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Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 6 Unit 2

Introducing Ratios

Lesson 1: Introducing Ratios and Ratio Language

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Topic
Closed Captioned Video: Ratios and Proportions: Scale Drawings

Closed Captioned Video: Ratios and Proportions: Scale Drawings

Closed Captioned Video: Ratios and Proportions: Scale Drawings

Video Tutorial: Ratios and Proportions: Scale Drawings. In this video, we look at the properties of similar figures and use proportions to find lengths of corresponding sides.

Ratios and Rates
Closed Captioned Video: Ratios and Proportions: Solving Proportions

Closed Captioned Video: Ratios and Proportions: Solving Proportions

Closed Captioned Video: Ratios and Proportions: Solving Proportions

Video Tutorial: Ratios and Proportions: Solving Proportions. In this video, we solve proportion problems algebraically.

Ratios and Rates
Closed Captioned Video: Ratios and Proportions: What Are Proportions?

Closed Captioned Video: Ratios and Proportions: What Are Proportions?

Closed Captioned Video: Ratios and Proportions: What Are Proportions?

Video Tutorial: Ratios and Proportions: What are Proportions?. In this video, we solve proportion problems using equivalent ratios.

Ratios and Rates
Closed Captioned Video: Ratios and Rates: Converting Measurement Units

Closed Captioned Video: Ratios and Rates: Converting Measurement Units

Closed Captioned Video: Ratios and Rates: Converting Measurement Units

Video Tutorial: Ratios and Rates: Converting Measurement Units. In this video, we show how to use conversion rates to convert from one unit of measurement to another. Students are shown how to create a conversion rate.

Ratios and Rates
Closed Captioned Video: Ratios and Rates: Rates and Slopes of Lines

Closed Captioned Video: Ratios and Rates: Rates and Slopes of Lines

Closed Captioned Video: Ratios and Rates: Rates and Slopes of Lines

Video Tutorial: Ratios and Rates: Rates and Slopes of Lines. In this video we connect the concept of rate of change for a set of linear data to the concept of slope. We use the slope formula to find the rate of change.

Ratios and Rates
Closed Captioned Video: Ratios and Rates: Rates from Data

Closed Captioned Video: Ratios and Rates: Rates from Data

Closed Captioned Video: Ratios and Rates: Rates from Data

Video Tutorial: Ratios and Rates: Rates from Data. In this video, we look at linear data sets that can be used to find the rate of change.

Ratios and Rates
Closed Captioned Video: Ratios and Rates: Ratios as Decimals

Closed Captioned Video: Ratios and Rates: Ratios as Decimals

Closed Captioned Video: Ratios and Rates: Ratios as Decimals

Video Tutorial: Ratios and Rates: Ratios as Decimals. In this video, students explore ratios whose terms are decimals. Students are shown techniques for simplifying these types of ratios in ;the context of solving real-world ratio problems.

Ratios and Rates
Closed Captioned Video: Ratios, Proportions, and Percents: Calculating Percents

Closed Captioned Video: Ratios, Proportions, and Percents: Calculating Percents

Closed Captioned Video: Ratios, Proportions, and Percents: Calculating Percents

Video Tutorial: Ratios and Percents: Calculating Percents. In this video, students will see the relationship between ratios, proportions, and percents. A percent formula is derived and used to solve several real-world percent problems.

Ratios and Rates
Closed Captioned Video: Ratios: Application of Ratios: Roofs and Ramps

Closed Captioned Video: Ratios: Application of Ratios: Roofs and Ramps

Closed Captioned Video: Ratios: Application of Ratios: Roofs and Ramps

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items. Let's look at an example.

Ratios and Rates and Applications of Ratios, Proportions, and Percents
Closed Captioned Video: Ratios: Equivalent Ratios

Closed Captioned Video: Ratios: Equivalent Ratios

Closed Captioned Video: Ratios: Equivalent Ratios

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items.

Ratios and Rates
Closed Captioned Video: Ratios: Fractional Ratios

Closed Captioned Video: Ratios: Fractional Ratios

Closed Captioned Video: Ratios: Fractional Ratios

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items.

Ratios and Rates
Closed Captioned Video: Ratios: Numerical Models for Ratios

Closed Captioned Video: Ratios: Numerical Models for Ratios

Closed Captioned Video: Ratios: Numerical Models for Ratios

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items.

Ratios and Rates
Closed Captioned Video: Ratios: Rates

Closed Captioned Video: Ratios: Rates

Closed Captioned Video: Ratios: Rates

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items.

Ratios and Rates
Closed Captioned Video: Ratios: Ratios and Fractions

Closed Captioned Video: Ratios: Ratios and Fractions

Closed Captioned Video: Ratios: Ratios and Fractions

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items.

Ratios and Rates
Closed Captioned Video: Ratios: Ratios with Three Items

Closed Captioned Video: Ratios: Ratios with Three Items

Closed Captioned Video: Ratios: Ratios with Three Items

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items.

Ratios and Rates
Closed Captioned Video: Ratios: Unit Rates

Closed Captioned Video: Ratios: Unit Rates

Closed Captioned Video: Ratios: Unit Rates

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items.

Ratios and Rates
Closed Captioned Video: Ratios: Visual Models for Ratios

Closed Captioned Video: Ratios: Visual Models for Ratios

Closed Captioned Video: Ratios: Visual Models for Ratios

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items. Let's look at an example.

Ratios and Rates
Closed Captioned Video: Ratios: Visual Models for Ratios and Percents

Closed Captioned Video: Ratios: Visual Models for Ratios and Percents

Closed Captioned Video: Ratios: Visual Models for Ratios and Percents

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items.

Ratios and Rates
Closed Captioned Video: Ratios: What Are Ratios?

Closed Captioned Video: Ratios: What Are Ratios?

Closed Captioned Video: Ratios: What Are Ratios?

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items.

Ratios and Rates
Definition--Ratios, Proportions, and Percents Concepts--Converting Units

Definition--Ratios, Proportions, and Percents Concepts--Converting Units

Converting Units

Topic

Ratios, Proportions, and Percents

Definition

Converting units involves changing a measurement from one unit to another using a conversion factor.

Description

Converting units is essential in various fields such as science, engineering, and everyday life. It involves using ratios and proportions to switch between different measurement systems, such as converting inches to centimeters or gallons to liters.

For example, to convert 5 miles to kilometers, knowing that 1 mile is approximately 1.60934 kilometers, you multiply 

5 × 1.60934 = 8.0467 kilometers

Ratios and Rates
Definition--Ratios, Proportions, and Percents Concepts--Equivalent Ratios

Definition--Ratios, Proportions, and Percents Concepts--Equivalent Ratios

Equivalent Ratios

Topic

Ratios, Proportions, and Percents

Definition

Equivalent ratios are ratios that express the same relationship between quantities.

Description

Equivalent ratios are fundamental in understanding proportions and scaling in mathematics. They represent the same relationship between quantities, even though the numbers themselves may differ. This concept is crucial in various applications, such as cooking, map reading, and creating models.

For instance, the ratios 2:3 and 4:6 are equivalent because they both simplify to the same ratio when reduced.

Ratios and Rates
Definition--Ratios, Proportions, and Percents Concepts--Part-to-Part Ratios

Definition--Ratios, Proportions, and Percents Concepts--Part-to-Part Ratios

Part-to-Part Ratios

Topic

Ratios, Proportions, and Percents

Definition

Part-to-part ratios compare different parts of a whole to each other.

Description

Part-to-part ratios are used to compare different parts of a whole, providing a way to understand the relationship between different components. This type of ratio is essential in fields such as statistics, biology, and economics.

For example, if a class has 10 boys and 15 girls, the part-to-part ratio of boys to girls is 10:15, which simplifies to 2:3.

Ratios and Rates
Definition--Ratios, Proportions, and Percents Concepts--Part-to-Whole Ratios

Definition--Ratios, Proportions, and Percents Concepts--Part-to-Whole Ratios

Part-to-Whole Ratios

Topic

Ratios, Proportions, and Percents

Definition

Part-to-whole ratios compare one part of a whole to the entire whole. These ratios are more commonly known as fractions.

Description

Part-to-whole ratios are used to compare a part of a whole to the entire whole, providing insights into the composition of a dataset or population. This type of ratio, more commonly referred to as fractions, is widely used in statistics, finance, and everyday decision-making.

Ratios and Rates
Definition--Ratios, Proportions, and Percents Concepts--Rate

Definition--Ratios, Proportions, and Percents Concepts--Rate

Rate

Topic

Ratios, Proportions, and Percents

Definition

A rate is a ratio that compares two quantities with different units.

Description

Rates are used to compare different quantities, such as speed (miles per hour) or price (cost per item). Understanding rates is essential for interpreting data and making informed decisions in various contexts, such as travel and budgeting.

For instance, if a car travels 60 miles in 2 hours, the rate is 30 miles per hour. Learning about rates helps students analyze real-world situations and apply mathematical reasoning to everyday problems.

Ratios and Rates
Definition--Ratios, Proportions, and Percents Concepts--Ratio

Definition--Ratios, Proportions, and Percents Concepts--Ratio

Ratio

Topic

Ratios, Proportions, and Percents

Definition

A ratio is a comparison of two quantities by division.

Description

Ratios are used to express the relationship between two quantities, providing a way to compare different amounts. They are fundamental in various fields, including mathematics, science, and finance.

For example, the ratio of 4 to 5 can be written as 4:5 or 4/5. Understanding ratios helps students analyze data, solve problems, and make informed decisions in real-world situations.

Ratios and Rates
Definition--Ratios, Proportions, and Percents Concepts--Ratios and Fractions

Definition--Ratios, Proportions, and Percents Concepts--Ratios and Fractions

Ratios and Fractions

Topic

Ratios, Proportions, and Percents

Definition

Ratios and fractions are both ways of comparing quantities, with fractions representing a part of a whole.

Description

Understanding the connection between ratios and fractions is crucial for solving problems involving proportions and scaling. Ratios can be expressed as fractions, providing a way to understand the relationship between quantities. A fraction is a part-whole ratio.

Ratios and Rates
Definition--Ratios, Proportions, and Percents Concepts--Ratios and Slope

Definition--Ratios, Proportions, and Percents Concepts--Ratios and Slope

Ratios and Slope

Topic

Ratios, Proportions, and Percents

Definition

The slope of a line is a ratio that represents the change in y over the change in x.

Description

Understanding the relationship between ratios and slope is essential for interpreting graphs and solving problems in algebra and geometry. The slope is a measure of how steep a line is, calculated as the ratio of the vertical change to the horizontal change between two points.

For example, if a line rises 2 units for every 3 units it runs horizontally, the slope is 2/3. This concept is crucial for understanding linear relationships and analyzing data in various fields.

Ratios and Rates
Definition--Ratios, Proportions, and Percents Concepts--Ratios with Decimals

Definition--Ratios, Proportions, and Percents Concepts--Ratios with Decimals

Ratios with Decimals

Topic

Ratios, Proportions, and Percents

Definition

Ratios with decimals involve comparing two quantities where one or both of the quantities are represented as decimal numbers.

Description

Ratios with decimals are crucial in various real-world applications, particularly in financial calculations, engineering, and scientific measurements. For instance, when calculating financial ratios such as the price-to-earnings ratio, decimals are often involved. Understanding how to work with these ratios allows for more precise and meaningful comparisons.

Ratios and Rates
Definition--Ratios, Proportions, and Percents Concepts--Ratios with Fractions

Definition--Ratios, Proportions, and Percents Concepts--Ratios with Fractions

Ratios with Fractions

Topic

Ratios, Proportions, and Percents

Definition

Ratios with fractions compare two quantities where one or both of the quantities are fractions.

Description

Ratios with fractions are essential in various mathematical and real-world contexts, such as cooking, where ingredients are often measured in fractions. Understanding these ratios allows for accurate scaling of recipes or other measurements. For example, if a recipe calls for 1/2 cup of sugar to 1/4 cup of butter, the ratio is 1/2:1/4, which simplifies to 2:1 by multiplying both terms by 4.

Ratios and Rates
Definition--Ratios, Proportions, and Percents Concepts--Ratios with Percents

Definition--Ratios, Proportions, and Percents Concepts--Ratios with Percents

Ratios with Percents

Topic

Ratios, Proportions, and Percents

Definition

Ratios with percents involve comparing quantities where one or both of the quantities are expressed as percentages.

Description

Ratios with percents are widely used in various fields, including finance, statistics, and everyday life. For example, when comparing interest rates, growth rates, or discount rates, percentages are often used. Understanding these ratios allows for better financial decision-making and data analysis.

Ratios and Rates
Definition--Ratios, Proportions, and Percents Concepts--The Golden Ratio

Definition--Ratios, Proportions, and Percents Concepts--The Golden Ratio

The Golden Ratio

Topic

Ratios, Proportions, and Percents

Definition

The Golden Ratio is a special number approximately equal to 1.618, often denoted by the Greek letter φ (phi), which appears in various aspects of art, architecture, and nature.

Applications of Ratios, Proportions, and Percents and Ratios and Rates
Definition--Ratios, Proportions, and Percents Concepts--Unit Rate

Definition--Ratios, Proportions, and Percents Concepts--Unit Rate

Unit Rate

Topic

Ratios, Proportions, and Percents

Definition

A unit rate is a comparison of any two separate but related measurements when one of the measurements is reduced to a single unit.

Description

Unit rates are commonly used in everyday life, such as calculating speed (miles per hour), cost per item, or efficiency (miles per gallon). For example, if a car travels 300 miles on 10 gallons of gas, the unit rate is 30 miles per gallon.

Ratios and Rates
Definition--Ratios, Proportions, and Percents Concepts--Visualizing Equivalent Ratios

Definition--Ratios, Proportions, and Percents Concepts--Visualizing Equivalent Ratios

Visualizing Equivalent Ratios

Topic

Ratios, Proportions, and Percents

Definition

Visualizing equivalent ratios involves using diagrams or models to show that two ratios are equivalent.

Description

Visualizing equivalent ratios is important in fields such as mathematics and engineering, where understanding proportional relationships is crucial. For example, using a double number line or a ratio table can help illustrate that the ratios 2:3 and 4:6 are equivalent.

Ratios and Rates
Definition--Ratios, Proportions, and Percents Concepts--Visualizing Ratios

Definition--Ratios, Proportions, and Percents Concepts--Visualizing Ratios

Visualizing Ratios

Topic

Ratios, Proportions, and Percents

Definition

Visualizing ratios involves using diagrams or models to represent and understand the relationship between two quantities.

Description

Visualizing ratios is essential in various fields, such as mathematics, science, and economics, where understanding the relationship between quantities is crucial. For example, using a bar model or a double number line can help illustrate the ratio of 3:4.

Ratios and Rates
Desmos activity

Desmos Activity: Slope As Rate of Change

Desmos Activity: Slope As Rate of Change

Use this activity to explore slope as a rate of change. In this Desmos activity, the slope of the line is the rate (cost per pound) for purchasing fruit. Students manipulate the slider for m to see the impact on the cost.

Slope and Ratios and Rates
Formulas--Converting Celsius to Fahrenheit

Formulas--Converting Celsius to Fahrenheit

Formulas--Converting Celsius to Fahrenheit

The formula for the Converting Celsius to Fahrenheit.

This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file.

Related Resources

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

Applications of Ratios, Proportions, and Percents, Proportions and Ratios and Rates
Formulas--Converting Days to Hours

Formulas--Converting Days to Hours

Formulas--Converting Days to Hours

The formula for Converting Days to Hours.

This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file.

Related Resources

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

Applications of Ratios, Proportions, and Percents, Proportions and Ratios and Rates
Formulas--Converting Days to Minutes

Formulas--Converting Days to Minutes

Formulas--Converting Days to Minutes

The formula for Converting Days to Minutes.

This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file.

Related Resources

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

Applications of Ratios, Proportions, and Percents, Proportions and Ratios and Rates
Formulas--Converting Days to Seconds

Formulas--Converting Days to Seconds

Formulas--Converting Days to Seconds

The formula for Converting Days to Seconds.

This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file.

Related Resources

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

Applications of Ratios, Proportions, and Percents, Proportions and Ratios and Rates
Formulas--Converting Degrees to Radians

Formulas--Converting Degrees to Radians

Formulas--Converting Degrees to Radians

The formula for Converting Degrees to Radians.

This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file.

Related Resources

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

Applications of Ratios, Proportions, and Percents, Proportions and Ratios and Rates
Formulas--Converting Fahrenheit to Celsius

Formulas--Converting Fahrenheit to Celsius

Formulas--Converting Fahrenheit to Celsius

The formula for Converting Fahrenheit to Celsius.

This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file.

Related Resources

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

Applications of Ratios, Proportions, and Percents, Proportions and Ratios and Rates
Formulas--Converting Hours to Minutes

Formulas--Converting Hours to Minutes

Formulas--Converting Hours to Minutes

The formula for Converting Hours to Minutes.

This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file.

Related Resources

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

Applications of Ratios, Proportions, and Percents, Proportions and Ratios and Rates
Formulas--Converting Hours to Seconds

Formulas--Converting Hours to Seconds

Formulas--Converting Hours to Seconds

The formula for Converting Hours to Seconds.

This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file.

Related Resources

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

Applications of Ratios, Proportions, and Percents, Proportions and Ratios and Rates
Formulas--Converting Minutes to Seconds

Formulas--Converting Minutes to Seconds

Formulas--Converting Minutes to Seconds

The formula for Converting Minutes to Seconds.

This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file.

Related Resources

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

Applications of Ratios, Proportions, and Percents, Proportions and Ratios and Rates
Formulas--Converting Radians to Degrees

Formulas--Converting Radians to Degrees

Formulas--Converting Radians to Degrees

The formula for Converting Radians to Degrees.

This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file.

Related Resources

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

Applications of Ratios, Proportions, and Percents, Proportions and Ratios and Rates
Formulas--Converting Seconds to Days

Formulas--Converting Seconds to Days

Formulas--Converting Seconds to Days

The formula for Converting Seconds to Days.

This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file.

Related Resources

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

Applications of Ratios, Proportions, and Percents, Proportions and Ratios and Rates
Formulas--Converting Seconds to Hours

Formulas--Converting Seconds to Hours

Formulas--Converting Seconds to Hours

The formula for Converting Seconds to Hours.

This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file.

Related Resources

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

Applications of Ratios, Proportions, and Percents, Proportions and Ratios and Rates
Formulas--Converting Seconds to Minutes

Formulas--Converting Seconds to Minutes

Formulas--Converting Seconds to Minutes

The formula for Converting Seconds to Minutes.

This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file.

Related Resources

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

Applications of Ratios, Proportions, and Percents, Proportions and Ratios and Rates
Fibonacci Sequence

Instructional Resource--Fibonacci Sequence, Lesson 4

Instructional Resource | Fibonacci Sequence, Lesson 4

This is a continuation of our exploration of the Fibonacci Sequence. In this lesson we look at the Golden Ratio phi.

—PRESS PREVIEW TO VIEW THE LESSON— To see the other lessons in this series, click on the link.

Note: The download is a PDF file.

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Sequences, Ratios and Rates and Proportions
Year of the Fibonacci Rabbit

Instructional Resource--Fibonacci Sequence, Lesson 5

Instructional Resource | Fibonacci Sequence, Lesson 5

This is a continuation of our exploration of the Fibonacci Sequence. In this lesson we look at the Golden Ratio phi.

—PRESS PREVIEW TO VIEW THE LESSON— To see the other lessons in this series, click on the link.

Note: The download is a PDF file.

Related Resources

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

Sequences, Ratios and Rates and Proportions