Representing Ratios with Tables and Navigating a Table of Equivalent Ratios

Learning Resource Type

Classroom Resource

Subject Area

Mathematics

Grade(s)

6

Overview

In this video lesson, students encounter situations in which using a double number line poses challenges and for which a different representation would be helpful. Students learn to organize a set of equivalent ratios in a table, a more abstract but also a more flexible tool for solving problems.  Students see that a table accommodates different ways of reasoning about equivalent ratios. They notice (MP8) that to determine an unknown quantity, they can find the multiplier or find an equivalent ratio with one quantity having a value of 1. Allowing students to use any representation that accurately represents a situation and encouraging them to compare different methods will develop their ability to make strategic choices about representations (MP5).

The video lesson strengthens students’ understanding of the multiplicative relationships between equivalent ratios. It also builds students’ awareness of how a table can facilitate this reasoning to varying degrees of efficiency, depending on the approach.

Grade 6, Episode 4: Unit 2, Lessons 11 & 12 | Illustrative Math

Mathematics (2019) Grade(s): 6

MA19.6.1

Use appropriate notations [a/b, a to b, a:b] to represent a proportional relationship between quantities and use ratio language to describe the relationship between quantities.

UP:MA19.6.1

Vocabulary

  • Ratio
  • Ratio Language
  • Part-to-Part
  • Part-to-Whole
  • Attributes
  • Quantity
  • Measures
  • Fraction

Knowledge

Students know:
  • Characteristics of additive situations.
  • Characteristics of multiplicative situations

Skills

Students are able to:
  • Compare and contrast additive vs. multiplicative contextual situations.
  • Identify all ratios and describe them using "For every…, there are…"
  • Identify a ratio as a part-to-part or a part-to whole comparison.
  • Represent multiplicative comparisons in ratio notation and language (e.g., using words such as "out of" or "to" before using the symbolic notation of the colon and then the fraction bar. for example, 3 out of 7, 3 to 5, 6:7 and then 4/5).

Understanding

Students understand that:
  • In a multiplicative comparison situation one quantity changes at a constant rate with respect to a second related quantity. -Each ratio when expressed in forms: ie 10/5, 10:5 and/or 10 to 5 can be simplified to equivalent ratios, -Explain the relationships and differences between fractions and ratios.

CR Resource Type

Audio/Video

Resource Provider

PBS

License Type

CUSTOM
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