Fall 2017 - Professor Kate Poirier

Month: September 2017

Complete all exercises in Venema Chapter 1. Bring your Geogebra file with you to class on Tuesday, October 3. You may like to save your .ggb files to a USB stick or you can upload them to your Geogebra online account.

It might seem like more exercises than it is, but most of them will have you perform a step-by-step construction in Geogebra, so the exercises build on each other.

$\LaTeX$ (pronounced LAY-teck) is a commonly used language for typesetting math. There are many ways to use $\LaTeX$ to create professional looking documents (most involve installing an implementation on your computer) but you can also use $\LaTeX$ to type math right in your OpenLab posts.

Professor Reitz has some great instructions for using $\LaTeX$ on the OpenLab here (scroll to “Typing math on the OpenLab”).

It can take some getting used to, your homework is to practice by submitting a comment on this post. Don’t worry about typing something that makes any mathematical sense, just try typing anything. Play around and make a giant mess in these comments. If something doesn’t work at first, don’t worry; just try again. (Note that your first OpenLab comment will have to be approved before it appears.)

You can mouse-over something to see what LaTeX code was. For example, mouse-over this: $\frac{d}{dx} \left( \int_a^x f(t)dt \right) = F(x)$ to see what I entered.

If you submit something that LaTeX doesn’t understand, it will display “formula does not parse” but you can also mouse-over that to see what was submitted.

Other resources:

Due date: Tuesday, October 24, 2:30pm

Individual topics will be assigned later. More details will be added later.

In addition to a presentation in class, your assignment is to include the following items in your ePortfolio:

1. The statement of the theorem/result that you have been assigned, written in $LaTeX$, in the body of the post. You may copy this statement word-for-word from the text, or paraphrase it. Either way, it must be complete and precise.
2. A link to a GeoGebra dynamic worksheet (uploaded to GeoGebra Tube) that helps students understand the statement of your theorem. The dynamic worksheet should be completely self contained. Think of the worksheet as playing the following role: You are teaching a geometry course and will be absent for one class. The lesson for that day is the topic you have been assigned for this project. The substitute teacher assigned to cover your class does not have a background in geometry, so your students will have to learn the topic exclusively from your dynamic worksheet. Your worksheet must take advantage of the benefits GeoGebra has over traditional paper worksheets (for example, you should make use of the drag test).

You may also include extra details either in the body of your post or in the dynamic worksheet, if you think they will be helpful. For example, you may include hints for the proof of your statement (why is the statement true?) or you may include helpful applications. These are optional and should only be included if they help students understand the statement.

There are many resources available online for help creating dynamic worksheets. Here’s one. Read Chapter 3 of the Venema text for other helpful tips. As a sample, here is the dynamic worksheet on Ceva’s theorem that we will explore in class.

Once again, your classmates will be asked to score your worksheet and offer detailed feedback. This will be similar to the rubric and feedback form for the Desmos mini-project.

Topic assignments

Chapter 0 of the Venema text has 11 short sections. Not all sections have exercises.

For Tuesday, read all 11 sections and complete all exercises in sections 0.3, 0.6, and 0.8 (8 questions total).

For each new geometric object introduced, try constructing the object in Geogebra. For each theorem stated, try performing a construction that illustrates the theorem when you apply the drag test.

NOTE: Since Tuesday follows a Thursday schedule, we’ll meet in G-208 (our usual Thursday room).

F-BF4

Inverse functions and their graphs

In this lesson, I want my students to explore the function and their inverse graphically. I am going to insert the function and its inverse in Desoms and I am going to insert x=y to help student to visualize the symmetry.

I will use 4 different pairs of functions and their inverse to make sure that students grasp the idea of function and their graphs.

then I will choose a random point from the function’s graph and show the student the inverse of that point and how that is connected to the inverse arithmetically.

The Transformation of the graph of quadratic function ax^(2) when a=1>0

In this lesson, i want to teach the transformation of quadratic function x^2 .I want to start the lesson by recalling quadratic equations, what is a quadratic equation, its standard form and when does a quadratic equation become a quadratic function. My goal for this lesson is to compare the original function y=x^2 with the graphs that we will get by shifting them horizontally and vertically , which at the end will make students to understand the point called vertex and the formula that helps to find a vertex. I also with use the blackboard plug values in the function, so I may ask students any question related to that.

Here is how the graphs on Desmos will look:

For the first project, I want to teach how students to interpret and create bar graphs and line plots by utilizing the Desmos program as a visual display. I made an example of both types of graphs by plotting points in a table for the line point graph. I spaced the points on the graph so that they represent the data correctly. I also used inequalities to fill certain spaces in order to fill the bar graphs.

https://www.desmos.com/calculator/gjjuusjxwv

In this lesson I will  give Examples about the inequalities  making sure that my student knows the different between the symbol  >,< or bigger than or equal or less than or equal  ,I will make sure they will knows where they have to shade in order to find the solution , where up the line or down the line, the line should be solid or should be dash line , and of course I will make them under stand the graph it self and how they use desoms  in order to solve the inequality equation.

Below is a copy of what a student submitted last fall for her Desmos project. As you can see, she included a brief description of the project, together with the Desmos link. For her presentation, she had prepared a detailed lesson using the board together with Desmos. In particular, she initially had most of her Desmos project hidden and then turned on the components one at a time during the lesson.

In this lesson, I am going to introduce the three basic transformations of a polygon in a 2 – coordinate plane using Desmos as a tool to present the work. I used Desmos to create polygons starting with creating points. Typically, I worked on basic transformations of a triangle: translation, reflection, and rotation. I used the table to create the points of a triangle. Also, I changed the point style to segment style so I can have the sides of a triangle. Then, I will use two main methods to do these transformations either by moving the points or writing out the coordinates of each point.

I will teach lesson explaining how to solve inequality and how you graph it using the graph line and also use  desmos  in order to benefit from using the technology in order to let the student understand the topic more clear, I have to mention to my student the meaning of the inequality and to make sure that the students have the ability to distinguish  between the   inequality

signs <, >  and also the signs bigger than or equal and smaller than and equal . I will teach my student how to solve those equation having the inequality signs and let them graph it at the board also I will make sure they knows how to use desoms  in order to show their solution for the inequality equation

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