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:

  • 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