ratios and proportional relationships 7.rp
Analyze proportional relationships and use them to solve real-world and mathematical problems.
1. 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 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.
See tncore.org for the following tasks: Salsa, Collecting Plant Species
2. Recognize and represent proportional relationships between quantities
See tncore.org for the following tasks, Coupon Book Sales, Walking, Salsa, Collecting Plant Species, Capture-Recapture
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.
See tncore.org for the following tasks: Gas Tank, Light Bulb
b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of
proportional relationships.
See tncore.org for the following tasks: Light Bulb
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.
See tncore.org for the following tasks: Gas Tank, Light Bulb, Capture-Recapture
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.
3. Use proportional relationships to solve multi-step ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
See tncore.org for the following task: Light Bulb, Collecting Plant Species, National Debt
1. 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 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.
See tncore.org for the following tasks: Salsa, Collecting Plant Species
2. Recognize and represent proportional relationships between quantities
See tncore.org for the following tasks, Coupon Book Sales, Walking, Salsa, Collecting Plant Species, Capture-Recapture
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.
See tncore.org for the following tasks: Gas Tank, Light Bulb
b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of
proportional relationships.
See tncore.org for the following tasks: Light Bulb
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.
See tncore.org for the following tasks: Gas Tank, Light Bulb, Capture-Recapture
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.
3. Use proportional relationships to solve multi-step ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
See tncore.org for the following task: Light Bulb, Collecting Plant Species, National Debt