Math - 2019-20
A.8 - Direct & Inverse Variation
A.8 The student, given a data set or practical situation, will analyze a relation to determine whether a direct or inverse variation exists, and represent a direct variation algebraically and graphically and an inverse variation algebraically.
- I can determine how much time
a diver will need to safely ascend to the surface from various depths, figure
how driving speed effects travel time and gallons of gas in tank, and find how
light intensity oscillates in relation to distance.
- I will be able to distinguish between situations where
one value increases or decreases in proportion to the other value increasing or
decreasing and those situations where one value changes in reverse to the other
UNDERSTANDING THE STANDARD
· Practical problems may be represented and solved by using direct variation or inverse variation.
· A direct variation represents a proportional relationship between two quantities. The statement “y is directly proportional to x” is translated as y = kx.
· The constant of proportionality (k) in a direct variation is represented by the ratio of the dependent variable to the independent variable and can be referred to as the constant of variation.
· A direct variation can be represented by a line passing through the origin.
· An inverse variation represents an inversely proportional relationship between two quantities. The statement “y is inversely proportional to x” is translated as y = .
· The constant of proportionality (k) in an inverse variation is represented by the product of the dependent variable and the independent variable and can be referred to as the constant of variation.· The value of the constant of proportionality is typically positive when applied in practical situations.
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
A.81 Given a data set or practical
situation, determine whether a
direct variation exists.
A.82 Given a data set or practical
situation, determine whether an
inverse variation exists.
A.83 Given a data set or practical
situation, write an equation for a
A.85 Given a data set or practical
situation, graph an equation
representing a direct variation.
A.84 Given a data set or practical
situation, write an equation for an
direct variation, inverse variation, set of
data, constant of proportionality, dependent variable, independent variable,