Make sense and persevere

I teach 8th grade Pre-Algebra in a Special Education resource room.  This year I have been blessed with an amazing group of students!  They all try so hard every day to grasp the concepts I am teaching them.  

This week I was particularly proud of them.  We are coming to the end of our unit on linear equations, and I came up with an activity which would really let them demonstrate their knowledge of linear equations and the flexibility to represent the information in various forms.  I knew it was a very challenging activity, but I had confidence that they would all give it 110% of their effort.  

Before we started, I warned them this was going to be really challenging.  They moaned and groaned.  I explained to them that this activity combines everything they've learned so far in this unit and will really show that they understand linear equations.  I first displayed a similar but blank problem up on the SmartBoard.  I pointed out that there were three forms of equations, a table, a graph, and the slope and x- and y-intercepts that needed to be identified.  I told them to all put their detective caps on because they were going to solve a puzzle.  I was going to give them just 1 piece of information, and they have to fill in every other piece of missing information.  You should have seen their faces!  Looks of panic, disbelief, and total lack of confidence.  

I get really math-geeky and excited at this point.  I explain to them that this is soooo cool because everything interconnects with everything else.  That there is more than one way to figure out each piece of the puzzle.  That there is more than one path to get from start to finish.  They look at me like I've totally lost it!

(Warning: I'm about to ramble!)

So, I put one piece of the puzzle up on the board -- a standard form equation.  I ask them what we can do with this?  What information can we get from the standard form of an equation?  They look at me with blank stares and shrugging shoulders.  I guided them to finding the intercepts.  Then I asked them what the intercepts could do for us?  I started to see some light bulbs go on.  I graphed the line using the intercepts. Then I explained that they could have also transformed the standard form into slope-intercept form first in order to graph it.  Then I asked them what we can get from the graph?  Someone volunteered "the slope!"  So we found the slope (and I reminded them that if we had found the slope-intercept form first, we would already have the slope), and I asked what can we do with the information we have so far?  No responses...  I asked if we could write one of the missing equations?  "Oh yeah!"  So we wrote the slope-intercept form of the equation.  (OK, here I go again with more questions -- I really had to drag it out of them the first time through!)  Can we fill in the table of values yet?  I saw mostly blank stares and shrugging shoulders again.  "Substitution" was my clue to them.  One students remembered that they could substitute the x-values I had provided them into the slope-intercept form of the equation to find y.  So we went through that process, painfully...  Then I erased all the y-values and asked them if they could think of another way to fill in the table without substitution.  No responses.  Which order pair do we already know?  What's the special ordered pair in the table?  "Oh, the y-intercept is the one with the zero for x!"  OK, so how can we fill in the rest of the table if we know this one ordered pair?  Can we use the fact that we already know the 'change in y over the change in x'?  "Oh yeah, we know the slope, so we can use that!"  We finished filling in the table using the slope.  Once we had the table complete, I asked if we could now write the point-slope form.  After we did, I explained that they could have also done that without the table since they had the slope and intercepts already and could have used one of the intercepts for the point in the point-slope form.  Phew!  Finally done!  It was exhausting...

But when we were done filling in all the information in, they said "Can we do another one?"  I was so excited that they wanted to do more!  I thought since they seemed so confused and frustrated by the whole process, that they would never in a million years want more!  But they were so persistent and determined to figure out how to put all the pieces of the puzzle together.  We did a few more "puzzles" where I gave them different pieces of information such as just the completed table of values, or just the graph.  When the class was almost over, they asked if we could do this again tomorrow!

My hope is that learning to be flexible and complete all the missing pieces of the puzzle from any starting point will help them truly understand linear equations.  They really demonstrated Mathematical Practice Standard #1 - Make sense of problems and persevere in solving them. I've never seen them work so hard and I was very proud!

Slope and Intercepts Review with ThingLink and Zaption

Before the holiday break, I had taught my classes about slope and intercepts.  Twelve days later, I did not expect them to recall anything about either of these concepts, so I planned a "Slope & Intercepts" review for the first day back. 




In the beginning of the school year, I had set up a "Know Your Fractions" review using ThingLink and ThatQuiz.  It was a self-paced review where students watched a video tutorial that I had created using Explain Everything, worked on some practice problems, and then took an assessment with ThatQuiz.  I decided that since it worked so well, I would use ThingLink again for this review, but as for the assessment piece, I changed from ThatQuiz to Zaption.

For those of you not familiar with it, Zaption allow you to create interactive videos by inserting text, images, or drawings, and assessment pieces such as open response, numerical response, multiple choice, checkboxes, or draw responses into the video of your choice.  You can also restrict viewers from skipping forward, allow them to skip backwards to review, and require viewers to answer all questions.  Zaption calls the final product a "tour".  You can share your tours by providing the link to your viewers or embedding it into a website.  (While my students used their Chromebooks to view my Zaption tours, Zaption also has an iPad app.)

notes were found throughout the videos 

questions were found at the end of each video

So I reused my own tutorial videos that I had created a few years ago, added some notes throughout the videos, and then 3-4 questions at the end of each video (you can add them at any point during the video, I just chose to place them at the end).  Zaption saves the analytics from your viewers' sessions so you can see how they did later on.  I kept an eye on the analytics as my students were completing each video so I could be proactive and meet with each student to discuss their errors and prevent them from repeating their errors on the practice problems they were to complete after the videos.  I also used the analytics to compile a list of the top 4 errors that were made by all of my students.  I used these 4 problems as my 'Do Now' for the following day to address the common errors with the entire class.

overall statistics for the tour

statistics per question

I really like the way Zaption made my videos more engaging and interactive, and the fact that it collects data for me.  One of my goals this year is to use data such as this for my formative assessments in order to address student error as quickly and efficiently as possible.  Zaption made this super easy!