In this unit, students will analyze proportional relationships and use them to solve real world and mathematical problems. Students will do this by completing the following:

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

Recognize and represent proportional relationships between quantities.

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.

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

Represent proportional relationships by equations. For example, if total cost t isproportional 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

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.

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.

Vocabulary

1. Multiplicative Inverse - Two numbers whose product is 1. Example: 3/4 and 4/3 are multiplicative inverses of one another because 3/4 x 4/3 = 4/3 x 3/4 = 1.

2. Percent Rate of Change - A rate of change expressed as a percent. Example: If a population grows from 50 to 55 in a year, it grows by (5/50) = 10% per year.

3. Ratio - A comparison of two numbers using division. The ratio of a to b (where b does not equal 0) can be written as a to b, or as a:b.

4. Proportion - An equation stating that two ratios are equivalent

5. Scale Factor - A ratio between two sets of measurements

September-October Lessons 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. Video: Calculate a unit rate with two fractions using division Video: Analyze a situation using a rate table

7.RP.2 Recognize and represent Video: Describe the relationship between measures by examining a graph Video: Quantify the relationship of two proportional measures Video: Determine the unit rate of a proportional relationship using a graph

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. Video: Determine if two rates are equivalent by dividing Video: Determine if two rates are equivalent by graphing Video: Determine whether 2-dimensional shapes are similar Video: Convert between currencies and find exchange rate

7.RP.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Video: Identify the constant of proportionality in ratio tables Video: Identify the constant of proportionality in graphs Video: Write an equation that expresses the relationship between two proportional quantities Video: Identify the constant of proportionality from a diagram Video: Identify the constant of proportionality by writing an equation in the form y=mx

7.RP.2c Represent proportional relationships by equations. Video: Write an equation that represents a proportional relationship between total cost and number of items Video: Determine the best deal by comparing equations Video: Write an equation that expresses the relationship between distance and time Video: Compare rates of speed by comparing equations that represent the relationship between distance and time

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. Video: Answer questions about a proportional relationship using a graph

7.RP.3 Use proportional relationships to solve multi-step ratio and percent problems. s. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, and fees. Video: Estimate a percent value using a bar model Video: Calculate percent of a number using a proportion model Video: Solve percent of a number problems using a proportion model Video: Apply taxes, tips, and discounts using a proportion and scale factor

7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. Video: Find scale factor using division Video: Generate a scale drawing Video: Generate a scale drawing using fraction and decimal scale factors Video: Generate a scale drawing using scale factors greater than and less than one Video: Identify scale factors using rectangle side lengths Video: Calculate distance on a map using a scale

## Overview

In this unit, students will analyze proportional relationships and use them to solve real world and mathematical problems. Students will do this by completing the following:

For example, if total cost t isproportional 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(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)whereris the unit rate.Examples:simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.## Vocabulary

1. Multiplicative Inverse - Two numbers whose product is 1. Example: 3/4 and 4/3 are multiplicative inverses of one another because 3/4 x 4/3 = 4/3 x 3/4 = 1.2. Percent Rate of Change - A rate of change expressed as a percent. Example: If a population grows from 50 to 55 in a year, it grows by (5/50) = 10% per year.

3. Ratio - A comparison of two numbers using division. The ratio of a to b (where b does not equal 0) can be written as a to b, or as a:b.

4. Proportion - An equation stating that two ratios are equivalent

5. Scale Factor - A ratio between two sets of measurements

September-October Lessons7.RP.1Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.Video: Calculate a unit rate with two fractions using division

Video: Analyze a situation using a rate table

7.RP.2Recognize and representVideo: Describe the relationship between measures by examining a graph

Video: Quantify the relationship of two proportional measures

Video: Determine the unit rate of a proportional relationship using a graph

7.RP.2aDecide 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.Video: Determine if two rates are equivalent by dividing

Video: Determine if two rates are equivalent by graphing

Video: Determine whether 2-dimensional shapes are similar

Video: Convert between currencies and find exchange rate

7.RP.2bIdentify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.Video: Identify the constant of proportionality in ratio tables

Video: Identify the constant of proportionality in graphs

Video: Write an equation that expresses the relationship between two proportional quantities

Video: Identify the constant of proportionality from a diagram

Video: Identify the constant of proportionality by writing an equation in the form y=mx

7.RP.2cRepresent proportional relationships by equations.Video: Write an equation that represents a proportional relationship between total cost and number of items

Video: Determine the best deal by comparing equations

Video: Write an equation that expresses the relationship between distance and time

Video: Compare rates of speed by comparing equations that represent the relationship between distance and time

7.RP.2dExplain 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.Video: Answer questions about a proportional relationship using a graph

7.RP.3Use proportional relationships to solve multi-step ratio and percent problems. s. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, and fees.Video: Estimate a percent value using a bar model

Video: Calculate percent of a number using a proportion model

Video: Solve percent of a number problems using a proportion model

Video: Apply taxes, tips, and discounts using a proportion and scale factor

7.G.1Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.Video: Find scale factor using division

Video: Generate a scale drawing

Video: Generate a scale drawing using fraction and decimal scale factors

Video: Generate a scale drawing using scale factors greater than and less than one

Video: Identify scale factors using rectangle side lengths

Video: Calculate distance on a map using a scale