Classroom Resource

Scaling Down, Scaling Up

Subject Area

Mathematics

Grade(s)

5, 6, 7

Overview

In this lesson, students learn about scaling an object, first smaller (1/10) and then larger (2x). This Cyberchase activity is motivated by two video clips in which the CyberSquad travels to Proporciona, where they visit a land of giants and a land of tiny people (similar to Gulliver's Travels).

Mathematics (2019) Grade(s): 5

MA19.5.13

Interpret multiplication as scaling (resizing).

Unpacked Content

UP:MA19.5.13

Vocabulary

  • Resizing
  • Scaling
  • Product
  • Factor

Knowledge

Students know:
  • How to interpret multiplicative comparisons.
  • Strategies to compare products with whole numbers using reasoning and justification.
    Example: Which is greater? 5 x 2 x 13 or 13 x 9? 10 x 13 is greater than 9 x 13 because both expressions contain a factor of 13, but the scale factor of 10 will result in a greater product than a scale factor of 9.
  • Fraction meaning and magnitude of fractions less than and greater than 1.

Skills

Students are able to:
  • Interpret multiplication as scaling.
  • Use reasoning to compare products of multiplication expressions.
  • Reason and explain when multiplying a given number by a fraction why the product will be greater than or less than the original number.

Understanding

Students understand that:
  • a product reflects the size of its factors.
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.

Unpacked Content

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.
Mathematics (2019) Grade(s): 7

MA19.7.2

Represent a relationship between two quantities and determine whether the two quantities are related proportionally.

Unpacked Content

UP:MA19.7.2

Vocabulary

  • Equivalent ratios
  • proportional
  • Coordinate plane
  • Ratio table
  • Unit rate
  • Constant of proportionality
  • Equation
  • ordered pair

Knowledge

Students know:
  • (2a) how to explain whether a relationship is proportional.
  • (2b) that the constant of proportionality is the same as a unit rate. Students know:
    • where the constant of proportionality can be found in a table, graph, equation or diagram.
    • (2c) that the constant of proportionality or unit rate can be found on a graph of a proportional relationship where the input value or x-coordinate is 1.

Skills

Students are able to:
  • (2a) determine if a proportional relationship exists when given a table of equivalent ratios or a graph of the relationship in the coordinate plane.
  • (2b) identify the constant of proportionality and express the proportional relationship using a variety of representations including tables, graphs, equations, diagrams, and verbal descriptions.
  • (2c) model a proportional relationship using coordinate graphing.
  • Explain the meaning of the point (1, r), where r is the unit rate or constant of proportionality.

Understanding

Students understand that:
  • (2a) A proportional relationship requires equivalent ratios between quantities. Students understand how to decide whether two quantities are proportional.
  • (2b) The constant of proportionality is the unit rate. Students are able to identify the constant of proportionality for a proportional relationship and explain its meaning in a real-world context. (2c) The context of a problem can help them interpret a point on a graph of a proportional relationship.
Link to Resource
https://aptv.pbslearningmedia.org/resource/vtl07.math.number.rat.lpscaledwn/sca…

CR Resource Type

Lesson/Unit Plan

Resource Provider

PBS
Accessibility
License

License Type

CUSTOM

Custom License Type (URL)

https://aptv.pbslearningmedia.org/help/terms-of-use/

Approved Date

ALSDE LOGO

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