Illustrative Math Alignment: Grade 6 Unit 9

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

What Are Ratios?

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

What Are Ratios?

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

This is the transcript for the video entitled, Desmos Geometry Exploration: Polygons. In this video tutorial the polygons are explored. Students are then shown how to construct polygons using the Desmos geometry tools. The Desmos geometry tools can be found at www.desmos.com/geometry.

This is the transcript for the video entitled, Desmos Geometry Exploration: Regular Polygons 1. In this video tutorial regular polygons are explored. The focus of this video is on triangles and quadrilaterals. Students are then shown how to construct regular polygons using the Desmos geometry tools. The Desmos geometry tools can be found at www.desmos.com/geometry.

This is the transcript for the video entitled, Desmos Geometry Exploration: Regular Polygons 2. In this video tutorial regular polygons are explored. The focus of this video is on pentagons and hexagons. Students are then shown how to construct regular polygons using the Desmos geometry tools. The Desmos geometry tools can be found at www.desmos.com/geometry.

Topic

Geometry

Description

Polygons are closed figures with straight sides. Regular polygons have congruent sides and angles, while irregular polygons do not. Desmos tools allow creating polygons like triangles and quadrilaterals and measuring their angles and sides. Key terms include congruent, vertices, and interior angles. Applications focus on understanding polygon properties and calculations.

Topic

Geometry

Description

This tutorial delves into constructing regular triangles and squares using Desmos. Regular polygons have congruent sides and angles. Techniques involve using circles and perpendicular bisectors. Key terms include equilateral, perpendicular bisector, and congruent. Applications explore creating and verifying geometric properties in polygons.

Topic

Geometry

Description

The video covers regular pentagons and hexagons, emphasizing their congruent sides and angles. Viewers use Desmos to construct these polygons, leveraging tools like circles and angle bisectors. Key terms include regular polygons, angle bisector, and transformations. Applications demonstrate advanced constructions and polygon properties.

This is the transcript for the video entitled, Desmos Geometry Exploration: Quadrilaterals with Parallel Lines. In this video tutorial the quadrilaterals with parallel sides are explored. This includes trapezoids, parallelograms, rhombuses, rectangles, and squares. Students are then shown how to construct such figures using the Desmos geometry tools.

This is the transcript for the video entitled, Desmos Geometry Exploration: Quadrilaterals with Parallel Lines. In this video tutorial the basics of quadrilaterals are explored. Students are then shown how to construct quadrilaterals using the Desmos geometry tools.

This is the transcript for the video entitled, Desmos Geometry Exploration: Quadrilateral Basics. In this video tutorial the basics of quadrilaterals are explored. Students are then shown how to construct quadrilaterals using the Desmos geometry tools.

To see the complete collection of video transcriptsy, click on this link.

Topic

Geometry

Description

The lesson focuses on quadrilaterals with non-parallel sides, such as scalene quadrilaterals and kites. It demonstrates using Desmos tools to construct and explore these shapes. Key terms include congruent adjacent sides, kite, and isosceles triangle. Applications showcase the geometric properties of kites, including perpendicular diagonals.

Topic

Geometry

Description

This video explores quadrilaterals with parallel sides, including parallelograms, rhombuses, rectangles, and squares. Using Desmos tools, viewers create and manipulate these shapes while learning properties like congruent sides and supplementary angles. Key terms include parallelogram, rhombus, and trapezoid. Applications emphasize understanding relationships between parallel sides and angles.

Topic

Geometry

Description

Quadrilaterals are four-sided figures with specific properties. Desmos tools show how to construct quadrilaterals, measure angles, and verify that their sum is always 360°. Key terms include diagonals, congruent triangles, and vertices. Applications emphasize building and analyzing quadrilaterals using geometric tools.

This is the transcript for the video entitled, Desmos Geometry Exploration: Classifying Triangle by Side. In this video tutorial triangles are classified by the side lengths that make up the triangle. Students are then shown how to construct such triangles using the Desmos geometry tools.

This is the transcript for the video entitled, Desmos Geometry Exploration: Classifying Triangle by Angle. In this video tutorial triangles are classified by the types of angles that make up the triangle. Students are then shown how to construct such triangles using the Desmos geometry tools.

The Desmos geometry tools can be found at www.desmos.com/geometry. The video is available for this tutorial at this link: https://www.media4math.com/library/video-tutorial-desmos-geometry-exploration-classifying-triangles-angle. Note: The download is a PDF file.

Related Resources

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

Desmos Collection

To see the complete collection of Desmos Resources go to this link: https://www.media4math.com/desmos-resources.

Note: The download is a PDF file.

This is the transcript for the video entitled, Desmos Geometry Exploration: Triangle Basics. In this video tutorial the basics of triangles are explored. Students are then shown how to construct triangles using the Desmos geometry tools.

To see the complete collection of video transcriptsy, click on this link.

Topic

Geometry

Description

Triangles are classified by side lengths: scalene (no congruent sides), isosceles (two congruent sides), and equilateral (three congruent sides). The video uses Desmos to explore these classifications. Key terms include congruent sides and scalene. Applications combine side and angle classifications for comprehensive triangle analysis.

Topic

Geometry

Description

The video classifies triangles by their angles, highlighting acute, right, and obtuse triangles. Using Desmos, viewers construct and manipulate triangles to understand these categories. Key terms include equiangular, isosceles, and base angles. Applications involve creating different types of triangles and analyzing their angle properties.

Topic

Geometry

Description

Triangles are defined as three-sided closed figures with internal angles summing to 180°. The video demonstrates creating triangles with Desmos tools and exploring their properties. Key terms include vertices, line segments, and angles. Applications include constructing and measuring triangles to verify their angle sums.

In this video tutorial points are defined. Students are shown how to construct and label points using the Desmos geometry tools. The Desmos geometry tools can be found at www.desmos.com/geometry. . . Related Resources To see additional resources on this topic click on the Related Resources tab above. Desmos Collection To see the complete collection of Desmos Resources click on this link.