Scale City | Inverse Proportions and Shadows in the Real World

Learning Resource Type

Classroom Resource

Subject Area

Mathematics

Grade(s)

6, 7

Overview

In this video, students take a quick trip through the history of drive-in theaters and are then asked to consider the question, "What is the relationship between the size of an object’s shadow and the object’s distance from a light source?" In the accompanying classroom activity, students do a hands-on experiment about the size of their own shadows at different distances from a projector or other light source. This resource is part of the Math at the Core: Middle School Collection.

 

More About This Resource

Although Inverse Proportions and Shadows in the Real World and the Inverse Proportions and Shadows in Practice interactive ("Shadow Puppets") can be used independently, they are deliberately designed to complement each other.

 

The video takes students to "Sky-Vue Drive-In" to explore what happens to the size of shadows as an object moves further away from a light source.

 

The matching interactive simulates three figures of different heights standing at various distances in front of a movie projector, allowing students to measure the corresponding shadows of the figures on the movie screen and to see how the relationship between the distance from the light source and the height of the shadow is represented graphically.

 

Be sure to use the Inverse Proportions and Shadows in the Real World Activity that can be found in the Support Materials for Teachers section for a great activity that teaches the standard(s).

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.
Mathematics (2019) Grade(s): 7

MA19.7.2

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

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.

CR Resource Type

Audio/Video

Resource Provider

PBS

License Type

PD
https://aptv.pbslearningmedia.org/resource/mket-math-rp-drivein/drivein/

Comments or Notes

This resource contains the following activities:

Drive-In Viewing Guide: PDF

Drive-In Viewing Guide Answer Key: PDF

Inverse Proportions and Shadows in the Real World - Activity

Inverse Proportions and Shadows in the Real World - Connections

Approved Date

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