## Weekly Overview

__Weekly Topics__

The focus of this week’s instruction is to deepen students’ understanding of:

- An Experience in Relationships as Measuring Rate
- Proportional Relationships
- Unit Rate as the Constant of Proportionality
- Representing Proportional Relationships with Equations
- Interpreting Graphs of Proportional Relationships

__Materials Needed__

- Student Print Packets for each day
- End of Week Assessment
- Linking Cubes (red and yellow if possible)
- Tape Diagrams
- Double Number Line Diagrams
- Ratio Tables
- Coordinate Plane

__Standard(s) Covered__

**7.RP.A.2 **Recognize and represent proportional relationships between quantities.

- Decide whether two quantities are in a proportional relationship.
- Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
- Represent proportional relationships by equations.
- 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.

__Representations__

- Ratio Table (See example below.)
- Coordinate Plane (See example below.)
- Equations of the Form
y = kx

__Additional Terms and Symbols__

**Constant of Proportionality**(If a proportional relationship is described by the set of ordered pairs that satisfies the equation , wherey = kx is a positive constant, thenk is called thek *constant of proportionality*. For example, toy isx to2 , then the constant of proportionality is \({2 \over 3}\), and3 \({2 \over 3}x\)y = *.*)**Miles per Hour**(One*mile per hour*is a proportional relationship between miles andd hours given by the equationt (bothd =1∙ t andd are positive real numbers). Similarly, for any positive real numbert ,v v *miles per hour*is a proportional relationship between miles andd hours given byt . The unit for the rate, mile per hour (or mile/hour) is often abbreviated as mph.)d = v ∙ t **Proportional Relationship****(description)**(A*proportional relationship*is a correspondence between two types of quantities such that the measures of quantities of the first type are proportional to the measures of quantities of the second type.- Note that proportional relationships and ratio relationships describe the same set of ordered pairs but in two different ways. Ratio relationships are used in the context of working with equivalent ratios, while proportional relationships are used in the context of rates.)

**Proportional To (description)**(Measures of one type of quantity are*proportional to*measures of a second type of quantity if there is a number so that for every measurek of a quantity of the first type, the corresponding measurex of a quantity of the second type is given byy ; that is,kx . The numbery =*kx* is called the constant of proportionality.)k

__Familiar Terms and Symbols __

- Equivalent Ratio
- Rate
- Ratio
- Ratio Table
- Unit Rate