Recognize and represent proportional
relationships between quantities.
a. Decide whether
two quantities are in a proportional relationship, e.g., by testing for
equivalent ratios in a table or graphing on a coordinate plane and
observing whether the graph is a straight line through the origin.
b. Identify the
constant of proportionality (unit rate) in tables, graphs, equations,
diagrams, and verbal descriptions of proportional relationships.
c. Represent
proportional relationships by equations.
For example, if total cost, t, is proportional to the number, n, of
items purchased at a constant price, p, the relationship between the total
cost and the number of items can be expressed as t = pn.
d. Explain what a
point (x,y) on the graph
of a proportional relationship means in terms of the situation, with
special attention to the points (0,0) and (1,r), where r is the unit rate.
*I
can determine that a proportion is a statement of equality between two
ratios.
*I
can analyze two ratios to determine if they are proportional to one another
with a variety of strategies (e.g., using tables, graphs, pictures, etc.).
*I
can define constant of proportionality as a unit rate.
*I
can analyze tables, graphs, equations, diagrams, and verbal descriptions of
proportional relationships to identify the constant of proportionality.
*I
can represent proportional relationships by writing equations.
*I
can recognize what (0,0) represents on the graph of a proportional
relationship.
*I
can recognize what (1,r) on a graph represents,
where r is the unit rate.
*I
can explain what the points on a graph of a proportional relationship mean
in terms of a specific situation.
