Recognize and Represent Proportional Relationships Between Quantities: Ratio, Proportion, Cross Multiply, and Divide

Learning Resource Type

Classroom Resource

Subject Area

Mathematics

Grade(s)

6

Overview

In this Cyberchase media gallery, learn about ratio and proportion and how to use an algebraic shortcut to solve proportion problems. In the accompanying classroom activity, students play a game called the "Pom-Pom Nose Push," in which they collect data and determine the ratio of time to distance. This resource is part of the Math at the Core: Middle School Collection.

In this video from Cyberchase, Harry describes ratio as a fixed relationship between two quantities and then provides examples to explain the concept further.

Mathematics (2019) Grade(s): 6

MA19.6.2

Use unit rates to represent and describe ratio relationships.

UP:MA19.6.2

Vocabulary

  • Unit rate
  • Ratio
  • Rate language
  • Per
  • Quantity
  • Measures
  • Attributes

Knowledge

Students know:
  • Characteristics of multiplicative comparison situations.
  • Rate and ratio language.
  • Techniques for determining unit rates.
  • To use reasoning to find unit rates instead of a rule or using algorithms such as cross-products.

Skills

Students are able to:
  • Explain relationships between ratios and the related unit rates.
  • Use unit rates to name the amount of either quantity in terms of the other quantity flexibly.
  • Represent contextual relationships as ratios.

Understanding

Students understand that:
  • A unit rate is a ratio (a:b) of two measurements in which b is one.
  • A unit rate expresses a ratio as part-to-one or one unit of another quantity.
Mathematics (2019) Grade(s): 6

MA19.6.3

Use ratio and rate reasoning to solve mathematical and real-world problems (including but not limited to percent, measurement conversion, and equivalent ratios) using a variety of models, including tables of equivalent ratios, tape diagrams, double number lines, and equations.

UP:MA19.6.3

Vocabulary

  • Rate
  • Ratio
  • Rate reasoning
  • Ratio reasoning
  • Transform units
  • Quantities
  • Ratio Tables
  • Double Number Line Diagram
  • Percents
  • Coordinate Plane
  • Ordered Pairs
  • Quadrant I
  • Tape Diagrams
  • Unit Rate
  • Constant Speed

Knowledge

Students know:
  • Strategies for representing contexts involving rates and ratios including. tables of equivalent ratios, changing to unit rate, tape diagrams, double number lines, equations, and plots on coordinate planes.
  • Strategies for finding equivalent ratios,
  • Strategies for using ratio reasoning to convert measurement units.
  • Strategies to recognize that a conversion factor is a fraction equal to 1 since the quantity described in the numerator and denominator is the same.
  • Strategies for converting between fractions, decimals and percents.
  • Strategies for finding the whole when given the part and percent in a mathematical and contextual situation.
  • Strategies for finding the part, given the whole and the percent in mathematical and contextual situation.
  • Strategies for finding the percent, given the whole and the part in mathematical and contextual situation.

Skills

Students are able to:
  • Represent ratio and rate situations using a variety of strategies (e.g., tables of equivalent ratios, changing to unit rate, tape diagrams, double number line diagrams, equations, and plots on coordinate planes).
  • Use ratio, rates, and multiplicative reasoning to explain connections among representations and justify solutions in various contexts, including measurement, prices and geometry.
  • Understand the multiplicative relationship between ratio comparisons in a table by writing an equation.
  • Plot ratios as ordered pairs.
  • Solve and justify solutions for rate problems including unit pricing, constant speed, measurement conversions, and situations involving percents.
  • Solve problems and justify solutions when finding the whole given a part and the percent.
  • Model using an equivalent fraction and decimal to percents.
  • Use ratio reasoning, multiplication, and division to transform and interpret measurements.

Understanding

Students understand that:
  • A unit rate is a ratio (a:b) of two measurements in which b is one.
  • A symbolic representation of relevant features of a real-world problem can provide for resolution of the problem and interpretation of the situation.
  • When computing with quantities the transformation and interpretation of the resulting unit is dependent on the particular operation performed.

CR Resource Type

Audio/Video

Resource Provider

PBS

License Type

PD
https://aptv.pbslearningmedia.org/resource/mwnet-math-rp-ratpro/recognize-and-r…

Approved Date

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