Operations With Numbers in Scientific Notation Day 1 of 2

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SWBAT extend previous understanding of exponents and the associative property to multiply values written in scientific notation.

Big Idea

Using the Associative Property to multiply values in scientific notation makes finding like bases easy and applying exponents valuable.

Bellringer - Opening the Lesson

15 minutes

Clarify for the students the learning goal of the lesson today.  The goal of the lesson today is to understand how the associative property can help students multiply strategically so they can apply their understanding of exponents to multiplication with numbers written in scientific notation.

Really, students have already been applying the associative property when multiplying two expressions, which is why the activity begins with multiplying two expressions with like and unlike bases.  The skills needed to complete this lesson warm-up are the same skills needed to complete the new work with scientific notation.  Therefore, after sharing the learning goals with students pass out the activity page and ask students to work within partner groups to complete questions one and two as the warm-up activity today.  

As students work, about 8 - 10 minutes, move about the room formatively assessing student progress with exponents and providing feedback that moves learning forward.  Select groups to present their work for each question as you are observing as well.  The opening activities are very important for setting the students' minds in a productive direction for the reaminder of the activity.  Therefore, as students are presenting their answers to questions one and two ask them to script neatly their work so that it can be left up on the board throughout the class period as inspiration for students as they work through the new material.


Cooperative Grouping Explained

Clarifying and Sharing Learning Intentions and Criteria for Success

Scripting Strategy

Providing feedback that moves learning forward 

Mini-Wrap Up Strategy Explained


Beginning the New Work

30 minutes

Allow students about 10 minutes to work through questions three, four, and five within their cooperative groups.  After the warm-up of answering and fully discussing the application of the associative property in questions one and two, students should be ready to work within groups to apply these same skills to scientific notation.  As students are working, move about the room providing feedback that moves learning forward and selecting students or student groups to present their thinking during a mini-wrap up over these questions.  As you move about the room, you will probably notice at least some students trying to put the entire expression into a calculator and getting strange results.  Someone is always going to grab a calculator and look for the easy way out.  Use this to your advantage.  Ask the "cheating" student to compare his/her answer on the calculator to the answer of others in the group.  Ask the members to write down both answers and then try to figure out what is meant by the e and number after the e on a calculator screen.  As you begin to develop experts at reading scientific notation on a calculator (a skill they must master anyway) then ask these groups to come to the front of the room duirng hte mini wrap-up and teach the rest of the class how to use the calculator.  This is a great teaching moment for the entire class if you have students who try using the calculator for everything.

After students have completed this work, pull everyone together for a thorough discussion of each question.  I want student lead discussions in my classroom, so as I am selecting groups to present I tell them why I want them to speak, what it is about their work that I need them to discuss most.

After the wrap up session, if your students are still struggling to understand the multiplication, allow them about five minutes to complete question six and then hold another whole group mini wrap-up session.  Together, then create a class answer for question seven and make sure everyone writes down the class description.  Allow students time to compete question eight within cooperative groups.

If your students are grasping the concept and after wrapping up questions three, four, and five they are ready to move on, then allow them time to work on questions six, seven, and eight within cooperative groups before holding a mini wrap-up over all three questions at once.


If you are in a hurry to teach multiplication and division with values written in scientific notation because you are running out of days in this unit, then I am also including a lesson I found online from a textbook that very quickly shows students the concepts discussed in this lesson and the lesson for tomorrow.  

Activating students as owners of their own learning

Activating students as resources for one another


Closing the Lesson

5 minutes

You have some options for closing the lesson today.  If your students completed the activity, including question number eight, and they are ready for more practice, then assign part of the questions from the homework page.  The included homework page has both multiplication and division with values written in scientific notation and can be use for additional practice with the lesson today and tomorrow.  If your student did not complete question eight, you may want to only assign question eight for additional practice.  It really depends on where your students finished the lesson and how ready they are for additional practice.  It is not productive for students to work ten practice problems and work each one incorrectly because there are still misconceptions.  When I assign practice, I very often post the answers to the homework on my website or in Edmodo.com so that students can check their work and in Edmodo.com students can ask each other questions and still work cooperatively from home.

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