Illustrative Math Alignment: Grade 7 Unit 5

Topic

Rational Functions

In this TI Nspire tutorial for the TI-Nspire CAS, the Calculator Window is used to combine and simplify rational expressions. This video supports the TI-Nspire Clickpad and Touchpad. This Mini-Tutorial Video includes a worksheet. .

Topic

Rational Functions

Topic

Rational Functions

Description

Explains submarine pressure and volume relationships using rational functions, illustrating depth impacts on vessel integrity and scuba safety.

This video provides a detailed explanation of explains submarine pressure and volume relationships using rational functions, illustrating depth impacts on vessel integrity and scuba safety. and its significance in understanding rational functions.

Topic

Rational Functions

Description

Examines surface area to volume ratios in animals using rational functions, connecting these ratios to evolutionary adaptations in different climates.

This video provides a detailed explanation of examines surface area to volume ratios in animals using rational functions, connecting these ratios to evolutionary adaptations in different climates and its significance in understanding rational functions.

Topic

Rational Functions

Description

Demonstrates the optics of the Hubble telescope through rational functions, analyzing lens properties and asymptotes for image clarity.

This video provides a detailed explanation of demonstrates the optics of the Hubble telescope through rational functions, analyzing lens properties and asymptotes for image clarity and its significance in understanding rational functions.

After briefly reviewing the concept of inverse variation, this video explores Boyle’s law, a real world example of an inversely proportional relationship between pressure and volume of a gas. Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, it goes on to examine similarities and differences among rational functions and numbers. Finally, it takes a look at rational functions graphs and ends with a delightful example merging Euclidean and analytic geometry, thanks to the TI-Nspire technology. Concepts explored: functions, rational expressions, rational functions, asymptotes

In this Investigation we look at an application of rational functions: Boyle's Law. This video is Segment 1 of a 4 segment series related to Algebra Nspirations: Rational Functions and Expressions. Segments 1 and 2 are grouped together.

In this Investigation we look at graphs of rational functions. This video is Segment 3 of a 4 segment series related to Algebra Nspirations: Rational Functions and Expressions. Segments 3 and 4 are grouped together.

In this TI Nspire tutorial for the TI-Nspire CAS, the Calculator Window is used to multiply rational expressions. This video supports the TI-Nspire Clickpad and Touchpad. This Mini-Tutorial Video includes a worksheet. .

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

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 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

Proportions are explained as equivalent ratios used to solve real-world problems. Examples include matching juice mixtures and adjusting recipes. The video uses ratio tables and number lines to scale ratios proportionally in practical applications.

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

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 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

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

Topic

Ratios

Description

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

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

This video explains generating and comparing equivalent ratios. Examples include simplifying fractions, determining similarity in geometric shapes, and integrating multiple ratios into a comprehensive ratio. Applications extend to geometry and proportional reasoning.

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

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.

Topic

Ratios

Description

This video introduces rates, a type of ratio comparing different units, such as distance over time (speed) or dollars per hour (wage). Examples demonstrate calculating rates and converting units. Applications include measuring efficiency and performing unit conversions.

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 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.

Topic

Ratios

Description

The video focuses on unit rates, where the denominator equals one. It includes practical examples like finding the cost per pound of bananas or determining hourly wages. Applications extend to conversions and scaling calculations for various real-world tasks.

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

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

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.

In this TI Nspire tutorial for the TI-Nspire CAS, the Calculator Window is used to combine and simplify rational expressions. This video supports the TI-Nspire Clickpad and Touchpad. This Mini-Tutorial Video includes a worksheet. .

Topic

Rationals and Radicals

Definition

An asymptote is a line that a graph approaches but never touches.

Description

Asymptotes are significant in the study of Rational Numbers, Expressions, Equations, and Functions. They help in understanding the behavior of graphs of rational functions, particularly as the values of the variables approach certain limits. Horizontal asymptotes indicate the value that the function approaches as the input grows infinitely large or small. Vertical asymptotes show the values that the function cannot take because they cause division by zero.

Topic

Rationals and Radicals

Definition

The conjugate of a radical expression is obtained by changing the sign between two terms in a binomial.

Description

In the context of Radical Numbers, Expressions, Equations, and Functions, the concept of conjugates is essential for simplifying expressions. When dealing with radicals, particularly in the denominator, multiplying by the conjugate can help to rationalize the expression. This process eliminates the radical from the denominator, making the expression easier to work with.

Topic

Rationals and Radicals

Definition

The cube root of a number is a value that, when multiplied by itself three times, gives the original number.

Description

The cube root is a fundamental concept in Radical Numbers, Expressions, Equations, and Functions. It is the inverse operation of raising a number to the power of three. Understanding cube roots is crucial for solving equations involving cubic terms and for simplifying radical expressions.

Cube roots also appear in various real-world applications, such as calculating volumes and in certain physics equations. They are an integral part of higher-level mathematics, including algebra and calculus.

Topic

Rationals and Radicals

Definition

An extraneous solution is a solution derived from an equation that is not a valid solution to the original equation.

Description

Extraneous solutions often arise in the context of Rational and Radical Equations. They are solutions that appear during the process of solving an equation but do not satisfy the original equation. This can happen when both sides of an equation are squared or when other operations introduce additional solutions.

Topic

Rationals and Radicals

Definition

Factoring a radical involves expressing it as a product of simpler expressions.

Description

Factoring radicals is a key technique in the study of Radical Numbers, Expressions, Equations, and Functions. It simplifies complex radical expressions, making them easier to work with. This process is essential for solving equations and for performing algebraic manipulations involving radicals.

Understanding how to factor radicals is also important for simplifying expressions in calculus and higher-level mathematics. It helps in breaking down complex problems into more manageable parts.

Topic

Rationals and Radicals

Definition

The fourth root of a number is a value that, when raised to the power of four, gives the original number.

Description

The fourth root is an important concept in Radical Numbers, Expressions, Equations, and Functions. It is the inverse operation of raising a number to the power of four. Understanding fourth roots is crucial for solving higher-degree equations and for simplifying radical expressions.

Fourth roots are also relevant in various scientific and engineering applications where higher-degree roots are required. They are a part of advanced mathematical studies, including algebra and calculus.

Topic

Rationals and Radicals

Definition

The geometric mean of two numbers is the square root of their product.

Description

The geometric mean is an example of using radical expressions to solve a problem. It provides a measure of central tendency that is particularly useful in situations where the numbers are multiplied together rather than added.

In geometry, the geometric mean appears in various theorems and constructions. It is also used in finance and statistics to calculate average growth rates and to compare different sets of data.