students have a solid conceptual understanding of proportionality.
• Students can use multiple strategies to solve proportions. Students should choose strategies based on the ease of computation and student confidence.