Rising Grade 7 Week 1: Weekly Overview

Weekly Topics

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

  • Tables of Equivalent Ratios
  • The Structure of Ratio Tables – Additive and Multiplicative
  • Comparing Ratios Using Ratio Tables
  • From Ratio Tables to Double Number Line Diagrams
  • From Ratio Tables to Equations Using the Value of the Ratio

Materials Needed

  • Student Print Packets for each day
  • End of Week Assessment
  • Linking Cubes (red and yellow if possible)
  • Tape Diagrams (See example below under Representations.)
  • Double Number Line Diagrams (See example below under Representations.)
  • Ratio Tables (See example below under Representations.)
  • Coordinate Plane (See example below under Representations.)

Standard(s) Covered

6.RP.A.3  Use ratio and rate reasoning to solve real-world and mathematical problems (e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations).

  1. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

Representations

The below examples are representing Equivalent Ratios for a Cake Recipe that uses 2 cups of sugar for every 3 cups of flour.

Tape Diagram and Double Number Line Example
Ratio and Coordinate Plan Example

Additional Terms and Symbols

  • Equivalent Ratios (Two ratios AB and CD are equivalent ratios if there is a nonzero number c such that =cA  and =cB. For example, two ratios are equivalent if they both have values that are equal.)
  • Rate (illustration) (A rate is a quantity that describes a ratio relationship between two types of quantities. For example, 1.25 \({miles \over hour}\) is a rate that describes a ratio relationship between hours and miles: If an object is traveling at a constant 1.25 \({miles \over hour}\) then after 1 hour it has gone 1.25 miles, after hours it has gone 2.50 miles, afterhours it has gone 3.75 miles, and so on. Rates differ from ratios in how they describe ratio relationships—rates are quantities and have the properties of quantities.  For example, rates of the same type can be added together to get a new rate, as in 30\({miles \over hour}\)+ 20\({miles \over hour}\)=50\({miles \over hour}\), whereas ratios cannot be added together.)
  • Ratio (A ratio is an ordered pair of numbers which are not both zero. A ratio is denoted Ato indicate the order of the numbers—the number A is first and the number B is second.)
  • Ratio Relationship (A ratio relationship is the set of all ratios that are equivalent ratios. A ratio such as 5:4 can be used to describe the ratio relationship {1:\({4 \over 5}\),\({5 \over 4}\):1, 5:4, 10:8, 15:12, …}.  Ratio language such as “5 miles for every 4 hours” can also be used to describe a ratio relationship. Ratio relationships are often represented by ratio tables, double number lines diagrams, and by equations and their graphs.) 
  • Unit Rate (When a rate is written as a measurement (i.e., a number times a unit), the unit rate is the measure (i.e., the numerical part of the measurement).  For example, when the rate of speed of an object is written as the measurement 1.25 mph, the number 1.25 is the unit rate.)
  • Value of a Ratio (The value of the ratio A:B is the quotient \({A \over B}\) as long as B is not zero.)