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In this KQED infographic, find out how much an adult in different-sized households needs to make to pay for basic monthly living expenses. In the accompanying classroom activity, students solve real-life problems involving rate and ratio that involve calculating whether minimum wage in their state is a living wage. They learn whether minimum-wage pay can cover expenses such as food, housing, transportation, and medical care. They then compare their findings with data shown on bar graphs representing living wage and minimum wage in California. To get the most out of this activity, students should be comfortable with arithmetic with dollars and cents into the ten thousands.

Subject:
Mathematics
Material Type:
Interactive
Provider:
PBS LearningMedia
11/06/2023
Educational Use
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Use math to learn about changes in US wealth distribution and poverty rate over time in this interactive from KQED. In the accompanying classroom activity, students interpret the graphs and consider how the poverty rate spike following the Great Recession of 2008 differs from poverty rate spikes of previous eras. To get the most from this lesson, students should able to interpret data involving percent increase and decrease, and they should be familiar with slope as rate of change over time.

Subject:
Mathematics
Material Type:
Interactive
Provider:
PBS LearningMedia
11/06/2023
Educational Use
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Gain a basic understanding of ratios and rates by watching this easy to understand video tutorial. Additional resources are available as part of a paid subscription service. [8:49]

Subject:
Mathematics
Material Type:
Audio/Video
Provider:
Math Antics
08/01/2022
Conditional Remix & Share Permitted
CC BY-NC
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Subject:
Mathematics
Provider:
Pearson
02/28/2022
Conditional Remix & Share Permitted
CC BY-NC
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Rate

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Solve problems involving all four operations with rational numbers.
Understand quantity as a number used with a unit of measurement.
Solve problems involving quantities such as distances, intervals of time, liquid volumes, masses of objects, and money, and with the units of measurement for these quantities.
Understand that a ratio is a comparison of two quantities.
Write ratios for problem situations.
Make and interpret tables, graphs, and diagrams.
Write and solve equations to represent problem situations.

Lesson Flow

In this unit, students will explore the concept of rate in a variety of contexts: beats per minute, unit prices, fuel efficiency of a car, population density, speed, and conversion factors. Students will write and refine their own definition for rate and then use it to recognize rates in different situations. Students will learn that every rate is paired with an inverse rate that is a measure of the same relationship. Students will figure out the logic of how units are used with rates. Then students will represent quantitative relationships involving rates, using tables, graphs, double number lines, and formulas, and they will see how to create one such representation when given another.

Subject:
Algebra
Mathematics
Provider:
Pearson
Conditional Remix & Share Permitted
CC BY-NC
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In this lesson, students define rate. After coming up with a preliminary definition on their own, students identify situations that describe rates and situations that do not.Students determine what is common among rate situations and then revise their definitions of rate based on these observations. Students present and discuss their work and together create a class definition. They compare the class definition of rate with the Glossary definition and revise the class definition as needed.Key ConceptsA good definition of rate has to be precise, yet general enough to be useful in a variety of situations. For example, the statement “a rate compares two quantities” is true, but it is so general that it is not helpful. The statement “speed is a rate” is true, but it is not useful in determining whether unit price or population density are rates.A good definition of rate needs to state that a rate is a single quantity, expressed with a unit of the form A per B, and derived from a comparison by division of two measures of a single situation.Goals and Learning ObjectivesGain a deeper understanding of rate by developing, refining, testing, and then refining again a definition of rate.Use a definition of rate to determine the kinds of situations that are rate situations and to recognize rates in new and different situations.Understand the importance of precision in communicating mathematical concepts.

Subject:
Algebra
Material Type:
Lesson Plan
Author:
02/28/2022
Conditional Remix & Share Permitted
CC BY-NC
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Subject:
Algebra
Material Type:
Lesson Plan
Author:
02/28/2022
Conditional Remix & Share Permitted
CC BY-NC
Rating
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In this lesson, students use their knowledge of rates, graphs of rates, and formulas to solve problems.Key ConceptsThe formula for a rate is a mathematical way of writing a rule for computing a value. Rate formulas describe a constant relationship between two quantities. Each point on the graph of a rate shows a pair of related values. A graph of a constant rate is a straight line.Goals for Learning ObjectivesUncover any partial understandings and misconceptions students have about rate, graphs of rates, and formulas.Develop a more robust understanding of rate.Help identify which Gallery problems students should work on.

Subject:
Algebra
Material Type:
Lesson Plan
Author:
02/28/2022
Conditional Remix & Share Permitted
CC BY-NC
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In this lesson, students first watch three racers racing against each other. The race is shown on a track and represented on a graph. Students then change the speed, distance, and time to create a race with different results. They graph the new race and compare their graph to the original race graph.Key ConceptsA rate situation can be represented by a graph. Each point on a graph represents a pair of values. In today's situation, each point represents an amount of time and the distance a racer traveled in that amount of time. Time is usually plotted on the horizontal axis. The farther right a point is from the origin, the more time has passed from the start. Distance is usually plotted on the vertical axis. The higher up a point is from the origin, the farther the snail has traveled from the start. A graph of a constant speed is a straight line. Steeper lines show faster speeds.Goals and Learning ObjectivesUnderstand that a graph can be a visual representation of an actual rate situation.Plot pairs of related values on a graph.Use graphs to develop an understanding of rates.

Subject:
Algebra
Material Type:
Lesson Plan
Author:
02/28/2022
Conditional Remix & Share Permitted
CC BY-NC
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In this lesson, students watch a video of a runner and express his speed as a rate in meters per second. Students then use the rate to determine how long it takes the runner to go any distance.Key ConceptsSpeed is a rate that is expressed as distance traveled per unit of time. Miles per hour, laps per minute, and meters per second are all examples of units for speed. The measures of speed, distance, and time are all related. The relationship can be expressed in three ways: d = rt, r = dt, t = dr.Goals and Learning ObjectivesExplore speed as a rate that measures the relationship between two aspects of a situation: distance and time.In comparing distance, speed, and time, understand how to use any two of these measures to find the third measure.

Subject:
Algebra
Material Type:
Lesson Plan
Author:
02/28/2022
Conditional Remix & Share Permitted
CC BY-NC
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Students use their knowledge of rates to solve problems.Key ConceptsGiven any two values in a rate situation, you can find the third value.These three equations are equivalent, and they all describe rate relationships:y = rx,  r = yx,  x = yrAt the beginning of this lesson (or for homework), students will revise their work on the pre-assessment Self Check. Their revised work will provide data that you and your students can use to reassess students' understanding of rate. You can use this information to clear up any remaining misconceptions and to help students integrate their learning from the past several days into a deeper and more coherent whole.The work students do in this lesson and in revising their pre-assessments will help you and your students decide how to help them during the Gallery. In this lesson, students will reveal the depth and clarity of their understanding of rate.Students whose understanding of rate is still delicate should get extra help during the Gallery.Students who feel that they have a robust understanding of rate may choose from any of the problem-solving or deeper mathematics problems in the Gallery.Goals and Learning ObjectivesUncover any partial understandings and misconceptions about rate.Develop a more robust understanding of rate.Identify which Gallery problems to work on.

Subject:
Algebra
Material Type:
Lesson Plan
Author:
02/28/2022
Conditional Remix & Share Permitted
CC BY-NC
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Getting Started

Type of Unit: Introduction

Prior Knowledge

Students should be able to:

Understand ratio concepts and use ratios.
Use ratio and rate reasoning to solve real-world problems.
Identify and use the multiplication property of equality.

Lesson Flow

This unit introduces students to the routines that build a successful classroom math community, and it introduces the basic features of the digital course that students will use throughout the year.

An introductory card sort activity matches students with their partner for the week. Then over the course of the week, students learn about the routines of Opening, Work Time, Ways of Thinking, Apply the Learning (some lessons), Summary of the Math, Reflection, and Exercises. Students learn how to present their work to the class, the importance of students’ taking responsibility for their own learning, and how to effectively participate in the classroom math community.

Students then work on Gallery problems, to further explore the resources and tools and to learn how to organize their work.

The mathematical work of the unit focuses on ratios and rates, including card sort activities in which students identify equivalent ratios and match different representations of an equivalent ratio. Students use the multiplication property of equality to justify solutions to real-world ratio problems.

Subject:
Mathematics
Provider:
Pearson
Educational Use
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Learn Alberta offers a real-world scenario of skateboarding to introduce the concept of square roots. This multimedia site offers two videos, printable exercises and interactive exercises of finding the square root through visual prompts of squares.

Subject:
Mathematics
Material Type:
Audio/Video
Provider:
08/28/2023
Educational Use
Rating
0.0 stars

The use of rate, ratio, and proportion is illustrated in this video about action photography. An additional interactive element allows students to explore equivalent ratios equivalencies through enlarging and reducing images to compare an original ratio and a target ratio. Finally, a print activity is also provided.

Subject:
Mathematics
Material Type:
Audio/Video
Provider:
08/28/2023
Educational Use
Rating
0.0 stars

This NASA video demonstrates how Newton's law of motion applies to the lift of an airplane. Watch as an instructor shows student how an airplane overcomes the downward force of its weight by changing the air molecules colliding with the wings. [14:10]

Subject:
Science
Material Type:
Audio/Video
Provider:
NASA
07/01/2022
Educational Use
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This interactive activity from the NOVA Web site samples Galileo's experiments with falling objects, projectiles, inclined planes, and pendulums.

Subject:
Science
Material Type:
Interactive
Lesson
Provider:
PBS
Provider Set:
NOVA
11/06/2023
Educational Use
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In this lesson, students will use ratios, rates, and unit rates to solve problems.

Subject:
Mathematics
Material Type:
Interactive
Lesson
Provider:
Nearpod
08/07/2023
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating
0.0 stars

Students deepen their understanding of ratios to investigate proportional relationships, in order to solve multi-step, real-world ratio problems using new strategies that rely on proportional reasoning.

Subject:
Mathematics
Material Type:
Unit of Study
Provider:
Fishtank Learning
Provider Set:
Mathematics
11/19/2021
Educational Use
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In this video from Cyberchase, the CyberSquad figures out how fast their broom must go so they can reach Motherboard before Wicked.

Subject:
Mathematics
Physics
Science
Material Type:
Lecture
Provider:
PBS LearningMedia
Author:
U.S. Department of Education
WNET
07/09/2008
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating
0.0 stars

Video explores rates and proportional relationships using a gas mileage problem. [3:18]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

Subject:
Mathematics
Material Type:
Audio/Video
Lesson
Provider: