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.

  1. Decide whether two quantities are in a proportional relationship.
  2. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
  3. Represent proportional relationships by equations.
  4. 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
Rising eighth grade week 1 example

Additional Terms and Symbols

  • Constant of Proportionality (If a proportional relationship is described by the set of ordered pairs that satisfies the equation y=kx, where k is a positive constant, then k is called the constant of proportionality.  For example, if the ratio of y to x is 2 to 3, then the constant of proportionality is \({2 \over 3}\), and y=\({2 \over 3}x\).)
  • Miles per Hour (One mile per hour is a proportional relationship between d miles and t hours given by the equation d=1∙t (both d and t are positive real numbers).  Similarly, for any positive real number v, v miles per hour is a proportional relationship between d miles and t hours given by d=vt. The unit for the rate, mile per hour (or mile/hour) is often abbreviated as mph.)
  • 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 k so that for every measure x of a quantity of the first type, the corresponding measure y of a quantity of the second type is given by kx; that is, y=kx.  The number k is called the constant of proportionality.)

Familiar Terms and Symbols

  • Equivalent Ratio
  • Rate
  • Ratio
  • Ratio Table
  • Unit Rate