Compare Numbers in Scientific Notation

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With this lesson plan, students learn how to compare numbers in scientific notation using the greater than, less than, and equal to symbols.

Included with this lesson are some adjustments or additions that you can make if you’d like, found in the “Options for Lesson” section of the Classroom Procedure page. One of the optional additions to this lesson is to have your students use negative exponents in their problems to emphasize the place of integers on a number line.

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Description

What our Compare Numbers in Scientific Notation lesson plan includes

Lesson Objectives and Overview: Compare Numbers in Scientific Notation teaches students how to compare numbers written in scientific notation using the greater than, less than, or equal to symbols. At the end of the lesson, students will understand the concept of combining like terms in algebraic expressions. This lesson is for students in 5th grade and 6th grade.

Classroom Procedure

Every lesson plan provides you with a classroom procedure page that outlines a step-by-step guide to follow. You do not have to follow the guide exactly. The guide helps you organize the lesson and details when to hand out worksheets. It also lists information in the blue box that you might find useful. You will find the lesson objectives, state standards, and number of class sessions the lesson should take to complete in this area. In addition, it describes the supplies you will need as well as what and how you need to prepare beforehand.

Options for Lesson

Included with this lesson is an “Options for Lesson” section that lists a number of suggestions for activities to add to the lesson or substitutions for the ones already in the lesson. One optional addition to this lesson is to have your students use negative exponents in their problems to emphasize the place of integers on a number line. You could also have your students compare three or more numbers. Finally, you could have your students order several numbers using scientific information such as the length of molecules.

Teacher Notes

The teacher notes page includes lines that you can use to add your own notes as you’re preparing for this lesson.

COMPARE NUMBERS IN SCIENTIFIC NOTATION LESSON PLAN CONTENT PAGES

Compare Numbers in Scientific Notation

The Compare Numbers in Scientific Notation lesson plan includes two pages of content. We use scientific notation to allow us to write very large and very small numbers in a format that is easy to understand. We call it scientific notation because scientists often deal with very large and very small numbers.

We write scientific notation in the following format: a x 10ᵇ where 1 ≤ |a| < 10. The exponent b is an integer, while the coefficient a is any real number greater than or equal to one and less than ten. We also call the coefficient the significand.

When comparing numbers, we have three potential outcomes: greater than (>), less than (<), or equal to (=). We use these symbols to show how the numbers relate to one another when we write in scientific notation. However, when comparing numbers in scientific notation, we need to make sure that the number is written in the correct notation. Next, we look at the exponent, which we also called the power of 10. Finally, we compare the coefficient.

We can rewrite those steps in the following way:

1. Determine that both numbers are correctly written in the a x 10ᵇ form.

2. Compare the exponents or powers of 10. The larger exponent is the greater number. If they are equal, compare the coefficients.

3. Compare the coefficients using place value. The larger coefficient is the greater number.

4. Write the correct symbol between the numbers.

Examples

The lesson next dives into a few examples that students can use to help them grasp the lesson concepts. In the first example, we need to compare 4.7 x 10⁵ to 4.3 x 10⁸. First, we need to determine that both numbers are correctly written in the a x 10ᵇ form. They are, so we can go to the next step, where we compare the exponents. In this example, the exponents are 5 and 8. 8 is larger so we know that 4.3 x 10⁸ is the greater number.

The next step is to compare the coefficients using place value. However, we don’t need to do this because the exponents were different values. Finally, we write the correct symbol between the numbers: 4.7 x 10⁵ < 4.3 x 10⁸.

The lesson includes two additional examples for students to look at.

COMPARE NUMBERS IN SCIENTIFIC NOTATION LESSON PLAN WORKSHEETS

The Compare Numbers in Scientific Notation lesson plan includes four worksheets: an activity worksheet, a practice worksheet, a homework assignment, and a quiz. You can refer to the guide on the classroom procedure page to determine when to hand out each worksheet.

INDEX CARD ACTIVITY WORKSHEET

For the activity worksheet, students will receive an index card with a number in scientific notation on it. They will then line up in order from largest to smallest. The whole class can participate or you can split them up into smaller groups.

MOVIES PRACTICE WORKSHEET

For the practice worksheet, students will look at a table that contains the data for the earnings of the top ten movies in 2017. They’ll complete the empty column in the table by converting the dollars earned into scientific notation. They will then answer a few questions about the table and will compare the earnings of different movies using <, >, and =.

COMPARE NUMBERS IN SCIENTIFIC NOTATION HOMEWORK ASSIGNMENT

The homework assignment asks students to compare each set of numbers on the worksheet using <, >, or =. They will also write whether they compared using the exponent, coefficient, or both to find each answer.

QUIZ

This lesson also includes a quiz that you can use to test students’ understanding of the lesson material. For the quiz, students will first label the symbols <, >, and =. They will also compare two numbers in scientific notation.

Worksheet Answer Keys

This lesson plan includes answer keys for the practice worksheet, the homework assignment, and the quiz. If you choose to administer the lesson pages to your students via PDF, you will need to save a new file that omits these pages. Otherwise, you can simply print out the applicable pages and keep these as reference for yourself when grading assignments.

Additional information

grade-level

6th Grade

subject

Math

State Educational Standards

None for Grade 6

Lessons are aligned to meet the education objectives and goals of
most states. For more information on your state objectives, contact
your local Board of Education or Department of Education in your state.