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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
Math Clip Art

Math Clip Art--Percent Visualizations 4

Math Clip Art--Percent Visualizations 4

This is a collection of clip art images that show visual models for percents.

Ratios and Rates and Percents
Math Clip Art

Math Clip Art--Percent Visualizations 5

Math Clip Art--Percent Visualizations 5

This is a collection of clip art images that show visual models for percents.

Ratios and Rates and Percents
Math Clip Art

Math Clip Art--Percent Visualizations 6

Math Clip Art--Percent Visualizations 6

This is a collection of clip art images that show visual models for percents.

Ratios and Rates and Percents
Math Clip Art

Math Clip Art--Percent Visualizations 7

Math Clip Art--Percent Visualizations 7

This is a collection of clip art images that show visual models for percents.

Ratios and Rates and Percents
Math Clip Art

Math Clip Art--Percent Visualizations 8

Math Clip Art--Percent Visualizations 8

This is a collection of clip art images that show visual models for percents.

Ratios and Rates and Percents
Math Clip Art

Math Clip Art--Percent Visualizations 9

Math Clip Art--Percent Visualizations 9

This is a collection of clip art images that show visual models for percents.

Ratios and Rates and Percents
Math Clip Art--Rates and Tape Diagrams: Cooking 1

Math Clip Art--Rates and Tape Diagrams: Cooking 1

Math Clip Art--Rates and Tape Diagrams: Cooking 1

This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems.

Ratios and Rates
Math Clip Art--Rates and Tape Diagrams: Cooking 10

Math Clip Art--Rates and Tape Diagrams: Cooking 10

Math Clip Art--Rates and Tape Diagrams: Cooking 10

This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems.

Ratios and Rates
Math Clip Art--Rates and Tape Diagrams: Cooking 11

Math Clip Art--Rates and Tape Diagrams: Cooking 11

Math Clip Art--Rates and Tape Diagrams: Cooking 11

This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems.

Ratios and Rates
Math Clip Art--Rates and Tape Diagrams: Cooking 2

Math Clip Art--Rates and Tape Diagrams: Cooking 2

Math Clip Art--Rates and Tape Diagrams: Cooking 2

This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems.

Ratios and Rates
Math Clip Art--Rates and Tape Diagrams: Cooking 3

Math Clip Art--Rates and Tape Diagrams: Cooking 3

Math Clip Art--Rates and Tape Diagrams: Cooking 3

This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems.

Ratios and Rates
Math Clip Art--Rates and Tape Diagrams: Cooking 4

Math Clip Art--Rates and Tape Diagrams: Cooking 4

Math Clip Art--Rates and Tape Diagrams: Cooking 4

This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems.

Ratios and Rates
Math Clip Art--Rates and Tape Diagrams: Cooking 5

Math Clip Art--Rates and Tape Diagrams: Cooking 5

Math Clip Art--Rates and Tape Diagrams: Cooking 5

This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems.

Ratios and Rates
Math Clip Art--Rates and Tape Diagrams: Cooking 6

Math Clip Art--Rates and Tape Diagrams: Cooking 6

Math Clip Art--Rates and Tape Diagrams: Cooking 6

This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems.

Ratios and Rates
Math Clip Art--Rates and Tape Diagrams: Cooking 7

Math Clip Art--Rates and Tape Diagrams: Cooking 7

Math Clip Art--Rates and Tape Diagrams: Cooking 7

This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems.

Ratios and Rates
Math Clip Art--Rates and Tape Diagrams: Cooking 8

Math Clip Art--Rates and Tape Diagrams: Cooking 8

Math Clip Art--Rates and Tape Diagrams: Cooking 8

This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems.

Ratios and Rates
Math Clip Art--Rates and Tape Diagrams: Cooking 9

Math Clip Art--Rates and Tape Diagrams: Cooking 9

Math Clip Art--Rates and Tape Diagrams: Cooking 9

This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems.

Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Rates, Image 1

Math Clip Art--Ratios, Proportions, Percents--Rates 01

Math Clip Art--Ratios, Proportions, Percents--Rates 01

Topic

Ratios, Proportions, and Percents

Description

The image shows a hurdler jumping over a hurdle, with an overlay of the golden ratio (1.618). It introduces the concept of rates by visually showing motion and proportions. This image sets the stage for understanding rates as a mathematical relationship and connects to the idea of proportion and efficiency, aligning with rates' use in describing relationships.

Ratios, Proportions, and Percents focuses on understanding and applying the concept of rates, which are comparisons of two quantities with different units.

Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Rates, Image 2

Math Clip Art--Ratios, Proportions, Percents--Rates 02

Math Clip Art--Ratios, Proportions, Percents--Rates 02

Topic

Ratios, Proportions, and Percents

Description

The image depicts a gas station with the formula Rate = a / b, where b ­≠ 0, defining rate as a ratio of two different units. It introduces the formal definition of rates, providing a foundation for subsequent examples that apply this definition in real-world contexts.

Ratios, Proportions, and Percents focuses on understanding and applying the concept of rates, which are comparisons of two quantities with different units.

Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Rates, Image 3

Math Clip Art--Ratios, Proportions, Percents--Rates 03

Math Clip Art--Ratios, Proportions, Percents--Rates 03

Topic

Ratios, Proportions, and Percents

Description

The image shows a car at a gas station with the formula Speed = Distance / Time, explaining speed as a specific example of rate. It connects the abstract concept of rates to a concrete example (speed), making the topic relatable and easier to understand.

Ratios, Proportions, and Percents focuses on understanding and applying the concept of rates, which are comparisons of two quantities with different units.

Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Rates, Image 4

Math Clip Art--Ratios, Proportions, Percents--Rates 04

Math Clip Art--Ratios, Proportions, Percents--Rates 04

Topic

Ratios, Proportions, and Percents

Description

The image highlights a gasoline pump with the formula Rate = Dollars / Gallon, illustrating the cost of gasoline as an example of rate. It applies the concept of rates to another common scenario, reinforcing the idea of rates in daily life and extending understanding from speed to cost per unit.

Ratios, Proportions, and Percents focuses on understanding and applying the concept of rates, which are comparisons of two quantities with different units.

Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Rates, Image 5

Math Clip Art--Ratios, Proportions, Percents--Rates 05

Math Clip Art--Ratios, Proportions, Percents--Rates 05

Topic

Ratios, Proportions, and Percents

Description

The image depicts a car with the formula Fuel Efficiency Rate = Miles / Gallon, explaining how fuel efficiency is measured as a rate. It introduces a third example of rates, connecting to environmental and economic considerations, and further solidifying understanding.

Ratios, Proportions, and Percents focuses on understanding and applying the concept of rates, which are comparisons of two quantities with different units.

Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Rates, Image 6

Math Clip Art--Ratios, Proportions, Percents--Rates 06

Math Clip Art--Ratios, Proportions, Percents--Rates 06

Topic

Ratios, Proportions, and Percents

Description

The image shows a fruit market with the formula Rate = Dollars / Pound, illustrating the cost of fruits and vegetables per unit weight. It expands the application of rates to another familiar scenario, demonstrating versatility in its use across contexts.

Ratios, Proportions, and Percents focuses on understanding and applying the concept of rates, which are comparisons of two quantities with different units.

Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Rates, Image 7

Math Clip Art--Ratios, Proportions, Percents--Rates 07

Math Clip Art--Ratios, Proportions, Percents--Rates 07

Topic

Ratios, Proportions, and Percents

Description

The image shows a carton of eggs priced at $4 a dozen, defining a unit rate where b = 1, expressed as whole numbers or decimals. It introduces the concept of unit rates, a special type of rate, laying the groundwork for calculations in subsequent images.

Ratios, Proportions, and Percents focuses on understanding and applying the concept of rates, which are comparisons of two quantities with different units.

Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Rates, Image 8

Math Clip Art--Ratios, Proportions, Percents--Rates 08

Math Clip Art--Ratios, Proportions, Percents--Rates 08

Topic

Ratios, Proportions, and Percents

Description

The image features lemons priced at $2.50 for 5, with the calculation Unit Rate = 2.50 / 5 = 0.50 per lemon. It provides a step-by-step calculation of unit rates, reinforcing the concept introduced earlier with practical application.

Ratios, Proportions, and Percents focuses on understanding and applying the concept of rates, which are comparisons of two quantities with different units.

Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Rates, Image 9

Math Clip Art--Ratios, Proportions, Percents--Rates 09

Math Clip Art--Ratios, Proportions, Percents--Rates 09

Topic

Ratios, Proportions, and Percents

Description

The image illustrates the cost of 5 pounds of ground beef at $15.75, with the calculation Unit Rate = 15.75 / 5 = 3.25 per pound. It demonstrates another example of calculating unit rates, solidifying the learner's ability to perform similar calculations.

Ratios, Proportions, and Percents focuses on understanding and applying the concept of rates, which are comparisons of two quantities with different units.

Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Rates, Image 10

Math Clip Art--Ratios, Proportions, Percents--Rates 10

Math Clip Art--Ratios, Proportions, Percents--Rates 10

Topic

Ratios, Proportions, and Percents

Description

The image shows a runner covering 8 miles in 1.25 hours, with the calculation Speed = 8 / 1.25 = 6.4 miles/hour. It reinforces the speed example from earlier, providing another opportunity to apply the concept of rates to motion.

Ratios, Proportions, and Percents focuses on understanding and applying the concept of rates, which are comparisons of two quantities with different units.

Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Ratios, Image 1

Math Clip Art--Ratios, Proportions, Percents--Ratios 01

Math Clip Art--Ratios, Proportions, Percents--Ratios 01

Topic

Ratios, Proportions, and Percents

Description

This image establishes the mathematical foundation for understanding ratios with an iconic example.

Ratios, Proportions, and Percents is a fundamental concept in mathematics that helps students understand proportional reasoning, scaling, and comparative analysis. These examples provide a bridge between abstract mathematical principles and real-world applications, helping students grasp the utility of ratios.

Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Ratios, Image 2

Math Clip Art--Ratios, Proportions, Percents--Ratios 02

Math Clip Art--Ratios, Proportions, Percents--Ratios 02

Topic

Ratios, Proportions, and Percents

Description

Definition of a ratio as a relationship between two quantities using sports balls. It introduces the concept of ratios in an accessible and relatable way.

Ratios, Proportions, and Percents is a fundamental concept in mathematics that helps students understand proportional reasoning, scaling, and comparative analysis. These examples provide a bridge between abstract mathematical principles and real-world applications, helping students grasp the utility of ratios.

Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Ratios, Image 3

Math Clip Art--Ratios, Proportions, Percents--Ratios 03

Math Clip Art--Ratios, Proportions, Percents--Ratios 03

Topic

Ratios, Proportions, and Percents

Description

Visual example of ratios using soccer balls and basketballs, expressed as 5:2, 5 to 2, and 5 / 2. Illustrates how ratios can be represented in multiple formats.

Ratios, Proportions, and Percents is a fundamental concept in mathematics that helps students understand proportional reasoning, scaling, and comparative analysis. These examples provide a bridge between abstract mathematical principles and real-world applications, helping students grasp the utility of ratios.

Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Ratios, Image 4

Math Clip Art--Ratios, Proportions, Percents--Ratios 04

Math Clip Art--Ratios, Proportions, Percents--Ratios 04

Topic

Ratios, Proportions, and Percents

Description

A table summarizing different ratios derived from the group of balls, e.g., soccer to baseball or soccer to basketball. Shows how to systematically calculate and organize ratios from a dataset.

Ratios, Proportions, and Percents is a fundamental concept in mathematics that helps students understand proportional reasoning, scaling, and comparative analysis. These examples provide a bridge between abstract mathematical principles and real-world applications, helping students grasp the utility of ratios.

Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Ratios, Image 5

Math Clip Art--Ratios, Proportions, Percents--Ratios 05

Math Clip Art--Ratios, Proportions, Percents--Ratios 05

Topic

Ratios, Proportions, and Percents

Description

Simplification of ratios in the table, e.g., 4 / 2 becomes 2 / 1. Highlights the importance of simplifying ratios for clarity and consistency.

Ratios, Proportions, and Percents is a fundamental concept in mathematics that helps students understand proportional reasoning, scaling, and comparative analysis. These examples provide a bridge between abstract mathematical principles and real-world applications, helping students grasp the utility of ratios.

Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Ratios, Image 6

Math Clip Art--Ratios, Proportions, Percents--Ratios 06

Math Clip Art--Ratios, Proportions, Percents--Ratios 06

Topic

Ratios, Proportions, and Percents

Description

Application of ratios to geometric shapes (circles, triangles, hexagons) with a table of ratios. Extends the concept of ratios to other objects, demonstrating versatility.

Ratios, Proportions, and Percents is a fundamental concept in mathematics that helps students understand proportional reasoning, scaling, and comparative analysis. These examples provide a bridge between abstract mathematical principles and real-world applications, helping students grasp the utility of ratios.

Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Ratios, Image 7

Math Clip Art--Ratios, Proportions, Percents--Ratios 07

Math Clip Art--Ratios, Proportions, Percents--Ratios 07

Topic

Ratios, Proportions, and Percents

Description

Simplified ratios in the table for geometric shapes. Reinforces the practice of simplifying ratios for better comprehension.

Ratios, Proportions, and Percents is a fundamental concept in mathematics that helps students understand proportional reasoning, scaling, and comparative analysis. These examples provide a bridge between abstract mathematical principles and real-world applications, helping students grasp the utility of ratios.

Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Ratios, Image 8

Math Clip Art--Ratios, Proportions, Percents--Ratios 08

Math Clip Art--Ratios, Proportions, Percents--Ratios 08

Topic

Ratios, Proportions, and Percents

Description

Example of a three-term ratio (Red : Yellow : Blue = 6 : 4 : 3) using lollipops. Expands understanding of ratios to include three quantities.

Ratios, Proportions, and Percents is a fundamental concept in mathematics that helps students understand proportional reasoning, scaling, and comparative analysis. These examples provide a bridge between abstract mathematical principles and real-world applications, helping students grasp the utility of ratios.

Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Ratios, Image 9

Math Clip Art--Ratios, Proportions, Percents--Ratios 09

Math Clip Art--Ratios, Proportions, Percents--Ratios 09

Topic

Ratios, Proportions, and Percents

Description

Three-term ratios applied to a recipe: Flour : Sugar : Milk = 3 : 2 : 1. Connects ratios to real-world applications, specifically in cooking.

Ratios, Proportions, and Percents is a fundamental concept in mathematics that helps students understand proportional reasoning, scaling, and comparative analysis. These examples provide a bridge between abstract mathematical principles and real-world applications, helping students grasp the utility of ratios.

Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Ratios, Image 10

Math Clip Art--Ratios, Proportions, Percents--Ratios 10

Math Clip Art--Ratios, Proportions, Percents--Ratios 10

Topic

Ratios, Proportions, and Percents

Description

Fractions in ratios: Milk to Water = 1/4 : 1/2, simplified to 1 : 2. Demonstrates handling fractional ratios and simplifying them to whole numbers.

Ratios, Proportions, and Percents is a fundamental concept in mathematics that helps students understand proportional reasoning, scaling, and comparative analysis. These examples provide a bridge between abstract mathematical principles and real-world applications, helping students grasp the utility of ratios.

Ratios and Rates
Math Clip Art--Ratios, Proportions, Percents--Ratios, Image 11

Math Clip Art--Ratios, Proportions, Percents--Ratios 11

Math Clip Art--Ratios, Proportions, Percents--Ratios 11

Topic

Ratios, Proportions, and Percents

Description

Demonstrates equivalent ratios by simplifying fractions for Red:Green (4:2 to 2:1) and Strawberries:Lemons (6:3 to 2:1). Emphasizes the concept of equivalent ratios by showing how they simplify to the same value, reinforcing previous examples.

Ratios, Proportions, and Percents is a fundamental concept in mathematics that helps students understand proportional reasoning, scaling, and comparative analysis. These examples provide a bridge between abstract mathematical principles and real-world applications, helping students grasp the utility of ratios.

Ratios and Rates
Math Clip Art--Simple Ratios 1

Math Clip Art--Simple Ratios 1

Math Clip Art--Simple Ratios 1

This is a collection of clip art images that show simple ratios.

Ratios and Rates
Math Clip Art--Simple Ratios 2

Math Clip Art--Simple Ratios 2

Math Clip Art--Simple Ratios 2

This is a collection of clip art images that show simple ratios.

Ratios and Rates
Math Clip Art--Simple Ratios 3

Math Clip Art--Simple Ratios 3

Math Clip Art--Simple Ratios 3

This is a collection of clip art images that show simple ratios.

Ratios and Rates
Math Clip Art--Simple Ratios 4

Math Clip Art--Simple Ratios 4

Math Clip Art--Simple Ratios 4

This is a collection of clip art images that show simple ratios.

Ratios and Rates
Math Clip Art

Math Clip Art: Slope vs. Rate

Math Clip Art: Slope vs. Rate

In these clip art images, show students the difference between ratios and rates. These images are useful when talking about slope as both a ratio and a rate. In particular, this is useful when talking about slope as a rate of change.

Slope and Ratios and Rates
Math Example--Ratios and Rates--Example 1

Math Example--Ratios and Rates--Example 1

Math Example--Ratios and Rates--Example 1

Topic

Ratios and Rates

Description

This math example focuses on understanding ratios using colored socks. The image displays a collection of red and blue socks, and students are asked to determine the ratio of red socks to blue socks. The solution demonstrates that there are 4 pairs of red socks and 4 pairs of blue socks, resulting in a ratio of 4 : 4, which simplifies to 1 : 1.

Ratios and Rates
Math Example--Ratios and Rates--Example 10

Math Example--Ratios and Rates--Example 10

Math Example--Ratios and Rates--Example 10

Topic

Ratios and Rates

Description

This example focuses on finding equivalent ratios using a collection of socks in various colors. The image shows socks arranged in rows, with black, green, white, and other colors present. Students are asked to find a ratio among three colors that is equivalent to 1 : 3 : 1.

Ratios and Rates
Math Example--Ratios and Rates--Example 11

Math Example--Ratios and Rates--Example 11

Math Example--Ratios and Rates--Example 11

Topic

Ratios and Rates

Description

This example focuses on finding equivalent ratios using a collection of socks in various colors. The image shows socks arranged in rows, with black, green, white, and other colors present. Students are asked to find a ratio among three colors that is equivalent to 1 : 4 : 1.

Ratios and Rates
Math Example--Ratios and Rates--Example 12

Math Example--Ratios and Rates--Example 12

Math Example--Ratios and Rates--Example 12

Topic

Ratios and Rates

Description

This example explores the concept of similar triangles using ratios. The image shows a right triangle with sides labeled as 9, 12, and 15 units. Students are asked to determine if this triangle is similar to a standard 3-4-5 Pythagorean triplet triangle.

Understanding similar triangles is an important application of ratios in geometry. This example demonstrates how ratios can be used to compare the sides of triangles and determine similarity. By scaling the sides of a known triangle (3-4-5) and comparing them to the given triangle, students can see how ratios maintain proportionality in similar shapes.

Ratios and Rates
Math Example--Ratios and Rates--Example 13

Math Example--Ratios and Rates--Example 13

Math Example--Ratios and Rates--Example 13

Topic

Ratios and Rates

Description

This example focuses on verifying the similarity of triangles using ratios. The image shows a right triangle with sides labeled 25, 60, and 65 units. Students are guided through a step-by-step process to determine if this triangle is similar to a 5-12-13 right triangle.

Ratios and Rates
Math Example--Ratios and Rates--Example 14

Math Example--Ratios and Rates--Example 14

Math Example--Ratios and Rates--Example 14

Topic

Ratios and Rates

Description

This example explores the concept of special right triangles using ratios. The image shows a right triangle with sides labeled 3, 3 2 2 ​ , and 6 units. Students are guided through a step-by-step process to verify if this triangle is similar to a 30°-60°-90° triangle.

Ratios and Rates
Math Example--Ratios and Rates--Example 15

Math Example--Ratios and Rates--Example 15

Math Example--Ratios and Rates--Example 15

Topic

Ratios and Rates

Ratios and Rates