The graphics are a solution to a problem for finding the general formula for Stellar Numbers. I changed the original graphic to two separate graphics make the solution easier to see, based on feedback my classmates in the course. The graphics are displayed as full size as the file sizes are reasonably small (around 100 KB). They are in PNG format with appropriate ‘alt’, ‘title’ and ‘caption’ fields. They support learning as it is much easier to visualize the solution through the use of graphics over methods such as explaining the solution using words.
Click here to download the audio file.
I created this audio file after receiving a suggestion from Keith about using audio to supplement teaching sound waves. I used an external microphone instead of the computer’s built-in one as I learned it makes a big difference in audio quality through this course. The sound files were downloaded from freesound.org which were licensed under the Creative Commons 0 License. I recorded my narration using Quicktime and stitched the parts together using GarageBand. The audio would be used to give students an introduction to the applications of sine waves in music.
The Video was one I created for the Multimedia Enhanced Lesson. In the lesson, my intent was for students to only have to refer to the video if they could not figure out how to find domain and range by looking at the gifs I created. I feel that students develop greater thinking skills if they are trying to understand concepts on their own rather than being told what they are. The video contains audio commentary that teaches step by step how to find the domain and range from the graph, which is the learning objective. I made the visuals to only include important elements without distractions. The video was made into .mp4 format using handbrake but 3bees.ca WordPress does not allow me to add .mp4 files to the Media Library as “this file type is not permitted for security reasons”. Therefore, I uploaded the video to YouTube and embedded it into the blog post. Normally, I would add a link to download the zipped .mp4 file (6.6 MB) also.
Understand how the graph of changes under the transformations and
In pairs, create a screencast that demonstrates your understanding of how changing variables for and for changes the graph of . The graphs should be transformed using sliders and the graphing tool on www.desmos.com and the screencast should include audio commentary by both students.
1. Go to Desmos Graphing Calculator and learn how to create sliders to change the values of variables and .
2. Investigate how changing for and for changes the graph of by testing various functions (for example: linear, rational, quadratic, cubic, exponential, logarithmic, trigonometric, modulus). You will need to test a wide range of values for and and take notes on when and how the graph changes.
3. Once you understand the effects of and , you are ready to create your screencast. Plan out what you want to show and a script for what you want to say. You can watch a sample screencast that I created for this task at the bottom of this post.
4. Be sure to check the assessment rubric so that you know what you should include and how you will be assessed.
5. Submit your screencast as a .mp4 video file to the assignment on our Google Classroom page.
Use of Desmos and Sliders
Does not contain sliders
Sliders are used but do not change the graphs correctly
Sliders are used correctly and effectively
Understanding of Transformations
Little to no understanding of how and transform the graphs is demonstrated
Some understanding of how and transform the graphs is demonstrated
Strong understanding of how and transform the graphs is demonstrated
Depth of Investigation
The effects of and are not investigated
The effects of and are investigated but in a general sense
The effects of and are investigated for different ranges of values such as
Both students do not present or the audio is difficult to hear
Both students present but the investigation results are unclear
Both students present and the investigation results are clear and the commentary is effective
I recently taught a unit on transformation of functions with my Grade 10 Math class and although I used an inquiry-based activity with a worksheet for them to fill out and demonstrate their understanding, I felt that there was room for the students to investigate on their own rather than completing a task just to fill in an answer. When I developed my own enhanced lesson, I realized how much understanding is needed in order to present on a topic and therefore felt that having students create their own presentation in the form of a screencast would require them to have a strong understanding of the learning objective. In the activity, I had students use Desmos Graphic Calculator which they are familiar with from other lessons, and get “hands-on” with the slider functionality which allows them to see how changes they make effect graphs in real time. I provided a sample screencast for students to refer to so they have an idea of what is expected. At first, I was undecided about providing this as I feared students would simply copy the format and all the submissions would seem the same. However, I have found from experience that when the task is too open-ended with little guidance or structure, students have a more difficult time reaching the learning objective. Also, this task requires much more investigation than the sample I provided which force students to have to inquire further. Finally, I provided a rubric on how they will be assessed so that students are aware of exactly what is required for the task. Some of the descriptors are also my way of guiding the students what exactly they need to be considering when studying this topic.
Here are some of the file storage systems I have used and some thoughts.
Google Drive and Google Backup and Sync
15GB – Free
100GB – $1.99/month
1TB – $9.99/month
(not sure if the CDN prices are accurate as I am in Japan)
This is what I currently use to backup all of my data because my school is a Google for Education school which means we get unlimited storage space. This is quite a nice perk because it means I can keep everything on my computer backed up in the cloud and not have to worry about choosing what to sync or reaching capacity. All of the school’s file sharing and storing for students and teachers is done on Google Drive.
Google Drive is my choice. I’m sure most people are familiar or use Google Drive or some other file syncing system but here are some features which you may not know about:
With the app downloaded on your computer, Google Drive becomes a folder on your Windows Explorer or Finder which you can drag and drop files into or browse seemlessly without waiting for pages to load (as with the browser version). The folder is continuously synced so whatever is in the folder is what is in the cloud.
Recently, Google launched Google Backup and Sync, which not only syncs your Google Drive folder but has the option to sync other folders and files on your computer. For example, you can Sync your desktop or your Photos for MacOS backup file.
If you right-click a file in Google Drive (on the browser), you can “manage versions” which allows you to download or go back to a previous version of a file. This has saved me many times when I hit save and close on a Word doc even though I didn’t want to save the changes I made.
You can share files and folders very easily with other people who have a gmail account.
The mobile app also allows you to access everything. Google Docs, Sheets, Slides look fine but other files such as Microsoft Word, Excel do not always display correctly.
2GB – Free
1TB – $9.99/month
I use Dropbox as a sub account. It works just fine and I don’t know if it does anything more or less than Google Drive. I do know that some of my app on my phone (like 1password) can link with Dropbox and backup the contents automatically.
1TB of photos – Free
10GB – Free
1TB – $9.99/month
I setup an account and tried it for the first time. It works very much like Google Drive and Dropbox.
One interesting thing I found was that you are able to create a new Microsoft Word, Excel or Powerpoint file right in the browser. I knew it was possible to create Microsoft Office documents from office.com but I found it interesting that this option was available from a third party.
Lesson Objective: Find the domain and range of a function from its graph.
We have learned that certain relationships between two variables are called functions. If a relationship is a function, then for every input there is only one output .
The domain is the set of all possible values of for a function. It is a set so we use set notation such as .
The range is the set of all possible values of for a function. It is also a set so we use set notation such as .
Find the domain and range of the function with the following graph.
Question #2 on Page 387
When I first started thinking about this assignment, I thought of topics that my students have struggled with in the past and Domain and Range topped my list. It is a difficult concept that diagrams in textbooks just don’t explain effectively. To enhance student learning, rather than relying on text and diagrams, I drew graphs of the function and domain/range on Desmos and used the animate feature with some Math tricks to show how the domain can be visualized. In addition to creating graphics using screenshots, I used GIPHY Capture to create short gifs for the lesson so the students can repeatedly watch the process. The minimal use of text is intentional so that students can try to develop understanding through visuals but I also added a video with explanations for students who need further support. To create the video, I used the screen recording feature in Quicktime, then used Handbrake to reduce the video file size from 113.3MB (.mov) to 7.2MB (.mp4). Finally, I uploaded the video to YouTube and embedded the video in the lesson. Quick LaTeX was used for all the Mathematical formulas.
The font used is Libre Franklin (a sans-serif font) for ease of reading and there is high contrast between the font and background colors for better comprehension and reading speed. Headers and lists with hyperlinks to anchors on the page are also used as organization tools (Webster, 2014). Domain and Range is a deep topic but this lesson focuses on one small chunk without extraneous elements in accordance to Cognitive Load Theory (Webster, 2010). I used interpretive graphics (Clark and Lyons, 2010) to show the relationship between the graph of the function and its domain and range. The gifs are provided so that students can learn at their own pace and watch an example over and over again until they understand, based on the Segmenting Principle (Mayer, 2014). The positioning of the diagrams, such as the static domain image shown directly below and the static range image shown directly to the right of the animation as well as the positions of the equations for the domain and range, are based on the Spacial Contiguity Principle (Mayer, 2014). I used narration for the video with no words on screen to avoid split attention and overloading the visual channel as prescribed by the Modality Principle (Mayer, 2014).
One of the components of the Math course I teach requires students to perform mental arithmetic and processing through audio cues so I thought it would be good to record a sample of what a test could sound like.
I recorded it a few times checking the audio quality and also shutting off the heater (it made a difference). I also edited the file in order to give the students 5 seconds to answer each question and also deleted sections with noise in the background.
This is a series of images that I created to teach the significance of the number ‘e’. I used Graphic for Mac, created the base image and then added layers with different colored parts. By showing and hiding different layers, I exported a series of images which I put into a slideshow to show the progression.
I created a graphic to use in my Grade 10 Math class to help with the learning objective: Continuation of a sequence of patterns and the determination of the general term. Many students were easily able to identify patterns for triangular and square numbers but had difficult when it came to these “Stellar numbers”. I tried to keep the selection of important information minimal and prominent and organize the graphic to help develop understanding of the underlying patterns. Some of the actions and tools I used were the simple color scheme of two colors to clearly identify the parts I was trying to highlight. After creating the graphic, I was unsure of the color choice as the cyan font is a little difficult to see.
I usually do my image editing in native apps like Pixelmator, Graphic and Preview for Mac. However, I thought I would try Sumopaint to crop and do some basic editing, like removing text, since students would have access to it when doing an assessment that requires editing images.
A cropped and “clean” version of the image that could be used to test the students
Through this activity, I also saw how limited the selection was for images of Mathematical diagrams on Creative Commons and on Flickr’s Creative Commons licensed photo selection. I had more success doing some searching in Wikimedia Commons but often the image is not exactly what I’m looking for. I hope to learn how to become better at creating my own images through this course.
Here I am experimenting with adding Math equations to my blog post. First, I (actually Keith) installed a plugin called QuickLaTeX on WordPress. If the shortcode is added to the page, it will send each piece of LaTeX code on the page to quicklatex.com, render them into images and return the URLs. I have noticed that the images are a little too low-res for my liking and I may experiment with other ways to get cleaner LaTeX equations on the page.