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# Khan Academy and Multiplying and Dividing with Scientific Notation

Lesson 10 of 22

## Objective: SWBAT to multiply and divide with numbers in scientific notation

*60 minutes*

#### Assessment Overview

*10 min*

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 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.

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 they 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.

**Teacher Note**: 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. Most students find this discouraging. If they work and work even after they understood the topic, they sometimes spend a lot of time trying to achieve "mastery" and the project gets derailed if they hit the wrong key on the keyboard. In order to overcome this, I encourage my students to stop and reflect: "Do I need more practice?"

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#### The Assessment

*40 min*

There are currently 5 scientific notation exercise sets on Khan Academy. This assessment might be best to do *before* the orders of magnitude activity (even though Khan lists the exercises in the reverse order). I like this activity because it give students a chance to master a fundamental topic.

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:

Mult. and Div. Scientific Notation

They could also go to the exercise dashboard and type in "multiplying and dividing scientific notation."

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. Finish the Multiplying and Dividing Scientific Notation Exercise 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 this exercise group.

5. Answer this question and use examples to support your reasoning: What is the product of (3 x 10^2) and (6 x 10^5) in scientific notation? What is the quotient of these numbers (try both orders)? Explain how you know you are right.

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 one student who has mastered the topic and one who is struggling with recent topics.

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#### Assessment Review

*10 min*

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.

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I assume you do this, but it should be told to other teachers that would not know to do so. But teaching scientific notation should be connected back to numbers that make sense to students. When you multiply 2000 x 3000 students understand the rules quite well. It would be 6,000,000. Then compare this with scientific notation, you know 2000 is 2x10^3, 3000 = 3x10^3 so how do I get my answer for 6x10^6? Do examples with addition and others as well. Avoid adding in another increase in power of ten until they've seen at least once multiplication and one addition and one of subtraction or division. Then introduce that. This sequence is how extremely gifted students in math understand scientific notation and algorithmic rules don't make sense to most, they just understand how to do it.

Also hanging up a number line with 0,1,10 posted on it and have students place 10^-1, 10^0 and 10^1 and 10^-4 on it is also really helpful.

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- UNIT 1: Starting Right
- UNIT 2: Scale of the Universe: Making Sense of Numbers
- UNIT 3: Scale of the Universe: Fluency and Applications
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- UNIT 5: Lines, Angles, and Algebraic Reasoning
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- UNIT 12: Gimme the Base: More with Exponents
- UNIT 13: Statistical Spirals
- UNIT 14: Algebra Spirals

- LESSON 1: Units and Vast Systems of Measurement
- LESSON 2: Adding and Subtracting in Scientific Notation
- LESSON 3: Mad Libs and Math Libs
- LESSON 4: Yuck! Word Problems...
- LESSON 5: The World of Microns
- LESSON 6: 100 People: An Assessment
- LESSON 7: Khan Academy and Scientific Notation Intuition
- LESSON 8: Khan Academy and Scientific Notation Conversions
- LESSON 9: Khan Academy and Orders of Magnitude
- LESSON 10: Khan Academy and Multiplying and Dividing with Scientific Notation
- LESSON 11: Khan Academy and Computations in Scientific Notation
- LESSON 12: Khan Academy Patterns in Zeros
- LESSON 13: Delta Math and Scientific Notation
- LESSON 14: Video Quiz (Alternative Assessment)
- LESSON 15: How far is that?
- LESSON 16: Long Distance Relationships Project
- LESSON 17: Long Distance Relationship Follow Up
- LESSON 18: How big is that?
- LESSON 19: The Universcale (A Project)
- LESSON 20: Universcale Project Follow Up
- LESSON 21: The Digital Scientific Notation Worksheet
- LESSON 22: The Cost of the Death Star