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# Operations with Numbers in Scientific Notation Day 2 of 2

Lesson 12 of 19

## Objective: SWBAT extend understanding of dividing exponents with like bases to include dividing values written in scientific notation.

## Big Idea: Like bases, come out come out where ever you are! Extend previous work with division and exponents to include scientific notation.

*50 minutes*

#### Bellringer - Lesson Opener

*15 min*

The warm-up exercises are within the activity today, just as they were during the activity yesterday. To open the lesson, you may choose to review homework material from the previous day or even begin with an entrance slip asking students to generate an equivalent expression in scientific notation for the given expression: 4.568 X 10^{-6}(3.67 X 10^{8}). Then pass out the activity sheet for the lesson today. Clarify your learning goals for students before asking them to begin work.

The learning goal today is that students will begin to make connections between dividing expressions with like and unlike bases to dividing expressions written in scientific notation, which include like and unlike bases. We are continuing to perform operations with numbers written in scientific notation. Tell students the review work in questions one and two are essential to understanding the new work today because the same math concepts are applied in both types of questions.

Allow students about 10 minutes to work in cooperative groups to complete questions one and two. As students are working move about the room assessing students and providing feedback that moves learning forward. Also select students or student groups to present their thinking about each of the three expressions. This presentation is essential to beginning the new work so ask students to script their work on the board where it can be seen by all students throughout the class period. As another means of formative assessment, you could ask groups to put simplified expressions on marker boards and hold them up for you to view everyone's equivalent expressions before students script work on the board.

**Cooperative Grouping Explained**

**Clarifying and Sharing Learning Intentions and Criteria for Success**

**Providing feedback that moves learning forward**

##### Resources (6)

#### Resources

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#### Beginning the New Work

*30 min*

The bulk of the new material is focused in questions three and four. Students should be familiar with the process of applying operations to values written in scientific notation after completing the multiplication activity. Allow students about eight minutes to work and talk in collaborative groups as they complete questions three and four. Move about the room providing feedback that moves their learning forward without directly telling them how to think and what to do in the given example. For the mini wrap-up on this section you could choose to two apply a new strategy for sparking whole group discussion. While moving about the room select two student papers, one correct process and one incorrect process. Tell the students as you collect their work that you plan to show these under the document camera without showing their name. Make sure to choose an incorrect paper from a student who knows his/her work is incorrect but would make great conversation because many other students are also incorrect in the room. Do not surprise the incorrect student with the announcement that his/her work is wrong. Show the class both sets of work, side by side if possible, under the document camera. As students to discuss in their cooperative groups what they like about both examples and what they disagree with because something is incorrect in this work. Allow students about two to three minutes to talk. Then ask first for what students like in both examples and script this on the board. Then ask for what students disagree with in the work and script this on the board. Ask students whose paper they would prefer to choose as there own and then together script a complete class answer to question four.

After wrapping up the discussion over questions three and four, allow students time in their groups to complete the examples in question five. Again move about the room providing feedback that moves learning forward without telling students how to think. Refer them back to all the scripting on the board. If you have students trying to use the calculator for all the division work, first of all take the calculator and ensure he/she knows how to accomplish the math without technology. Then, ask him/her to interpret the answer on the screen including what does the E mean? How does the answer on the calculator compare to what the student just generated by hand?

**Activating students as owners of their own learning**

**Mini-Wrap Up Strategy Explained**

**Activating students as resources for one another**

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#### Wrapping Up the Lesson

*5 min*

Hold one last mini wrap-up to review solutions and thinking about the example problems in question five. Assign the same homework practice page as used in the previous lesson. If students already practiced examples of multiplication then assign about ten more practice problems that involved division. If students have not yet practiced anything from this handout, then you could assign ten multiplication problems and ten division problems. Again, I like to post the solutions to my website or Edmodo.com so students can check their work as they practice.

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- LESSON 1: Understanding Perfect Squares and Square Roots
- LESSON 2: Understanding Perfect Squares and Square Roots Continued
- LESSON 3: Understanding Perfect Cubes and cube Roots
- LESSON 4: Understanding Perfect Cubes and Cube Roots Continued
- LESSON 5: Law of Exponents - Multiplication with Like Bases
- LESSON 6: Laws of Exponents - Division with Like Bases
- LESSON 7: Laws of Exponents - Power Raised to a Power
- LESSON 8: Laws of Exponents - Negative and Zero Powers
- LESSON 9: Laws of Exponents - Negative and Zero Powers Continued
- LESSON 10: Reviewing Scientific Notation
- LESSON 11: Operations With Numbers in Scientific Notation Day 1 of 2
- LESSON 12: Operations with Numbers in Scientific Notation Day 2 of 2
- LESSON 13: Comparing Computer Bytes Day 1 of 2
- LESSON 14: Comparing Computer Bytes Day 2 of 2
- LESSON 15: Applying Scientific Notation - Formative Assessment Lesson
- LESSON 16: Applying Scientific Notation - Formative Assessment Lesson Continued
- LESSON 17: Applying Scientific Notation - Formative Assessment Lesson Completed
- LESSON 18: Exponents and Radicals Unit Assessment Day 1 of 2
- LESSON 19: Exponents and Radicals Unit Assessment Day 2 of 2