Khan Academy and Squares

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SWBAT to work efficiently with perfect squares and be able to truncate irrational roots to the nearest whole number

Big Idea

Students need as many opportunities to practice and reflect as we can give them.

Assessment Overview

10 minutes

In working with my students, Khan Academy is a nice platform to help me differentiate learning opportunities. For an assessment like this one, I offer multiple modules. Sometimes there are even bonus modules.

Today, there are two practice modules. The assessment can be done in class or at home as a flipped lesson. Either way, I ask students to prepare for the assignment by watching the video I created to help students. 


The video covers perfect squares and will not take most students a long time. The only students who struggle with this module are those who struggle with basic multiplication facts. For students who continue to struggle with these facts into Grade 8, I use this module as a catalyst for intervention. I then review the basic facts with them and help them recognize some common patterns (I find that most of my students like patterns with 9's).

Once they finish with the perfect squares, they can work on some basic integer truncation. The prompts I give in this second assessment are very different from the Khan module. I expect students to show work and indicate which integer the root is closest to. 



Khan Academy is constantly changing its layout and its scoring system, but for this activity I would ask students to log in (optional) and work until their achieve mastery. This is a topic you need to discuss with 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?" 

The Assessment

40 minutes

This is one of the first times students in class have to transition between two assessments. I make sure that they understand the expectations and I make consistent announcements on time. I outline the steps of the assessment on the board and see if they have any questions. I expect them to manage their time here. My goal is to help them where I can. 

I have something like this on the board:

Assessment Steps:

Take Notes On All Steps

1) Review Perfect Square Intro 

2) Master Perfect Square Module

3) Review Estimating Square Roots Intro

4) Master Estimation Module

5) Write about experience

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

They could also go to the exercise dashboard and type in "square roots of perfect squares."

For the second exercise, they could click this link:

Or they could search "estimating square roots."

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

This exercise is new and was not used last year, but I will use it in future assessment lessons.

The key is to ask students a follow up question. The guidelines are as follows:

1) Create a more interesting problem involving only perfect squares. Show how to solve the problem. Hint: you could make it more interesting by adding a story, making an expression with operations, etc.

2) Truncate two numbers. Explain your reasoning with a number line.

I usually ask for these parts via email, but I prefer that students write out these specific prompts by hand.

As for their progress, I can monitor them directly through Khan Academy. 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.

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.