Illustrative Math Alignment: Grade 8 Unit 3

A set of resources for the TI-Nspire, TI-Nspire CX, and the Nspire App.

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Each Jeopardy game comes with a large bank of questions, so each game experience is unique. These games are great for practice and review.

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The "Functions and Relations" collection from Media4Math provides a comprehensive set of definitions essential for understanding key mathematical concepts. This collection includes terms such as domain, range, function, relation, inverse function, and composite function. These definitions are crucial for students as they form the foundation for more advanced topics in mathematics, such as calculus and algebra.

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This collection of math examples provides a comprehensive exploration of function equations. These examples are designed to build and reinforce key skills, including understanding the structure of functions, solving function equations, and analyzing their graphical representations. The examples progress in complexity, allowing students to develop a deeper understanding of functions as they advance.

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Media4Math’s collection of examples on Building Functions offers a comprehensive exploration of function-related concepts. This curated set of examples is designed to progressively build students’ understanding, starting with foundational ideas and advancing to more complex applications. These examples cover a wide range of skills, such as identifying functions, constructing function rules, interpreting function graphs, and analyzing real-world applications.

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Here is a collection of PowerPoint presentations on selected topics in Quadratics.

This is a collection of instructional resources that use the Desmos graphing calculator. These are Google Slide Shows. Subscribers can download these as PPT presentation.

Here we gather key terms, definitions, and formulas around Measures of Central Tendency.

Here are a number of PowerPoint presentations that focus on different applications of linear functions.

This is the Teacher's Guide that accompanies Algebra Applications: Functions and Relations.

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This is the Teacher's Guide that accompanies Algebra Applications: Linear Functions.

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This is the Teacher's Guide that accompanies Algebra Applications: Quadratic Functions.

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Paleontologists rely on fossils to learn about dinosaurs. They also rely on certain algebraic concepts to help them estimate the sizes of dinosaurs based on the measurements of dinosaur footprints. In this activity, walk students through the solution of several proportions to estimate the sizes of different dinosaurs.

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This is the Teacher's Guide that accompanies Algebra Nspirations: Inequalities.

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To see resources related to this topic click on the Related Resources tab above.

This is the Teacher's Guide that accompanies Algebra Nspirations: Linear Functions.

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To see resources related to this topic click on the Related Resources tab above.

In this program, internationally acclaimed mathematics educator Dr. Monica Neagoy, explores the nature of linear functions through the use TI graphing calculators. Examples ranging from air travel, construction, engineering, and space travel provide real-world examples for discovering algebraic concepts. All examples are solved algebraically and then reinforced through the use of the TI-Nspire. Algebra teachers looking to integrate hand-held technology and visual media into their instruction will benefit greatly from this series. Concepts explored: Standard form, slope-intercept form, point-slope form, solving linear equations.

In this presentation we show how to convert a linear equation in Standard Form to a linear function in Slope Intercept Form. We go over the reason for such a conversion and applications that give rise to these equations. Note: The download is a PPT.

Linear Expressions, Equations, and Functions

Linear Expressions, Equations, and Functions

Linear Expressions, Equations, and Functions

Linear Expressions, Equations, and Functions

Linear Expressions, Equations, and Functions

Functions are relationships between quantities that change. Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, this video explores the definition of a function, its vocabulary and notations, and distinguishes the concept of function from a general relation. Multiple representations of functions are provided using the TI-Nspire, while dynamic visuals and scenarios put them into real-world contexts. Concepts explored: functions, relations, equations, quadratic functions, linear functions, multiple representations.

In this program, internationally acclaimed mathematics educator Dr. Monica Neagoy, explores the nature of linear functions through the use TI graphing calculators. Examples ranging from air travel, construction, engineering, and space travel provide real-world examples for discovering algebraic concepts. All examples are solved algebraically and then reinforced through the use of the TI-Nspire. Algebra teachers looking to integrate hand-held technology and visual media into their instruction will benefit greatly from this series. Concepts explored: Standard form, slope-intercept form, point-slope form, solving linear equations.

In this Investigation we look at linear models for objects moving at a constant speed. This video is Segment 1 of a 4 segment series related to Algebra Nspirations: Linear Functions. Segments 1 and 2 are grouped together.

In this Investigation we look at a linear regression for carbon dioxide emission data. This video is Segment 3 of a 4 segment series related to Algebra Nspirations: Linear Functions. Segments 3 and 4 are grouped together.

Topic

Functions and Relations

Definition

An absolute value function is a function that contains an algebraic expression within absolute value symbols. It is defined as 

$$ f(x) = |x| $$

where |x| denotes the absolute value ofx.

Description

The absolute value function is significant in mathematics because it measures the distance of a number from zero on the number line, regardless of direction. This function is linear in nature, as it can be broken into two linear pieces: one for 

$$ x \geq 0 $$

 and one for 

$$ x < 0 $$

Topic

Functions and Relations

Definition

A composite function is a function that is formed when one function is applied to the result of another function.

Description

Composite functions are significant in mathematics because they allow the combination of two functions to form a new function. This is denoted as (f∘g)(x) = f(g(x)). Composite functions are widely used in various fields, including computer science for function composition in programming and in calculus for chain rule applications. For example, if f(x) = 2x and g(x) = x + 3, then the composite function 

(f∘g)(x) = f(g(x)) = 2(x + 3) = 2x+6

Topic

Functions and Relations

Definition

Conic sections are the curves obtained by intersecting a plane with a double-napped cone.

Description

Conic sections include circles, ellipses, parabolas, and hyperbolas, which are fundamental in the study of geometry and algebra. These shapes are described by quadratic equations and have numerous applications in physics, engineering, and astronomy. For example, the orbits of planets are ellipses, and parabolic mirrors are used in telescopes and satellite dishes. The general quadratic equation for conic sections is 

Ax2 + Bxy + Cy2 + Dx + Ey + F = 0

Topic

Functions and Relations

Definition

A constant function is a function that always returns the same value, no matter the input.

Description

The constant function is one of the simplest types of functions in mathematics, expressed as 

f(x) = c

Topic

Functions and Relations

Definition

A continuous function is a function that does not have any breaks, holes, or gaps in its domain.

Description

Continuous functions are fundamental in calculus and mathematical analysis because they allow for the application of limits, derivatives, and integrals. A function f(x) is continuous if, for every point 𝑐 c in its domain, 

lim x→c ​ f(x) = f(c)