7th grade
ratios and proportional RELATIONSHIPS
CC.7.RP.1 Analyze proportional relationships and use them to solve real-world and mathematical problems. 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.
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How do we use ratios to compute unit rates? How can I apply these strategies to real-world problems?
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CC.7.RP.2 Analyze proportional relationships and use them to solve real-world and mathematical problems. Recognize and represent proportional relationships between quantities.
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CC.7.RP.2a 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.
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How can you tell if a table represents proportional relationships? When would it be useful to create a table to show equivalency? Why would graphing on a coordinate plane help determine proportionality?
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CC.7.RP.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
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Why is it important to recognize proportionality? How might a graph, equation, table or diagram be a useful tool in identifying proportions?
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CC.7.RP.2c 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.
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How can you translate from words to equations? What strategies could you use to create the equations?
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CC.7.RP.2d 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.
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How can you visually inspect a graph to determine information about rates? How can labels on a graph be used to interpret the representation of the points?
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CC.7.RP.3 Analyze proportional relationships and use them to solve real-world and mathematical problems. 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.
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How does understanding percent relate to practical situations, such as: interest, taxes, and sales? What strategies can be used to set up the proportions?
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