Illustrative Math Alignment: Grade 6 Unit 3

Topic

Ratios, Proportions, and Percents

Description

This image contrasts proportionality with non-proportional groups of coins (dimes and nickels). Ratios differ, clarifying when proportions do not exist. It explains non-proportionality to deepen understanding of proportional relationships.

Proportions are a foundational concept in mathematics, connecting ratios to real-world applications. Examples like those in this collection help students visualize and reason about proportional relationships in meaningful contexts, solidifying their understanding.

Topic

Ratios, Proportions, and Percents

Description

This image poses a question about proportional triangles, asking for the missing value (x) to maintain proportionality. It introduces problem-solving involving proportions, encouraging engagement and application.

Proportions are a foundational concept in mathematics, connecting ratios to real-world applications. Examples like those in this collection help students visualize and reason about proportional relationships in meaningful contexts, solidifying their understanding.

Topic

Ratios, Proportions, and Percents

Description

This image solves the posed proportion problem by finding the value of x using equivalent ratios (x/6 = 7/3). It breaks down the process of solving proportions, reinforcing mathematical reasoning.

Proportions are a foundational concept in mathematics, connecting ratios to real-world applications. Examples like those in this collection help students visualize and reason about proportional relationships in meaningful contexts, solidifying their understanding.

Topic

Ratios, Proportions, and Percents

Description

This image demonstrates proportionality in coins by calculating the number of nickels required for proportional groups (2/5 = 6/x). It closes the sequence with a real-world problem, consolidating the topic and providing a practical application.

Proportions are a foundational concept in mathematics, connecting ratios to real-world applications. Examples like those in this collection help students visualize and reason about proportional relationships in meaningful contexts, solidifying their understanding.

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.

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.

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.

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, 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.

This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents.

This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents.

This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents.

This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents.

This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents.

This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents.

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Fractions

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Fractions

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Fractions

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Fractions

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Fractions

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Fractions

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Fractions

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Fractions

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Fractions

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Fractions

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Fractions

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Fractions

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Fractions

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Fractions

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Fractions

Topic

The Math of Money

Description

What is the tax due on a $1000 purchase when the sales tax rate is 5%? The example shows how to apply the formula Tax Due = Cost * Tax Rate.

Calculating tax is a fundamental skill in understanding financial literacy. This example and others like it help illustrate how percentages are applied in real-world scenarios, such as shopping and services.

Seeing multiple worked-out examples allows students to recognize patterns and reinforce their understanding of applying formulas consistently in various contexts. It ensures they can adapt to different numbers and situations.

Topic

The Math of Money

Description

What is the tax due on a $9999.99 purchase when the sales tax rate is 9.9%? The example shows how to apply the formula Tax Due = Cost * Tax Rate.

Calculating tax is a fundamental skill in understanding financial literacy. This example and others like it help illustrate how percentages are applied in real-world scenarios, such as shopping and services.

Seeing multiple worked-out examples allows students to recognize patterns and reinforce their understanding of applying formulas consistently in various contexts. It ensures they can adapt to different numbers and situations.

Topic

The Math of Money

Description

What is the tax due on a $1500 purchase when the sales tax rate is 6%? The example shows how to apply the formula Tax Due = Cost * Tax Rate.

Calculating tax is a fundamental skill in understanding financial literacy. This example and others like it help illustrate how percentages are applied in real-world scenarios, such as shopping and services.

Seeing multiple worked-out examples allows students to recognize patterns and reinforce their understanding of applying formulas consistently in various contexts. It ensures they can adapt to different numbers and situations.

Topic

The Math of Money

Description

What is the tax due on a $2550 purchase when the sales tax rate is 7%? The example shows how to apply the formula Tax Due = Cost * Tax Rate.

Calculating tax is a fundamental skill in understanding financial literacy. This example and others like it help illustrate how percentages are applied in real-world scenarios, such as shopping and services.

Seeing multiple worked-out examples allows students to recognize patterns and reinforce their understanding of applying formulas consistently in various contexts. It ensures they can adapt to different numbers and situations.