Adding and Subtracting with Scientific Notation Part I

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Objective

SWBAT perform operations with numbers expressed in scientific notation.

Big Idea

Now that students are comfortable expressing numbers in scientific notation, they can begin to apply their skills to real-world problems involving addition and subtraction.

Warm Up

25 minutes

As is typical for Wednesdays, warm up is replaced today with Continuous Improvement (CI) Quiz #6. These quizzes, 12 in all, are designed to be given weekly and cover important number sense topics with which students typically struggle including fractions, decimals, percents, cube and square roots, simplifying and estimating radical expressions, among others.  Students are give 15 minutes to complete the 10-question quiz.  Answer sheets are collected and checked for accuracy (but not put as a grade in the grade book!) and returned the following week to the students.  Students keep individual "run charts" of their progress each week.  We also maintain a class run chart and celebrate our "all time bests" when our class average exceeds a previous best class average.  For additional information on the Continuous Improvement model, see my strategy folder!

Once the timer sounds after 15 minutes, I collect the papers and quickly review each answer with the class. If the question covers a concept we have already studied this year, I ask for a "thumbs up" or "thumbs down" as to whether they got the problem correct or not. This gives me a good sense about what type of problems to review during subsequent Warm Ups.

 

Adding and Subtracting Numbers in Scientific Notation

15 minutes

After reviewing the answers for the CI Quiz, I explain that we are going to begin solving problems with numbers in scientific notation. I go on to explain that scientists use these skills on a daily basis as do other professions that deal with very large and very small numbers.

I explain that in today's lesson, we are going to explore the universe by comparing size and distances between planets. I provide students with a table and pose a question: How much more is the mass of the Earth than Venus?

I ask students to work at their tables to find the answer to the problem using any method they would like.  The majority of groups simply expanded the numbers, subtracted them, and then wrote the resulting answers in scientific notation.  I posed another question: How much more is the mass of Mars than Mercury?  I challenged students to find a different way of solving this problem.

I then circulate through the room to seek out students who were employing different strategies. When I found several, I asked them privately if they would be willing to share their work. Both were willing, so when I called time, I asked a group who had used the expanded algorithm to share their work with the class.  I then invited the alternative algorithm contributors to share. One student explained that since both planets were about the same size in magnitude, he could just subtract the two front numbers ("Coefficients?" I offered) and keep the ten to the 22 power.

I responded that the student's method seemed much more efficient.  I pushed his thinking by asking, "So what if the numbers you are working with aren't the same magnitude.  Then, what would you do?" The student shrugged his shoulders and looked to his partner who looked on silently.

I explained that we would be spending more time the next day exploring these questions and I challenged students to continue thinking about it at home and bring their ideas the following day.