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.