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Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 6 Unit 3

Unit Rates and Percentages

Lesson 9: Solving Rate Problems

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Nodes
Math Example--Ratios and Rates--Example 17 Math Example--Ratios and Rates--Example 17 Math Example--Ratios and Rates--Example 17

Topic

Ratios and Rates

Description

This example explores the concept of unit rates using the cost of gasoline. The image shows a red gasoline container, and students are asked to calculate the cost per gallon of gas given the total cost and volume.

Understanding unit rates is a fundamental skill in mathematics with numerous real-world applications. This example demonstrates how to calculate a unit rate by dividing the total cost by the total quantity, illustrating the practical use of division in everyday scenarios like purchasing gasoline.

Ratios and Rates
Math Example--Ratios and Rates--Example 18 Math Example--Ratios and Rates--Example 18 Math Example--Ratios and Rates--Example 18

Topic

Ratios and Rates

Description

This example focuses on calculating unit rates in a restaurant context. The image shows a hamburger, and students are asked to determine the cost per pound of ground beef given the total cost and weight purchased.

Understanding unit rates is essential in various real-world scenarios, particularly in business and economics. This example illustrates how to calculate a unit rate by dividing the total cost by the total quantity, demonstrating the practical application of division in a restaurant supply context.

Ratios and Rates
Math Example--Ratios and Rates--Example 19 Math Example--Ratios and Rates--Example 19 Math Example--Ratios and Rates--Example 19

Topic

Ratios and Rates

Description

This example explores the concept of flow rates using a backyard pool scenario. The image shows a backyard pool, and students are asked to calculate the rate of water flow in gallons per minute given the pool's capacity and the time taken to fill it.

Understanding flow rates is important in various fields, including engineering and physics. This example demonstrates how to calculate a rate by dividing the total volume by the total time, illustrating the practical application of division in real-world scenarios involving fluid dynamics.

Ratios and Rates
Math Example--Ratios and Rates--Example 2 Math Example--Ratios and Rates--Example 2 Math Example--Ratios and Rates--Example 2

Topic

Ratios and Rates

Description

This example explores ratios using purple and black socks. The image shows a collection of socks, and students are asked to determine the ratio of purple socks to black socks. The solution reveals that there is 1 pair of purple socks and 2 pairs of black socks, resulting in a ratio of 1 : 2, which is already in its simplest form.

Ratios and Rates
Math Example--Ratios and Rates--Example 20 Math Example--Ratios and Rates--Example 20 Math Example--Ratios and Rates--Example 20

Topic

Ratios and Rates

Description

This example focuses on unit conversion using the height of the Statue of Liberty. The image shows the Statue of Liberty, and students are asked to convert its height from feet to inches.

Understanding unit conversions is crucial in many fields, including science, engineering, and everyday life. This example demonstrates how to use a conversion factor to change units, illustrating the practical application of multiplication in real-world measurement scenarios.

Ratios and Rates
Math Example--Ratios and Rates--Example 21 Math Example--Ratios and Rates--Example 21 Math Example--Ratios and Rates--Example 21

Topic

Ratios and Rates

Description

This example focuses on unit conversion, specifically converting the height of the Statue of Liberty from feet to yards. The image shows the iconic Statue of Liberty, providing a real-world context for the mathematical problem.

Understanding unit conversions is crucial in many fields, including engineering, science, and everyday life. This example demonstrates how to use a conversion factor to change units, illustrating the practical application of division and multiplication in real-world measurement scenarios.

Ratios and Rates
Math Example--Ratios and Rates--Example 22 Math Example--Ratios and Rates--Example 22 Math Example--Ratios and Rates--Example 22

Topic

Ratios and Rates

Description

This example explores unit conversion, specifically converting the height of the Statue of Liberty from feet to miles. The image depicts the Statue of Liberty, providing a tangible reference for the mathematical problem.

Understanding unit conversions, especially between widely different scales like feet and miles, is important in various fields such as geography, engineering, and urban planning. This example showcases how to use a conversion factor to change units, demonstrating the practical application of division and multiplication in real-world measurement scenarios.

Ratios and Rates
Math Example--Ratios and Rates--Example 23 Math Example--Ratios and Rates--Example 23 Math Example--Ratios and Rates--Example 23

Topic

Ratios and Rates

Description

This example focuses on unit conversion, specifically converting the height of columns from inches to feet. The image shows columns, providing a visual context for the mathematical problem.

Understanding unit conversions between inches and feet is crucial in many practical applications, including construction, interior design, and everyday measurements. This example demonstrates how to use a conversion factor to change units, illustrating the practical application of division and multiplication in real-world measurement scenarios.

Ratios and Rates
Math Example--Ratios and Rates--Example 24 Math Example--Ratios and Rates--Example 24 Math Example--Ratios and Rates--Example 24

Topic

Ratios and Rates

Description

This example explores unit conversion in a sports context, specifically converting a quarterback's pass distance from yards to feet. The image shows a silhouette of a quarterback throwing a football, providing a real-world scenario for the mathematical problem.

Understanding unit conversions between yards and feet is crucial in many sports, especially American football. This example demonstrates how to use a conversion factor to change units, illustrating the practical application of multiplication in sports-related measurement scenarios.

Ratios and Rates
Math Example--Ratios and Rates--Example 25 Math Example--Ratios and Rates--Example 25 Math Example--Ratios and Rates--Example 25

Topic

Ratios and Rates

Description

This example focuses on unit conversion in a geographic context, specifically converting the distance between San Antonio and Austin from miles to feet. The image shows a map of the route between these two Texas cities, providing a real-world scenario for the mathematical problem.

Understanding unit conversions between miles and feet is important in various fields, including geography, transportation, and urban planning. This example demonstrates how to use a conversion factor to change units, illustrating the practical application of multiplication in distance-related measurement scenarios.

Ratios and Rates
Math Example--Ratios and Rates--Example 26 Math Example--Ratios and Rates--Example 26 Math Example--Ratios and Rates--Example 26

Topic

Ratios and Rates

Description

This example focuses on time unit conversion, specifically converting hours to minutes in the context of a standardized test duration. The image shows a clock, providing a visual representation of time for the mathematical problem.

Understanding time unit conversions is crucial in many aspects of daily life, including scheduling, time management, and test-taking. This example demonstrates how to use a conversion factor to change units, illustrating the practical application of multiplication in time-related scenarios.

Ratios and Rates
Math Example--Ratios and Rates--Example 27 Math Example--Ratios and Rates--Example 27 Math Example--Ratios and Rates--Example 27

Topic

Ratios and Rates

Description

This example explores time unit conversion, specifically converting hours and minutes to seconds in the context of baking a pie. The image shows a steaming pie, providing a real-world scenario for the mathematical problem.

Understanding time unit conversions, especially when dealing with mixed units, is important in various fields such as cooking, manufacturing, and project management. This example demonstrates how to use conversion factors to change units, illustrating the practical application of multiplication in time-related scenarios.

Ratios and Rates
Math Example--Ratios and Rates--Example 28 Math Example--Ratios and Rates--Example 28 Math Example--Ratios and Rates--Example 28

Topic

Ratios and Rates

Description

This example focuses on time unit conversion in a sports context, specifically converting minutes and seconds to seconds for a horse race lap time. The image shows a horse, providing a visual context for the mathematical problem.

Understanding time unit conversions is crucial in many sports, especially those involving racing and timed events. This example demonstrates how to use conversion factors to change units and add different time units, illustrating the practical application of multiplication and addition in sports-related time scenarios.

Ratios and Rates
Math Example--Ratios and Rates--Example 29 Math Example--Ratios and Rates--Example 29 Math Example--Ratios and Rates--Example 29

Topic

Ratios and Rates

Description

This example explores time unit conversion in an IT context, specifically converting seconds to minutes for user session duration. The image shows a computer tower, providing a real-world scenario for the mathematical problem.

Understanding time unit conversions is crucial in many technological fields, especially in IT and user experience analysis. This example demonstrates how to use a conversion factor to change units, illustrating the practical application of division in time-related measurement scenarios. It also introduces the concept of mixed numbers in the result.

Ratios and Rates
Math Example--Ratios and Rates--Example 3 Math Example--Ratios and Rates--Example 3 Math Example--Ratios and Rates--Example 3

Topic

Ratios and Rates

Description

This example focuses on ratios using black and green socks. The image displays a collection of socks, and students are tasked with determining the ratio of black socks to green socks. The solution shows that there are 2 pairs of black socks and 6 pairs of green socks, resulting in a ratio of 2 : 6, which simplifies to 1 : 3.

Ratios and Rates
Math Example--Ratios and Rates--Example 30 Math Example--Ratios and Rates--Example 30 Math Example--Ratios and Rates--Example 30

Topic

Ratios and Rates

Description

This example focuses on time unit conversion in an IT context, specifically converting seconds to hours for user session duration. The image shows a computer tower, providing a real-world scenario for the mathematical problem.

Ratios and Rates
Math Example--Ratios and Rates--Example 31 Math Example--Ratios and Rates--Example 31 Math Example--Ratios and Rates--Example 31

Topic

Ratios and Rates

Description

This example focuses on temperature unit conversion, specifically converting Celsius to Fahrenheit for the boiling point of water. The image shows a beaker of boiling water, providing a visual context for the mathematical problem.

Understanding temperature unit conversions is crucial in many scientific fields, including chemistry, physics, and meteorology. This example demonstrates how to use a conversion formula to change units, illustrating the practical application of mathematical equations in real-world temperature scenarios.

Ratios and Rates
Math Example--Ratios and Rates--Example 32 Math Example--Ratios and Rates--Example 32 Math Example--Ratios and Rates--Example 32

Topic

Ratios and Rates

Description

This example explores temperature unit conversion, specifically converting Fahrenheit to Celsius for the freezing point of water. The image shows icicles, providing a visual representation of the freezing temperature for the mathematical problem.

Ratios and Rates
Math Example--Ratios and Rates--Example 4 Math Example--Ratios and Rates--Example 4 Math Example--Ratios and Rates--Example 4

Topic

Ratios and Rates

Description

This example explores ratios using purple and red socks. The image shows a collection of socks, and students are asked to determine the ratio of purple socks to red socks. The solution reveals that there is 1 pair of purple socks and 4 pairs of red socks, resulting in a ratio of 1 : 4, which is already in its simplest form.

Ratios and Rates
Math Example--Ratios and Rates--Example 5 Math Example--Ratios and Rates--Example 5 Math Example--Ratios and Rates--Example 5

Topic

Ratios and Rates

Description

This example focuses on ratios using black and green socks among a variety of colored socks. The image displays pairs of socks in black, green, orange, yellow, blue, and red. Students are asked to determine the ratio of black socks to green socks. The solution shows that there are 2 pairs of black socks and 10 pairs of green socks, resulting in a ratio of 2 : 10, which simplifies to 1 : 5.

Ratios and Rates
Math Example--Ratios and Rates--Example 6 Math Example--Ratios and Rates--Example 6 Math Example--Ratios and Rates--Example 6

Topic

Ratios and Rates

Description

This example explores ratios using geometric shapes of different colors. The image displays various shapes in yellow, blue, red, and green. Students are asked to determine the ratio of circular shapes to yellow objects. The solution reveals that there are 2 circular shapes and 1 yellow object, resulting in a ratio of 2 : 1, which is already in its simplest form.

Ratios and Rates
Math Example--Ratios and Rates--Example 7 Math Example--Ratios and Rates--Example 7 Math Example--Ratios and Rates--Example 7

Topic

Ratios and Rates

Description

This example focuses on ratios using geometric shapes. The image displays various shapes in yellow, blue, red, and green. Students are asked to determine the ratio of triangles to quadrilaterals. The solution shows that there are 4 triangles and 6 quadrilaterals, resulting in a ratio of 4 : 6, which simplifies to 2 : 3.

Ratios and Rates
Math Example--Ratios and Rates--Example 8 Math Example--Ratios and Rates--Example 8 Math Example--Ratios and Rates--Example 8

Topic

Ratios and Rates

Description

This example explores ratios using geometric shapes and colors. The image displays various shapes in yellow, blue, red, and green. Students are asked to determine the ratio of octagons to blue shapes. The solution reveals that there are 2 octagons and 5 blue shapes, resulting in a ratio of 2 : 5, which is already in its simplest form.

Ratios and Rates
Math Example--Ratios and Rates--Example 9 Math Example--Ratios and Rates--Example 9 Math Example--Ratios and Rates--Example 9

Topic

Ratios and Rates

Description

This example introduces the concept of ratios in genetics using a Punnett square. The image shows genetic combinations for a flower's color, including RR, Rw, and ww, with corresponding images of red and white flowers. Students are asked to determine the ratio of different gene combinations.

Ratios and Rates
Math Example--Ratios and Rates--Ratios with Fractions--Example 1 Math Example--Ratios and Rates--Ratios with Fractions--Example 1 Ratios with Fractions--Example 1

Topic

Ratios and Fractions

Description

In many scenarios, ratios are expressed using whole numbers, yet there are instances, like in recipes, where fractions play a significant role. This example illustrates a ratio involving fractions and demonstrates how to convert it into a ratio with whole numbers. Students will engage in understanding the process of converting these fractions to whole numbers, enhancing their comprehension of ratios and their practical applications such as cooking or mixing. The focus is on the fundamental skill of fraction conversion and applying it in a ratio context.

Ratios and Rates
Math Example--Ratios and Rates--Ratios with Fractions--Example 10 Math Example--Ratios and Rates--Ratios with Fractions--Example 10 +Ratios with Fractions--Example 10

Topic

Ratios and Fractions

Description

In many scenarios, ratios are expressed using whole numbers, yet there are instances, like in recipes, where fractions play a significant role. This example illustrates a ratio involving fractions and demonstrates how to convert it into a ratio with whole numbers. Students will engage in understanding the process of converting these fractions to whole numbers, enhancing their comprehension of ratios and their practical applications such as cooking or mixing. The focus is on the fundamental skill of fraction conversion and applying it in a ratio context.

Ratios and Rates
Math Example--Ratios and Rates--Ratios with Fractions--Example 11 Math Example--Ratios and Rates--Ratios with Fractions--Example 11 Ratios with Fractions--Example 11

Topic

Ratios and Fractions

Description

In many scenarios, ratios are expressed using whole numbers, yet there are instances, like in recipes, where fractions play a significant role. This example illustrates a ratio involving fractions and demonstrates how to convert it into a ratio with whole numbers. Students will engage in understanding the process of converting these fractions to whole numbers, enhancing their comprehension of ratios and their practical applications such as cooking or mixing. The focus is on the fundamental skill of fraction conversion and applying it in a ratio context.

Ratios and Rates
Math Example--Ratios and Rates--Ratios with Fractions--Example 2 Math Example--Ratios and Rates--Ratios with Fractions--Example 2 Ratios with Fractions--Example 2

Topic

Ratios and Fractions

Description

In many scenarios, ratios are expressed using whole numbers, yet there are instances, like in recipes, where fractions play a significant role. This example illustrates a ratio involving fractions and demonstrates how to convert it into a ratio with whole numbers. Students will engage in understanding the process of converting these fractions to whole numbers, enhancing their comprehension of ratios and their practical applications such as cooking or mixing. The focus is on the fundamental skill of fraction conversion and applying it in a ratio context.

Ratios and Rates
Math Example--Ratios and Rates--Ratios with Fractions--Example 3 Math Example--Ratios and Rates--Ratios with Fractions--Example 3 Ratios with Fractions--Example 3

Topic

Ratios and Fractions

Description

In many scenarios, ratios are expressed using whole numbers, yet there are instances, like in recipes, where fractions play a significant role. This example illustrates a ratio involving fractions and demonstrates how to convert it into a ratio with whole numbers. Students will engage in understanding the process of converting these fractions to whole numbers, enhancing their comprehension of ratios and their practical applications such as cooking or mixing. The focus is on the fundamental skill of fraction conversion and applying it in a ratio context.

Ratios and Rates
Math Example--Ratios and Rates--Ratios with Fractions--Example 4 Math Example--Ratios and Rates--Ratios with Fractions--Example 4 Ratios with Fractions--Example 4

Topic

Ratios and Fractions

Description

In many scenarios, ratios are expressed using whole numbers, yet there are instances, like in recipes, where fractions play a significant role. This example illustrates a ratio involving fractions and demonstrates how to convert it into a ratio with whole numbers. Students will engage in understanding the process of converting these fractions to whole numbers, enhancing their comprehension of ratios and their practical applications such as cooking or mixing. The focus is on the fundamental skill of fraction conversion and applying it in a ratio context.

Ratios and Rates
Math Example--Ratios and Rates--Ratios with Fractions--Example 5 Math Example--Ratios and Rates--Ratios with Fractions--Example 5 Ratios with Fractions--Example 5

Topic

Ratios and Fractions

Description

In many scenarios, ratios are expressed using whole numbers, yet there are instances, like in recipes, where fractions play a significant role. This example illustrates a ratio involving fractions and demonstrates how to convert it into a ratio with whole numbers. Students will engage in understanding the process of converting these fractions to whole numbers, enhancing their comprehension of ratios and their practical applications such as cooking or mixing. The focus is on the fundamental skill of fraction conversion and applying it in a ratio context.

Ratios and Rates
Math Example--Ratios and Rates--Ratios with Fractions--Example 6 Math Example--Ratios and Rates--Ratios with Fractions--Example 6 Ratios with Fractions--Example 6

Topic

Ratios and Fractions

Description

In many scenarios, ratios are expressed using whole numbers, yet there are instances, like in recipes, where fractions play a significant role. This example illustrates a ratio involving fractions and demonstrates how to convert it into a ratio with whole numbers. Students will engage in understanding the process of converting these fractions to whole numbers, enhancing their comprehension of ratios and their practical applications such as cooking or mixing. The focus is on the fundamental skill of fraction conversion and applying it in a ratio context.

Ratios and Rates
Math Example--Ratios and Rates--Ratios with Fractions--Example 7 Math Example--Ratios and Rates--Ratios with Fractions--Example 7 Ratios with Fractions--Example 7

Topic

Ratios and Fractions

Description

In many scenarios, ratios are expressed using whole numbers, yet there are instances, like in recipes, where fractions play a significant role. This example illustrates a ratio involving fractions and demonstrates how to convert it into a ratio with whole numbers. Students will engage in understanding the process of converting these fractions to whole numbers, enhancing their comprehension of ratios and their practical applications such as cooking or mixing. The focus is on the fundamental skill of fraction conversion and applying it in a ratio context.

Ratios and Rates
Math Example--Ratios and Rates--Ratios with Fractions--Example 8 Math Example--Ratios and Rates--Ratios with Fractions--Example 8 Ratios with Fractions--Example 8

Topic

Ratios and Fractions

Description

In many scenarios, ratios are expressed using whole numbers, yet there are instances, like in recipes, where fractions play a significant role. This example illustrates a ratio involving fractions and demonstrates how to convert it into a ratio with whole numbers. Students will engage in understanding the process of converting these fractions to whole numbers, enhancing their comprehension of ratios and their practical applications such as cooking or mixing. The focus is on the fundamental skill of fraction conversion and applying it in a ratio context.

Ratios and Rates
Math Example--Ratios and Rates--Ratios with Fractions--Example 9 Math Example--Ratios and Rates--Ratios with Fractions--Example 9 Ratios with Fractions--Example 9

Topic

Ratios and Fractions

Description

In many scenarios, ratios are expressed using whole numbers, yet there are instances, like in recipes, where fractions play a significant role. This example illustrates a ratio involving fractions and demonstrates how to convert it into a ratio with whole numbers. Students will engage in understanding the process of converting these fractions to whole numbers, enhancing their comprehension of ratios and their practical applications such as cooking or mixing. The focus is on the fundamental skill of fraction conversion and applying it in a ratio context.

Ratios and Rates
Math Example--Ratios and Rates--Trig Ratios--Example 1 Math Example--Ratios and Rates--Trig Ratios--Example 1 Math Example--Ratios and Rates--Trig Ratios--Example 1

This is part of a collection of math examples that focus on ratios and rates.

Trig Expressions and Identities
Math Example--Ratios and Rates--Trig Ratios--Example 2 Math Example--Ratios and Rates--Trig Ratios--Example 2 Math Example--Ratios and Rates--Trig Ratios--Example 2

This is part of a collection of math examples that focus on ratios and rates.

Trig Expressions and Identities
Math Example--Ratios and Rates--Trig Ratios--Example 3 Math Example--Ratios and Rates--Trig Ratios--Example 3 Math Example--Ratios and Rates--Trig Ratios--Example 3

This is part of a collection of math examples that focus on ratios and rates.

Trig Expressions and Identities
Math Example--Ratios and Rates--Trig Ratios--Example 4 Math Example--Ratios and Rates--Trig Ratios--Example 4 Math Example--Ratios and Rates--Trig Ratios--Example 4

This is part of a collection of math examples that focus on ratios and rates.

Trig Expressions and Identities
Math Example--Ratios and Rates--Trig Ratios--Example 5 Math Example--Ratios and Rates--Trig Ratios--Example 5 Math Example--Ratios and Rates--Trig Ratios--Example 5

This is part of a collection of math examples that focus on ratios and rates.

Trig Expressions and Identities
Math Example--Ratios and Rates--Trig Ratios--Example 6 Math Example--Ratios and Rates--Trig Ratios--Example 6 Math Example--Ratios and Rates--Trig Ratios--Example 6

This is part of a collection of math examples that focus on ratios and rates.

Trig Expressions and Identities
Math Example--Ratios and Rates--Trig Ratios--Example 7 Math Example--Ratios and Rates--Trig Ratios--Example 7 Math Example--Ratios and Rates--Trig Ratios--Example 7

This is part of a collection of math examples that focus on ratios and rates.

Trig Expressions and Identities
Math Example--Ratios and Rates--Trig Ratios--Example 8 Math Example--Ratios and Rates--Trig Ratios--Example 8 Math Example--Ratios and Rates--Trig Ratios--Example 8

This is part of a collection of math examples that focus on ratios and rates.

Trig Expressions and Identities
Math Example--Ratios and Rates--Trig Ratios--Example 9 Math Example--Ratios and Rates--Trig Ratios--Example 9 Math Example--Ratios and Rates--Trig Ratios--Example 9

This is part of a collection of math examples that focus on ratios and rates.

Trig Expressions and Identities
MITN Math in the News: Issue 121--NFL Concussion Statistics Math in the News: Issue 121 | NFL Concussion Statistics

February 2023. In this issue of Math in the News we look at NFL statistics for the number of concussions. The NFL now tracks concussion, and this is an opportunity to analyze this data and draw conclusions.

—PRESS PREVIEW TO SEE THE SLIDE SHOW— This is part of the Math in the News collection. To see the complete collection, click on this link.

Note: The download is a PPT file.

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Math in the News: Issue 46--The Unemployment Rate Math in the News: Issue 46--The Unemployment Rate Math in the News: Issue 46--The Unemployment Rate

February 2012. In this issue we look at unemployment statistics from the Bureau of Labor Statistics.

This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.

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Data Analysis
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July 2015. This edition of Math in the News focuses on the severe drought currently taking place in California, and how it has impacted the water resources available to the state. In this edition, students will see how to use percentages given to determine actual amounts, and to determine percents out of a whole.

This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.

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To see resources related to this topic click on the Related Resources tab above.

Applications of Ratios, Proportions, and Percents and Proportions
Math in the News: Issue 99--What Is Bitcoin? Math in the News: Issue 99--What Is Bitcoin? Math in the News: Issue 99--What Is Bitcoin?

May 2014. In this issue of Math in the News we explore Bitcoin. We look at how it's used for making purchases and how it differs from other currencies. This provides an opportunity to apply the concept of currency exchange.

This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.

Related Resources

To see resources related to this topic click on the Related Resources tab above.

Applications of Ratios, Proportions, and Percents and Proportions
Math Video Definition 15--Multiplication and Division Concepts--Division Strategy Math Video Definition 15--Multiplication and Division Concepts--Division Strategy Math Video Definition 15--Multiplication and Division Concepts--Division Strategy

This is part of a collection of math video definitions related to the topics of Multiplication and Division, ideal for use in an early elementary classroom. Note: The download is an MP4 video.

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This is part of a collection of math video definitions related to the topics of Multiplication and Division, ideal for use in an early elementary classroom. Note: The download is an MP4 video.

Multiplication Expressions and Equations