Illustrative Math Alignment: Grade 7 Unit 2

Topic

Linear Functions

Description

Applies linear functions to cycling, calculating hill grades and distances using slope formulas and graphing.

This video explores the mathematics behind Linear Functions, providing clear examples and engaging visuals to enhance understanding. It is an excellent resource for both introduction and reinforcement of key concepts.

Topic

Linear Functions

Description

Applies linear functions to cycling, calculating hill grades and distances using slope formulas and graphing.

This video explores the mathematics behind Linear Functions, providing clear examples and engaging visuals to enhance understanding. It is an excellent resource for both introduction and reinforcement of key concepts.

Topic

Linear Functions

Topic

Linear Functions

Topic

Linear Functions

Description

Introduces linear functions with examples like staircases, explaining slope, intercepts, and applications in real-world scenarios.

This video explores the mathematics behind Linear Functions, providing clear examples and engaging visuals to enhance understanding. It is an excellent resource for both introduction and reinforcement of key concepts.

Topic

Linear Functions

Description

Introduces linear functions with examples like staircases, explaining slope, intercepts, and applications in real-world scenarios.

This video explores the mathematics behind Linear Functions, providing clear examples and engaging visuals to enhance understanding. It is an excellent resource for both introduction and reinforcement of key concepts.

Topic

Linear Functions

Description

Uses linear regression to analyze US oil consumption trends, projecting future usage and potential impact of Alaskan oil production.

This video explores the mathematics behind Linear Functions, providing clear examples and engaging visuals to enhance understanding. It is an excellent resource for both introduction and reinforcement of key concepts.

Topic

Linear Functions

Description

Uses linear regression to analyze US oil consumption trends, projecting future usage and potential impact of Alaskan oil production.

This video explores the mathematics behind Linear Functions, providing clear examples and engaging visuals to enhance understanding. It is an excellent resource for both introduction and reinforcement of key concepts.

Topic

Linear Functions

Description

Models maximum heart rate during aerobic exercise with linear equations, creating exercise charts for various age groups.

This video explores the mathematics behind Linear Functions, providing clear examples and engaging visuals to enhance understanding. It is an excellent resource for both introduction and reinforcement of key concepts.

Topic

Linear Functions

Description

Models maximum heart rate during aerobic exercise with linear equations, creating exercise charts for various age groups.

This video explores the mathematics behind Linear Functions, providing clear examples and engaging visuals to enhance understanding. It is an excellent resource for both introduction and reinforcement of key concepts.

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 develop a linear mathematical model based on the maximum heart rate during exercise based on age. Using this model, students investigate heart rate for moderate and vigorous workouts. The math topics covered include: Mathematical modeling, Linear functions, Families of functions, Computational thinking. The culminating activity is for students to create a simple program (using either a spreadsheet or a programming language like Python) to develop an exercise chart. 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.

In this Algebra Application, students develop a linear mathematical model based on the maximum heart rate during exercise based on age. Using this model, students investigate heart rate for moderate and vigorous workouts. The math topics covered include: Mathematical modeling, Linear functions, Families of functions, Computational thinking. The culminating activity is for students to create a simple program (using either a spreadsheet or a programming language like Python) to develop an exercise chart. 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.

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 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 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 examine the budding industry of commercial space travel. Using data from the Bureau of Transportation Statistics, students build a mathematical model from historical airfare data. This model is used to predict when commercial space travel will become affordable. This also includes a discussion of inflation-adjusted costs and the future value of money. Topics covered: Mathematical modeling, Linear regression, Exponential functions, The time value of money.

In this Algebra Application, students examine the budding industry of commercial space travel. Using data from the Bureau of Transportation Statistics, students build a mathematical model from historical airfare data. This model is used to predict when commercial space travel will become affordable. This also includes a discussion of inflation-adjusted costs and the future value of money. Topics covered: Mathematical modeling, Linear regression, Exponential functions, The time value of money.

In this Algebra Application, students examine the budding industry of commercial space travel. Using data from the Bureau of Transportation Statistics, students build a mathematical model from historical airfare data. This model is used to predict when commercial space travel will become affordable. This also includes a discussion of inflation-adjusted costs and the future value of money. Topics covered: Mathematical modeling, Linear regression, Exponential functions, The time value of money.

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.

In this Slide Show, apply concepts of linear functions to the context of circumference vs. diameter.

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In this Slide Show, apply concepts of linear functions to the context of cost vs. time data and graphs.

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In this Slide Show, apply concepts of linear functions to the context of cricket chirps.

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In this Slide Show, apply concepts of linear functions to the context of distance vs. time data and graphs.

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In this Slide Show, apply concepts of linear functions to the context of Hooke's law.

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In this Slide Show, apply concepts of linear functions to the context of Hooke's law.

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In this Slide Show, apply concepts of linear functions to the context of momentum and impulse.

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In this Slide Show, apply concepts of linear functions to the context of rectangular perimeter.

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In this Slide Show, apply concepts of linear functions to the context of saving money.

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In this Slide Show, apply concepts of linear functions to the context of speed and acceleration.

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