Guided Dragging Activity
In this activity we were exploring one of the types of dragging you can do with this technology: Guided Dragging. With guided dragging you can move points of a figure to give it a particular shape. While doing this, the drawing keeps its discovered property, and the points move along a certain path. We used the drag mode in this activity to explore the expectations of how what we constructed would act when moved and if it met our expectations when drug. We first had to create the triangle in a specific way so that points C, and D were on the x-axis but less than zero. Have point E be placed in between C and D. Have a line perpendicular to CD that also passed through E. Have a point F somewhere on that line that made the rest of the triangle, then we had to describe what changed and what stayed the same when dragging point F (Step 1). In step 2, we had to drag point F and notice how the area of the triangle changed as the height changed. Then envision a scatter plot what happened as we drug point F, what path did G follow. We got more of a clear answer after we traced the path of G. In step 3, we animated point F and the perpendicular line and described the line that appeared created by the point G, determined the equation of the line and talked about how the slope and y-intercept are related to the geometrical situation.
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Kaleidoscope Activity
In this activity, we were exploring the transformations in sketchpad. We first had to create two connecting segments in the shape of a V and construct a polygon on the inside of this V. Then we had to explain if we could rotate the polygon interior by reflection, and then reflect it and change the color of the reflected polygon. We then reflected the new polygon over the other segment and had to see what happened as we drug various points around, what were the reflective properties, and what would happen if we continued reflecting the final image through the two lines and repeated this. After doing this we created a custom tool when the V was at 45°. After using the custom tool multiple times, there were many reflected polygons in the form of a circle around the V. we then had to investigate how many concurrent interior angles and angles given (30°, 36°, 45°, 60°, and 72°) were there. Then at 60°, we had undo all the custom tool reflections until there were about seven reflections left so that, we could select three and dilate them (-1/2) about the vertex of V and change the color. The new dilated polygons were dilated again and changed colors. We then selected the remaining three original polygons and did the same thing. Then we answered how will animating the interior of the original pentagon affect the other figures. After doing all of this, we merged two points from the original polygon to the segments and then created three circles and merged the remaining three points to the circles and animated it. Thus creating a kaleidoscope.
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PowerPoint Activity
For this activity, we had to create a lesson within a PowerPoint that could be used to teach students a particular topic in math. The PowerPoint lesson was to be created to be used at the Augmentation level of the SAMR (Substitution, Augmentation, Modification, Redefinition) model. We had to use different functionalities of the PowerPoint and media to make the lesson more engaging. Within this lesson we needed to have a a warm up activity, a statement of objectives, and what students need to know, the teacher input, we had to add in potential questions we may ask in class, and a slide summarizing the main ideas of the lesson and what they will do n the next lesson or next day. I used a lesson I helped teach in my internship placement on Piecewise Functions. All the questions I put into the PowerPoint were questions that either I asked in class, or that came up in discussion. This PowerPoint that you will see is not how it was taught at the time, but would be taught like this in the future. To add more to this PowerPoint, I added a video that connected the lesson to something in real life. I also got the students to be more engaged in the lesson, by having them answer the questions throughout the PowerPoint in Padlet. I also added in some poll everywhere questions for the bellwork that shows the students participated and did the bellwork. At the end of the PowerPoint there is a link to the Homework, if you sign in and can't access it, I've also added to the right as a link.
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Representations-Slope Lesson Activity
For this activity we had to design a lesson to teach the concepts of slopes on a line. In order to do this we had to read Connecting Slope, Steepness, and Angles by Courtney R. Nagle and Deborah Moore-Russo from NCTM's The Mathematics Teacher, to help us come up with a lesson and use it as a basis. We had to design the lesson on Ti-Nspire's publish view. The lesson was to include the full range of functionalities and affordances in the publish view environment, so we had to use many Ti-Nspire Apps, Links and hyperlinks, Representations, Dynamic Representations, have Multiple Representations, have the correct Math Concepts, and have multiple math practices addressed. I used the concepts of rise over run, relating angles and the measure of a line's slope, and angles of elevation through a hot-air balloon scenario.
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Solving a Linear Equation Activity
In this activity we had to solve a linear two systems of linear equations by graphing but we had to do it differently then you normally would. We graphed the two equations, and showed their tables to see their intersection point. We then added the two equations together and showed each step along this process. At each step you can see the different graphs and how they were affected and the end result which is the same as the original.
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