Unpacked Content
Knowledge
Students know:
- (2a) how to explain whether a relationship is proportional.
- (2b) that the constant of proportionality is the same as a unit rate.
- (2b) where the constant of proportionality can be found in a table, graph, equation or diagram.
- (2c) that the constant of proportionality or unit rate can be found on a graph of a proportional relationship where the input value or x-coordinate is 1.
Skills
Students are able to:
- (2a) model a proportional relationship using a table of equivalent ratios.
- Use a coordinate graph to decide whether a relationship is proportional by plotting ordered pairs and observing whether the graph is a straight line through the origin.
- (2b) translate a written description of a proportional relationship into a table, graph, equation or diagram.
- Read and interpret these to find the constant of proportionality.
- (2c) model a proportional relationship using coordinate graphing.
- Explain the meaning of the point (1, r), where r is the unit rate or constant of proportionality.
Understanding
Students understand that:
- (2a) a proportional relationship requires equivalent ratios between quantities. Students understand how to decide whether two quantities are proportional.
- (2b) the constant of proportionality is the unit rate. Students are able to identify the constant of proportionality for a proportional relationship and explain its meaning in a real-world context.
- (2c) the context of a problem can help them interpret a point on a graph of a proportional relationship.
Vocabulary
- Equivalent ratios proportional
- Coordinate plane
- Ratio table
- Unit rate
- Constant of proportionality
- Equation
- Ordered pair
