Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

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.

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.

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

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.

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. For example, if a person walks `sf text (1)/sf text (2)` mile in each `sf text (1)/sf text (4)` hour, compute the rate as the complex fraction `sf(1/2)/(1/4)` miles per hour, equivalently 2 miles per hour with 2 being the unit rate.

Investigate chance processes and develop, use, and evaluate probability models.

Draw informal comparative inferences about two populations.

Use random sampling to draw inferences about a population.

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.