ALEX | Alabama Learning Exchange

Representing Ratios with Tables and Navigating a Table of Equivalent Ratios

Classroom Resource Information

Title:

Representing Ratios with Tables and Navigating a Table of Equivalent Ratios

URL:

https://aptv.pbslearningmedia.org/resource/our20-math-621112/representing-ratios-with-tables-and-navigating-a-table-of-equivalent-ratios/

Content Source:

PBS

Type:

Audio/Video

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

Content Standard(s):

Mathematics
MA2019 (2019)
Grade: 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.

Unpacked Content

Evidence Of Student Attainment:

Students: Given contextual or mathematical situations involving multiplicative comparisons.

Communicate the relationship of two or more quantities using ratio language.

Teacher 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.

Diverse Learning Needs:

Essential Skills:

Learning Objectives:
M.6.1.1: Define quantity, fraction, and ratio.
M.6.1.2: Identify the units or quantities being compared.
Example: Read 2/3 as 2 out of 3.
M.6.1.3: Write a ratio in appropriate notation;[a/b, a to b, a:b].
M.6.1.4: Draw a model of a given ratio or fraction.
M.6.1.5: Identify the numerator and denominator of a fraction.

Prior Knowledge Skills:

Compare two fractions with the same numerator or the same denominator by reasoning about their size.
Addition and subtraction of fractions as joining and separating parts referring to the same whole.
Label numerator, denominator, and fraction bar.
Recognize fraction 1 as the quantity formed by 1 part when a whole is partitioned into b equal parts.

Alabama Alternate Achievement Standards

AAS Standard:
M.AAS.6.1 Demonstrate a simple ratio relationship using ratio notation given a real-world problem.

Tags:

multiplicative, number line, ratio, table

License Type:

Custom Permission Type
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For full descriptions of license types and a guide to usage, visit :
https://creativecommons.org/licenses

Accessibility

Video resources: includes closed captioning or subtitles

Comments

Additional activity and practice pages are provided for this video lesson.

This resource provided by:

Author:

Kristy Lacks

ALEX Classroom Resource

Representing Ratios with Tables and Navigating a Table of Equivalent Ratios