Illustrative Math Alignment: Grade 6 Unit 2

Topic

Equations

Description

This segment explores the impact of colony collapse disorder on honey production using statistical data. It introduces box and whisker plots and the calculation of mean as statistical tools to analyze honey yields. Key vocabulary includes colony collapse disorder, box plot, and mean. Applications include modeling bee population declines and their broader ecological and agricultural implications.

Topic

Ratios

Description

The video covers practical applications of ratios for measuring slopes of roofs and ramps. Examples include comparing roof pitches, calculating base lengths of roofs, and determining ramp heights. Ratios provide clarity for gradual slopes.

Topic

Ratios, Proportions, and Percents

Definition

Calculating tax involves determining the percentage amount to be added to the base price of a product or service.

Description

Calculating tax is a fundamental application of percentages in real-world scenarios. When purchasing goods or services, the total cost is often the sum of the base price and the tax applied. Understanding how to calculate tax is essential for budgeting and financial literacy.

For example, if a product costs $50 and the tax rate is 8%, the tax amount is calculated as 

50 × 0.08 = 4

Therefore, the total cost is 

Topic

Ratios, Proportions, and Percents

Definition

Calculating tips involves determining the amount of money to give as a gratuity based on a percentage of the total bill.

Description

Calculating tips is a common use of percentages in everyday life, particularly in service industries such as dining. Tips are usually calculated as a percentage of the total bill, and understanding how to compute this is important for both customers and service providers. 

For instance, if a meal costs $80 and you want to leave a 15% tip, the tip amount is calculated as 

80 × 0.15 = 12

Topic

Ratios, Proportions, and Percents

Definition

Dimensional analysis is a method used to convert one unit of measurement to another using conversion factors.

Description

Dimensional analysis is a powerful tool in mathematics and science for converting units and solving problems involving measurements. It uses the principle of multiplying by conversion factors to ensure that units cancel out appropriately, leading to the desired unit.

For example, to convert 50 meters per second to kilometers per hour, you use the conversion factors  1 meter = 0.001 kilometers and 1 hour = 3600 seconds: 

Topic

Ratios, Proportions, and Percents

Definition

Ratios in simplest form are ratios that have been reduced to their smallest whole number terms.

Description

Reducing ratios to their simplest form is similar to the process of simplifying fractions, making it easier to compare and interpret data. A ratio is in simplest form when the greatest common divisor of the terms is 1.

For example, the ratio 8:12 simplifies to 2:3 by dividing both terms by their greatest common divisor, 4. This skill is essential for solving problems involving proportions and understanding relationships between quantities.

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.

The formula for the Converting Celsius to Fahrenheit.

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The formula for Converting Days to Hours.

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The formula for Converting Days to Minutes.

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The formula for Converting Days to Seconds.

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The formula for Converting Degrees to Radians.

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The formula for Converting Fahrenheit to Celsius.

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The formula for Converting Hours to Minutes.

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The formula for Converting Hours to Seconds.

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The formula for Converting Minutes to Seconds.

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The formula for Converting Radians to Degrees.

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The formula for Converting Seconds to Days.

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The formula for Converting Seconds to Hours.

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The formula for Converting Seconds to Minutes.

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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.

In this Algebra Application, students study the direction between diameter and circumference of a circle. Through measurement and data gathering students analyze the line of best fit and explore ways of calculating pi. The math topics covered include: Mathematical modeling, Linear functions, Data gathering and analysis, Ratios, Direct variation. This is a great back-to-school activity for middle school or high school students. This is also a great crossover activity that ties algebra and geometry.

In this Algebra Application, students learn about wildfires and the measurement of air quality. The math topics covered include: Scientific notation, Rates, Density, Data Analysis. The specific focus of this investigation is the health hazards from wildfire smoke. This includes a discussion of air density, measurement in microns, and measurement of air quality. Links to various web sites, including the EPA's site, provide relevant background information and data. The culminating activity is a case study of the wildfires in the Lake Tahoe area. Students analyze historical data and make a recommendation on the air quality. This is a great back-to-school activity for middle school or high school students. A relevant real-world application allows them to review math concepts.

This collection of clip art images includes images of 3D figures and composite figures.

This collection of clip art images includes images of 3D figures and composite figures.

This collection of clip art images includes images of 3D figures and composite figures.

February 2023. In this issue of Math in the News we look at NFL statistics for the number of concussions. The NFL now tracks concussion, and this is an opportunity to analyze this data and draw conclusions.

Note: The download is a PPT file.

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July 2015. This edition of Math in the News focuses on the severe drought currently taking place in California, and how it has impacted the water resources available to the state. In this edition, students will see how to use percentages given to determine actual amounts, and to determine percents out of a whole.

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May 2014. In this issue of Math in the News we explore Bitcoin. We look at how it's used for making purchases and how it differs from other currencies. This provides an opportunity to apply the concept of currency exchange.

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This is the transcript for the video of same title. Video contents: Why do rivers meander instead of traveling in a straight line? In going from point A to point B, why should a river take the circuitous route it does instead of a direct path? Furthermore, what information can the ratio of the river's length to its straight-line distance tell us? In this segment the geological forces that account for a river's motion are explained. In the process, the so-called Meander Ratio is explored. Students construct a mathematical model of a meandering river using the TI-Nspire. Having built the model, students then use it to generate data to find the average of many Meander Ratios. The results show that on average the Meander Ratio is equal to pi.

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.

Topic

Ratios

Description

This video introduces the concept of ratios, which describe relationships between quantities. Key concepts include writing ratios in different forms (e.g., 2:3, 2/3, and 2 to 3) and simplifying ratios. It also covers part-to-part ratios and part-to-whole ratios using examples like sports balls and colored shapes. Applications include categorizing objects and exploring numerical relationships in sets.

Topic

Ratios

Description

This video focuses on solving proportions algebraically, converting them into equations to solve real-world problems. Examples include predator-prey ratios, scaling pizza dough recipes, and creating shades of paint. The video demonstrates methods for handling terms in denominators and simplifying ratios to whole numbers.

Topic

Ratios

Description

The video explains how proportions are used to create scale drawings, ensuring geometric figures remain proportional. Examples include finding dimensions in similar triangles, scaling architectural models, and solving geometric problems. The concept of proportional relationships is key to accurate scaling.

Topic

Ratios

Description

This video demonstrates calculating rates from data sets, focusing on patterns like distance-time relationships and wages. Examples include determining car speeds, hourly wages, and unit costs of gasoline. Data tables are used to visualize and compute rates.

Topic

Ratios

Description

Rates are linked to slopes in linear functions. The video explores calculating rates of change for graphs of speed, savings growth, and loan repayment. It highlights using the slope formula to interpret and solve practical problems.

Topic

Ratios

Description

This video covers converting units using rates, with examples like speed conversion, currency exchange, and calculating seconds in a year. It emphasizes multiplication by conversion rates to transition between units effectively.

Topic

Ratios

Description

Ratios are connected to percentages in this video. Examples include finding percentages of items in collections. It develops a formula for converting part-to-whole ratios into percentages.

Relevance to the Topic: This video is a crucial resource for understanding the concept of Ratios. It delves into mathematical foundations by exploring how ratios function in real-life scenarios, such as scaling, comparisons, or visual representations. The mathematical principles demonstrated include proportional reasoning, equivalence, and fraction comparisons.

Topic

Ratios

Description

This video illustrates converting ratios to percents using visual aids like area models and grids. Examples include determining percentages of colored eggs, fruit types, and combinations of colored lights.

Topic

Ratios

Description

The video explores working with ratios involving decimals, such as finding unit costs or recycling rates. Scientific notation and multi-step conversions are used to calculate speeds of spacecraft like Voyager I.

Topic

Ratios

Description

The video covers practical applications of ratios for measuring slopes of roofs and ramps. Examples include comparing roof pitches, calculating base lengths of roofs, and determining ramp heights. Ratios provide clarity for gradual slopes.

Topic

Ratios

Description

The video covers practical applications of ratios for measuring slopes of roofs and ramps. Examples include comparing roof pitches, calculating base lengths of roofs, and determining ramp heights. Ratios provide clarity for gradual slopes.

Topic

Ratios

Description

The video explains ratios involving more than two items, such as 1:3:4, and how they encompass multiple pairwise ratios. Applications include recipes where ingredients are combined in specific proportions. It demonstrates working forward and backward with ratios to identify components or adjust quantities proportionally.

This is part of a collection of video tutorials on the topic of Ratios and Proportions. This series includes a complete overview of ratios, equivalent ratios, rates, unit rates, and proportions. The following section will provide additional background information for the complete series of videos.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items. The purpose of a ratio is find the relationship between two or more items in the collection.

Let's look at an example.

This is part of a collection of video tutorials on the topic of Ratios and Proportions. This series includes a complete overview of ratios, equivalent ratios, rates, unit rates, and proportions. The following section will provide additional background information for the complete series of videos.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items. The purpose of a ratio is find the relationship between two or more items in the collection.

Let's look at an example.

Topic

Ratios

Description

This video focuses on ratios written with fractions, showing how to convert fractional ratios into whole-number ratios by eliminating denominators. Applications include recipes and ensuring proportions are maintained in measurements. It emphasizes mathematical manipulation to align ratios with practical uses.

Topic

Ratios

Description

Ratios are compared to fractions, emphasizing differences between part-to-part and part-to-whole relationships. Examples include finding fractions of subsets within a collection and modeling classroom demographics. The video highlights deriving fractional equivalents from given ratios.

Topic

Ratios

Description

The video showcases visual representations like tape diagrams, snap cubes, and grids to solve ratio problems. It includes examples such as determining quantities in coin collections and paint mixtures. Applications involve modeling real-world problems using clear, visual methods.

Topic

Ratios

Description

Numerical methods for handling ratios are explored, such as double number lines and ratio tables. Examples include tropical punch recipes and fruit stand inventories. These methods simplify complex ratio calculations and are adaptable to various practical scenarios.