Khan Academy on Positive and Zero Exponents
Lesson 3 of 17
Objective: SWBAT to work efficiently with basic positive and zero exponents
This assessment can be done at home or in class. Either way, I ask students to prepare for the assignment by watching the video I created to help students.
This video is a bit different from other Khan Academy prep videos I use in my class. Instead of preparing them directly for the practice module, it gives them an in depth lecture aimed at explaining the why and how connected to the Khan Academy exercise.
The video is about 6 minutes and I recommend that all students watch about 2 minutes of it. Then, I recommend that they pause and decide if they need more support. In the classroom, I set them up with headphones and a notebook. Writing notes encourages active listening. (This can not just be another YouTube video experience.) These mini videos are meant to help students grasp complex concepts and get started on mastering basic exponential algorithms
Source URL: http://youtu.be/lTrPkx5cdEw (accessed Aug 12, 2014)
Later in this lesson, as I teach, I make that connection for my students. To do that, I end each class with a discussion about the problems they tried and even review them in the beginning of the next class session. The goal is to consistantly spiral concepts, taking as many approaches as possible.
A challenge to using Khan Academy effectively is that KA is constantly changing its layout and its scoring system (as of Aug 2013), but for this activity I would ask students to log in (optional) and work until their achieve mastery. This is a topic I will need to discuss with my students. "Mastery" in Khan Academy might mean something like getting 20 correct, but I want students to complete about 10 questions and only continue if they think they need more practice.
I have had many students complain about Khan Academy. They get frustrated, because if they make a single mistake they need to basically start from the beginning. They find this discouraging. They kept working and working even when they understood the topic. They spent hours trying to get "mastery" and would give up if they hit the wrong button or number. Instead, they need to stop and reflect. They need to think, "do I need more practice?"
There are currently 12 exponent exercise sets on Khan Academy. They don't all apply to the 8th grade standards, but this is a nice opportunity to differentiate up and challenge students. I like to offer each assessment that is required and then point out the exercises that would be "awesome" to master. I have tried different incentive systems around the challenge concepts (challenges = badges), but the biggest hook is in the presentation of the challenge. Students have a natural tendency to want success. We are just giving them a chance to show how smart they really are.
The structure of the site is overwhelming to many students. To simplify the process, I have them log in to Khan Academy and then open a second tab and go straight to this link:
They could also go to the exercise dashboard and type in "exponents."
Last year I set this up in a series of assignments through my website so my students typically work from here:
A key to making these flipped lessons work is to ask students a follow-up question. The guidelines for the Positive and Zero Exponents Work are as follows:
- Finish the "Positive and Zero Exponents" Exercise Until you reach "mastery"
- As you work, write the questions and answers in your notebook
- When you are finished, annotate your notes and explain some general observations you made as you worked.
- Create solve and explain a challenge problem that would fit in this exercise group.
- Answer this question and use examples to support your reasoning: Many students could solve all these problems in their head. Could you explain how you might do something like 8^3 in your head? How would you argue that 8^0 does not equal 0?
I usually ask for the parts 4 and 5 via email. Since all students have set me up as a coach I can easily monitor their progress after class. I circulate during class and help students by asking them reflective questions, like "when you move the decimal, what are you doing to the number?"
I collect the notes from at least 1 student who has mastered the topic and 1 who is struggling.
I finish this lesson by reviewing questions with the class. I log into Khan Academy and project the tasks for the whole class to see. Then, I popcorn around the room and ask students to solve and explain.
For each question I usually ask for and get at least 2 algorithms, since students love to hear other strategies. I have noticed that many students use one strategy throughout all the problems and are usually so tired of it by the end that they crave a more efficient strategy. I wait until the end to share all strategies because I believe that process of struggling helps them process the importance of a more efficient strategy. If we just shared at the start, I think many students would blindly plug in the more efficient strategy without understanding why or how it is efficient.