8: Appendix
- Page ID
- 238758
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 8.1: How to upload an image to Desmos
- This page offers a comprehensive guide for uploading images to Desmos, detailing steps for both web browser and app usage. It covers initiating graphing, signing in, setting axes values, and inserting images from devices, alongside instructions for moving and resizing them. It emphasizes the advantages of larger screens like iPads or computers for better analysis, as phone screens may hinder precision.
- 8.2: Getting set up with Desmos
- This page introduces Desmos, a free online calculator that enhances understanding of mathematical concepts through its statistical features. It outlines the account creation process at student.desmos.com for saving progress and receiving feedback. Basic graphing skills are covered, including equation input, domain restrictions, and graph customization. Users can find intersection points and access additional symbols via a keyboard icon.
- 8.3: Desmos User Guide.
- This page offers a comprehensive guide to the Desmos graphing calculator, covering function graphing, data table manipulation, and variable usage with sliders. It explains saving and sharing graphs, improving visibility settings, and utilizing various graphing modes, including Cartesian and Polar. Inputting expressions such as inequalities, piecewise functions, and parametric equations is also detailed, alongside useful keyboard shortcuts for enhanced navigation.
- 8.4: Using Desmos to Model Mathematics in the Real World
- This page describes a project using the Desmos graphing calculator for students to investigate how algebraic functions represent real-world objects. Students photograph instances of linear, quadratic, and power functions, then overlay graphs on these images. Instructions cover image importation, point creation, and equation development.
- 8.5: Activities using Desmos
- This page offers links to Desmos activities designed to improve understanding of mathematical concepts such as graphing, equations, and functions. Topics include plotting points, solving equations, linear equations and inequalities, domain and range, systems of equations, and function transformations. Each interactive activity can be accessed with a specific code, promoting engagement and collaborative learning.
- 8.6: Different forms of a quadratic relation using Desmos
- This page offers a guide for graphing parabolic equations with adjustable parameters ('k', 'a', 'h'). It explains how these parameters influence the parabola's shape and position, detailing vertices and direction of opening. The page also covers converting forms of equations and identifying key points like vertices and zeros. Real-world examples, such as a baseball’s flight, are used to demonstrate the practical application of these concepts.
- 8.8: Instructor Guide on using the Workbok
- This page suggests using the Math 140 Workbook to promote active learning through small group work and an initial mini lecture. Instructors should support rather than direct group activities, prioritizing engagement and inclusivity. Key practices include encouraging feedback and conducting a wrap-up session to discuss solutions. It concludes with a focus on self-reflection for instructors to enhance their teaching methods.