Khan Academy and Simplifying Radicals

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SWBAT to work efficiently with basic radical expressions.

Big Idea

We can use prime factorization to break down the number inside a radical sign and then use those factors to simplify the expression.

Assessment Overview

10 minutes

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. The assessment has two parts and covers essential 8th grade work with radicals. The first assessment on simplifying radicals only works with basic values like the square root of 20.

Source URL

The second series deals with radicals and coefficients. For example, students will see problems like 3 times the square root of 20. I use this assessment at different times, but 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 unit).

Source URL

This activity is incredibly helpful if students slow down and take the time needed to think about what they are doing and why it makes sense.

The Assessment

40 minutes

For this Khan Academy based class session, I have students work on two modules:

My idea is to have them log in and work during class and then we review their progress at the end via a whole class discussion.

Teacher's Note: There are currently 12 exponent exercise sets on Khan Academy. They don't all apply to the 8th grade standards, but these two are both critical to my curriculum (they also tie nicely to 9th grade CCSS).

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

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

1. Finish each 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 would fit in each exercise group. 

I usually ask for 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.


The structure of the Khan Academy site is overwhelming to many students. To simplify the process, I have them log in and then open a second tab and go straight to this link:

They could also go to the exercise dashboard and type in "simplifying radicals."


For the second set, they could click this link:

Or they could just search "simplifying radicals" in the exercise dashboard.


Assessment Review

10 minutes

I finish this assessment lesson 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 different strategy, often wondering if there is a better way.

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 (MP1). 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 (MP5).