Illustrative Math Alignment: Grade 6 Unit 1

This is the transcript for the video of same title. Video contents: In this Investigation we look at functions.

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Learn the basics of decreasing functions. Graphical and algebraic representations of decreasing functions are shown, as well as examples of such functions.

This video looks at the identity function. Students review the identity properties of addition and multiplication as a means of better understanding the identity function.

Learn the basics of increasing functions. Graphical and algebraic representations of increasing functions are shown, as well as examples of such functions.

This video looks at multiple representations of functions, including symbolic, tabular, and graphic. Examples of linear, quadratic, polynomial, and exponential functions are shown.

Topic

Functions and Relations

Topic

Functions and Relations

Topic

Functions and Relations

Description

This segment focuses on the circular orbit of the Orion capsule around Earth as it docks with the International Space Station. Key concepts include the circle as a conic section and its equation. Parametric equations with sine and cosine functions are introduced to model periodic motion. Applications involve understanding how the capsule maintains a stable orbit, completes periodic motion every 90 minutes, and prepares for the Mars journey.

Topic

Functions and Relations

Description

This segment describes the elliptical paths of Earth and Mars around the sun and how the Orion capsule follows a transfer ellipse to reach Mars. Key concepts include ellipses as conic sections, their equations, eccentricity, and quadratic relations. Applications involve modeling planetary orbits and calculating orbital equations using data like eccentricity and semi-major axis values. The segment also explores graphing ellipses with tools like the TI-Nspire.

Topic

Functions and Relations

Description

This section defines relations and functions, emphasizing domain, range, and dependent versus independent variables. Using examples like USB flash drive pricing, it illustrates tabular, graphical, and mapping representations. Key concepts include ordered pairs, Cartesian plane, and scatter plots. The TI-Nspire is utilized to model relationships and introduce functional analysis.

Topic

Functions and Relations

Description

In this Math Lab explore domain-to-range mappings for functions and relations.

Relevance to the Topic: This video is an essential resource for understanding Functions and Relations. By exploring the concepts and examples in this video, students will gain insights into the practical applications and theoretical underpinnings of Functions and Relations. It builds a strong foundation for future learning.

Topic

Functions and Relations

Description

Building on the prior section, this video elaborates on function rules and notation, graphing diverse functions such as linear, quadratic, and step functions. Key terms include domain, range, and vertical line test. Applications highlight real-world uses like analyzing study hours and grades. Technology aids in demonstrating increasing and decreasing functions visually.

Topic

Functions and Relations

Description

In this Math Lab use toothpicks to create unit squares and square arrays. Explore the functional relationship between length of the side of the square and the total number of toothpicks.