## Intermediate Math 1 - Ratios and Proportions

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## 1- Expressions and Equations 2- Geometry 3- Number Systems

4- Ratios and Proportions 5- Statistics and Probability

## Analyze proportional relationships and use them to solve real-world and mathematical problems.

7.RP.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 ½ mile in each ¼ hour, compute the unit rate as the complex fraction ½/¼ miles per hour, equivalently 2 miles per hour. |
7.RP.1 I can compute unit rates associated with ratios of complex fractions such as: lengths, areas, and other quantities given in like or different units. For example: If a person walks ½ mile in each ¼ hour, compute the unit rate as the complex fraction ½/¼ miles per hour, equivalently 2 miles per hour. For example: Every ¾ inch on a map represents 6 ½ miles, what is the unit scale of the map? |

7.RP.2 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 whether 2 quantities are proportional 7.RP.2.a For example: Students can compare the side lengths of 2 rectangles using a table, the graphical representation at the right, or other methods to determine if the rectangles are proportional.7.RP.2.b I can determine the constant of proportionality (unit rate) from a variety of representations (tables, graphs, equations, diagrams, and verbal descriptions). For example: Find the unit rate for a snail that has crawled 6 inches in 2 hours.7.RP.2.c I can represent proportional relationships by equations. 7.RP.2.d.1 I can explain the meaning of the x-value and y-value on the graph of a proportional relationship in terms of the contextual situation.7.RP.2.d.2 I can explain why r is the unit rate when the graph passes through the points (0,0) and (1,r).For example: Given the line passes through (0,0) and (1,12), we know that the unit rate is $12 per hat. |

7.RP.3 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. |
7.RP.3 I can use proportional reasoning to solve multistep ratio and percent problems.For example: Simple interest, tax, markups, markdowns, gratuities, commissions, fees, percent increase, decrease, and percent error, etc… |