Illustrative Math Alignment: Grade 7 Unit 4

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.

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.

Learn different strategies for finding the percent of a number. The Strategy Packs provide alternate ways of solving the same problem, giving your students different approaches to the same problem. The goal of the Strategy Packs is to encourage your students to think strategically when solving math problems.

Note: The download is a PPT file.

Learn different strategies for finding the number that is a given percentage of another number. The Strategy Packs provide alternate ways of solving the same problem, giving your students different approaches to the same problem. The goal of the Strategy Packs is to encourage your students to think strategically when solving math problems.

Note: The download is a PPT file.

Learn different strategies for finding the percent one number is of another. The Strategy Packs provide alternate ways of solving the same problem, giving your students different approaches to the same problem. The goal of the Strategy Packs is to encourage your students to think strategically when solving math problems.

Note: The download is a PPT file.

Learn different strategies for finding the percent one number is of another. The Strategy Packs provide alternate ways of solving the same problem, giving your students different approaches to the same problem. The goal of the Strategy Packs is to encourage your students to think strategically when solving math problems.

Note: The download is a PPT file.

In this Algebra Application, students study the life cycles of 13- and 17-year cicadas, as well as the populations of bird predators. Students develop a mathematical model using spreadsheets and investigate why the prime number life cycles help the cicadas. The math topics covered include: Mathematical modeling, Data gathering and analysis, Percent increase and decrease, Prime numbers and composites. This real world application of math concepts will engage your students.

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

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

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

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

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

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

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

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

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

Topic

Ratios, Proportions, and Percents

Description

The image introduces the concept of percent change with the formula: Percent Change = (New - Original) / Original * 100%. It establishes the formula as the foundation for understanding percent change throughout the sequence.

Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills.

Topic

Ratios, Proportions, and Percents

Description

This image explains that percent increase measures the change from one number to a greater number. It provides context for when to apply the concept of percent increase in real-life scenarios.

Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills.

Topic

Ratios, Proportions, and Percents

Description

This image highlights that the numerical increase is the difference between the new and original values. It adds clarity by breaking down the calculation into a numerical difference.

Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills.

Topic

Ratios, Proportions, and Percents

Description

This image demonstrates how numerical increase is represented as fractional change using the formula: (b - a) / a. It bridges numerical increase to fractional change, setting up for conversion to percent increase.

Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills.

Topic

Ratios, Proportions, and Percents

Description

This image shows the formula for percent change as a fractional change expressed as a percentage: (b - a) / a * 100%. It reinforces the connection between fractional change and percent increase as part of the calculation process.

Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills.

Topic

Ratios, Proportions, and Percents

Description

This image provides an example of a percent increase calculation from 8 to 10, resulting in 25%. It offers a practical example to illustrate how the formula is applied to real numbers.

Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills.

Topic

Ratios, Proportions, and Percents

Description

This image reiterates the example calculation, emphasizing that the change from 8 to 10 is a 25% increase. It reinforces understanding by repeating the example with emphasis on the interpretation of the result.

Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills.

Topic

Ratios, Proportions, and Percents

Description

This image defines percent decrease as the change from one number to a lesser number. It introduces the complementary concept of percent decrease to show both directions of percent change.

Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills.

Topic

Ratios, Proportions, and Percents

Description

This image explains that numerical decrease is the difference between the new and original values. It mirrors the earlier explanation of numerical increase, ensuring consistency in presenting both cases.

Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills.

Topic

Ratios, Proportions, and Percents

Description

This image demonstrates fractional change for a decrease using the formula: (b - a) / a. It completes the explanation of percent change by connecting numerical decrease to fractional representation.

Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills.

Topic

Ratios, Proportions, and Percents

Description

This image explains that percent decrease represents fractional change expressed as a percentage: (b - a) / a * 100%. It extends the explanation to show how fractional change can be converted to percent decrease.

Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills.

Topic

Ratios, Proportions, and Percents

Description

This image provides an example of a percent decrease calculation from 10 to 8, resulting in -20%. It offers a practical example illustrating the application of the formula to calculate percent decrease.

Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills.

Topic

Ratios, Proportions, and Percents

Description

This image reiterates the example, emphasizing that the change from 10 to 8 represents a 20% decrease. It reinforces understanding by summarizing the example with focus on the final interpretation of the result.

Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills.

Topic

Ratios, Proportions, and Percents

Description

The image illustrates the concept of an introductory image that visually connects percents with proportions, showcasing a grid and a formula (a / b = c / d) next to a hurdler and a large percent sign. The golden ratio a / b = 1.618 is also present, symbolizing relationships, and expands on this idea by showing that serves as a thematic and conceptual introduction to percents by emphasizing proportional relationships and the idea of ratios.

Topic

Ratios, Proportions, and Percents

Description

The image illustrates the concept of fractions with different denominators: 1/4, 2/5, 5/6, and 5/8, each depicted as shaded portions of circles. and expands on this idea by showing that highlights the challenge of comparing fractions with different denominators, setting up the need for a common framework such as percents.

Topic

Ratios, Proportions, and Percents

Description

The image illustrates the concept of and expands on the previous image by comparing and ordering the fractions using inequality symbols: 1/4 < 2/5 < 5/8 < 5/6. This image expands on this idea by emphasizing the difficulty of comparing fractions and transitions to the rationale for using percents as a standard for comparison.

Topic

Ratios, Proportions, and Percents

Description

The image illustrates the concept of converting the fractions 1/4, 2/5, 5/6, and 5/8 into percents (25%, 40%, 83.33%, 62.5%) with their corresponding pie diagrams. It expands on this idea by showing that introduces percents as an easier method for comparing fractions by representing them with a common denominator of 100.

Topic

Ratios, Proportions, and Percents

Description

The image illustrates the concept of how fractions such as 3/4 and 3/5 convert to percents (75% and 60%) using shaded 10 x 10 grids. It expands on this idea by showing the concept of percents using a visual and tangible representation, reinforcing the idea of 100 as the base for comparison.

Topic

Ratios, Proportions, and Percents

Description

The image illustrates the concept of connecting coins (1¢, 5¢, 10¢, 25¢) to their percent values of a dollar (1%, 5%, 10%, 25%). It expands on this idea by establishing a real-world application of percents, showing their utility in everyday contexts like money.

The topic of Ratios, Proportions, and Percents explores fundamental math concepts by using practical examples. This collection aids in visualizing the connection between different mathematical forms such as ratios, percents, and fractions, making abstract concepts more accessible to students.

Topic

Ratios, Proportions, and Percents

Description

The image illustrates percentages as fractions with a denominator of 100, such as 10% = 10 / 100, 15% = 15 / 100, and so on. It expands on this idea by showing how percents relate to fractions, reinforcing their equivalency and further grounding the concept.

The topic of Ratios, Proportions, and Percents explores fundamental math concepts by using practical examples. This collection aids in visualizing the connection between different mathematical forms such as ratios, percents, and fractions, making abstract concepts more accessible to students.

Topic

Ratios, Proportions, and Percents

Description

The image illustrates how to convert 1/4 to a percent using the proportion method: (1 / 4 = x / 100), solving for x = 25%. and expands on this idea by showing that provides a step-by-step method to convert fractions to percents, introducing proportional reasoning.

The topic of Ratios, Proportions, and Percents explores fundamental math concepts by using practical examples. This collection aids in visualizing the connection between different mathematical forms such as ratios, percents, and fractions, making abstract concepts more accessible to students.

Topic

Ratios, Proportions, and Percents

Description

The image illustrates the concept of converting a fraction to a percent using proportions, with 2/5 converting to 40%. and expands on this idea by showing that reinforces the proportion method with another example, building understanding through repetition.

The topic of Ratios, Proportions, and Percents explores fundamental math concepts by using practical examples. This collection aids in visualizing the connection between different mathematical forms such as ratios, percents, and fractions, making abstract concepts more accessible to students.

Topic

Ratios, Proportions, and Percents

Description

The image illustrates the concept of converting fractions to percents, dividing 5 by 8 to get 62.5% and expands on this idea by showing an alternative method for conversion, allowing for flexibility in approaches.

The topic of Ratios, Proportions, and Percents explores fundamental math concepts by using practical examples. This collection aids in visualizing the connection between different mathematical forms such as ratios, percents, and fractions, making abstract concepts more accessible to students.

Topic

Ratios, Proportions, and Percents

Description

The image illustrates the concept of the general equation for percents: a% * x = y, using the example 10% * 50 = 5. It emphasizes the three components of a percent equation: the percent, a base number, and the result, and expands on this idea by showing that establishes the foundational equation for solving percent problems, serving as a gateway to explore specific types of percent equations.

Topic

Ratios, Proportions, and Percents

Description

The image illustrates the concept of how to solve the question 'what is 15% of 250?' using the equation a% * x = y, with calculations explicitly shown as 15 * 2.5 = 37.5. and expands on this idea by showing that provides a clear, step-by-step example to apply the general percent equation, enhancing comprehension through practical application.

Topic

Ratios, Proportions, and Percents

Description

The image illustrates the concept of solving '150 is 30% of what number?' using the same equation a% * x = y and algebraic manipulation to find x = 500 and expands on this idea by showing that explains how to rearrange the percent equation to solve for different variables, expanding on problem-solving strategies.

Topic

Ratios, Proportions, and Percents

Description

The image illustrates solving the problem 'what percent of 90 is 45?' using the equation a% * x = y, and algebraically finding a% = 50% and expands on this idea by showing that demonstrates how to find the percent in percent equations, further developing flexibility in solving percent-related problems.

Topic

Ratios, Proportions, and Percents

Description

The image summarizes the three types of percent equations in a table format, highlighting the unknown variable in each scenario (percent, part, or whole) and expands on this idea by providing a comprehensive overview and categorization of percent problems, solidifying the framework introduced in earlier examples.

Topic

Ratios, Proportions, and Percents

Description

This image showcases the concept of proportions using a dynamic visual of a runner in action framed within a golden ratio spiral. The proportion is represented algebraically as a/b = c/d, linking visual and mathematical representations. It introduces proportions conceptually and visually, setting the foundation for the subsequent examples.

Topic

Ratios, Proportions, and Percents

Description

This image illustrates proportions using two equivalent ratios, represented by measuring cups and cupcakes. It simplifies proportions to relatable everyday examples. It connects proportions to practical examples, emphasizing the real-world relevance.

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 uses coins to demonstrate proportions. The image compares groups of quarters and nickels to highlight equivalent ratios (3:1 and 6:2). It solidifies the concept of equivalent ratios through another real-life example, reinforcing the idea.

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 proportions through a scale model example, comparing the height and width ratios of the Eiffel Tower in two scales. It highlights the application of proportions in scaling and models, bridging abstract and practical understanding.

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 shows proportionality between dimes and pennies using equivalent ratios (1:4 and 3:12). Mathematical steps verify proportionality. It introduces proportional reasoning and calculation steps to ensure clarity in identifying 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 presents proportional triangles, with side lengths maintaining equivalent ratios (2:3:4 and 6:9:12). It demonstrates geometric applications of proportions, extending the concept to shapes and measurements.

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.