Shaun Errichiello Middle School 255 SALK SCHOOL OF SCIENCE, NEW YORK, NY
8th Grade Math : Unit #12 - Gimme the Base: More with Exponents : Lesson #6

Khan Challenge Adding and Subtracting Radicals

Objective: SWBAT to add and subtract terms in radical expressions.
Standards: 8.EE.A.1 8.EE.A.2 MP6 MP8
Subject(s): Math
60 minutes
1 Assessment Overview - 10 minutes

Like yesterday's lesson, everyone can take on today's challenge (See Khan Academy and Simplifying Radicals for more background on this strand of lessons). Many students can also use this time to review earlier topics from the year. My students keep track of their progress in each standard, so an alternative choice would be to go back to an earlier module on something we covered from the year, take notes on their work and create solve and explain a similar problem. Whatever choice they make, there needs to be a feedback loop between them and myself. They still need to turn in or share something. Since there are many different modules being done in this lesson at the same time, we have a very interesting and rich share at the end. Students get a great review of the year as students share different challenges from the modules that they chose. 

If students are unsure if they should undertake today's challenge, explain to them what is required to "get it": They need to understand how to combine like terms and Simplify Radical Expressions. In my class, we completed this topic in the previous class. If students are comfortable with those two topics, then they can work their way through this one. 

The assessment has two parts and it covers essential 8th grade work with radicals. The first assessment on simplifying radicals only works with basic values like the square root of 20. The second series deals with radicals and coefficients. For example, students will see problems like 3 times the square root of 20.

Students need to be familiar with prime factorization in order to approach the more complex problems. If I use this lesson to teach the topic, I make sure to set up a quick demonstration of prime factorization at the start (although I usually teach prime factorization in my number sense nit).

Link

Source URLhttp://youtu.be/JqYHHQHU1_Y (accessed Sept 9 2014)

This activity can be incredibly helpful if students slow down and take the time needed to think about what they are doing and why it makes sense. The series of exponent activities on Khan Academy can be done all in a row or spread out. They can be placed anywhere in the unit with great success. I wouldn't worry if students are perfectly prepared for any particular exercise at any time. Instead, use these assessments whenever you want. The digital environment is such a different experience that students will approach the problems with excitement and will often not connect the work to their experiences in class (at least not automatically and especially not in the beginning). 

For this activity I would ask students to log in (optional) and work until their achieve mastery. "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. They need to stop and reflect. They need to think, "do I need more practice?" 

2 The Assessment - 40 minutes

To access today's work, I have my students log into Khan Academy and then open a second tab and go straight to this link:

http://www.khanacademy.org/math/arithmetic/exponents-radicals/radical-radicals/e/adding_and_subtracting_radicals

Students can also go to the exercise dashboard and type in "adding and subtracting radicals."

http://www.khanacademy.org/exercisedashboard

Last year I set this up in a series of assignments through my website: 

https://sites.google.com/site/shaunteaches/khan-academy-notes

These are newer activities and haven't incorporated them onto my site yet, but the format will be similar.  

In my role today, the key is to ask students good follow up questions. The guidelines for their work are as follows:

  1. Finish the module until you reach "mastery."
  2. As you work, write the questions and answers in your notebook
  3. When you are finished, annotate your notes and explain some general observations you made as you worked. 
  4. Create solve and explain a challenge problem that be more challenging then the problems in this set. (I usually have several samples on the board which involve radical terms in a fraction and radical terms that can't be combined) 

I usually ask for the Part 4 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.

3 Assessment Review - 10 minutes

I finish this assessment by reviewing questions with the class. I log into Khan Academy and project for the whole class to see. I popcorn around the room and ask students to solve and explain. For each question I 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.