## The Large and Small of It

### Sharla ShultsBay District Schools

#### Description

It is hard to envision the distance to the Moon without thinking about a very large number. Yet, a lunar dust particle is so small, several fit on the tip of a pinhead! Students explore the extreme solving problems related to the Apollo space missions.

#### Objectives

The student refines vocabulary for interpersonal, academic, and workplace situations, including figurative, idiomatic, and technical meanings.

The student locates, gathers, analyzes, and evaluates written information for a variety of purposes, including research projects, real-world tasks, and self-improvement.

Understands the relative size of integers, rational numbers, irrational numbers, real numbers and complex numbers.

Understands concrete and symbolic representations of real and complex numbers in real-world situations.

#### Materials

-Copies of documents found in the associated file prepared for class discussion and formative assessment (See Teacher Preparation for list.)
-Scientific Calculators – one per student

#### Preparations

1. Have folders ready for distribution at the beginning of class

2. Download and duplicate copies of the following documents located in the associated file:
a) Warm-Up Activity #4 – one per student (See Associated File.)
b) Warm-Up Activity #4 Answer Key – one copy for teacher use
c) Scientific Notation in the Real World Activity sheet – one per student
d) Scientific Notation in the Real World Activity Sheet Answer Key – one copy for teacher use
e) All for a Walk on the Moon Problem Solving – one copy per student
f) All for a Walk on the Moon Problem Solving Answer Key – one copy per student
g) Guidelines for Original Math Problem

3. Set up overhead projector and have enough overhead pens for demonstration.

4. Download, print, and make transparencies of Example of Created Math Problem and Writing Integers in Scientific Notation found in the associated file.

5. Secure a set of classroom scientific calculators, or request students to furnish their own.

6. Prepare extra worksheets as needed for students having difficulty with basic arithmetic skills. These reflect areas of difficulty as demonstrated in problem solving dealing with scientific notation.

7. Review the Websites listed in Steps 3 and 5 of procedures.

#### Procedures

Day 9 of the unit The Math Connection

NOTE: Irrational numbers and complex numbers are not addressed or assessed in this lesson.

1. With student assistance, distribute student folders at the beginning of the class period.

2. Return the Percent in the Real World Problem Solving practice sheets with feedback on weak areas for students to place in folders. Especially note to students any areas of weakness in arithmetic skills. Tell students to be mindful of any additional practice sheets attached. Remind students to place the problem-solving practice sheets in their folders and take home the attached sheets for extra practice.

3. Begin the class discussion with the homework question. What is the name of the highest possible number? Students’ answers will probably vary. Ask students if they recognize the fallacy in the wording of the question. Because a largest number does not exist, the appropriate question would read, ‘What is the largest number that anyone has ever decided to give a specific name to?’ (See Weblinks below for the reference site Univ. of Toronto Mathematics Network – Largest Possible Number.)

4. Reward students that recognize infinity and the fact there is no such thing as a highest possible number. You could always add 1 to any number to get still another larger number. As discussed on the Internet site, the largest number ever given a name to is the googleplex, which is a 1 followed by a googol of zeros, where a googol is 10 to the 100th power (a 1 followed by 100 zeros).

5. Continue class discussion with questions, such as: Who created scientific notation? What is the use of scientific notation in every day life? What are the uses for it in the work field? (See Weblinks below for the reference site Univ. of Toronto Mathematics Network – Scientific Notation in Everyday Life.)

Discuss with students that scientific notation is needed any time you are dealing with numbers that are very large or very small.

6. Distribute the Warm-Up Activity #4. (See Associated File.) This warm-up ensures students understand the symbolic representation of scientific notation, both in decimal placement and exponents. The activity is designed to review and refresh the understanding of the writing of very large or very small numbers in a more precise form. For starters, a review of powers of 10 is necessary and then the relocation of the decimal point. Emphasize the number to the left of the decimal must be between 1 and 10. Go over answers thoroughly and reinforce student understanding of the significance of counting digits and not just zeros!

7. Give a precise definition of scientific notation: Scientific notation reproduces a very large or very small number as a rational number between 1 and 10 multiplied by a significant power of 10. Use the Transparency Model for Writing NUmbers in Scientific Notation found in the associated file to demonstrate the appropriate procedure for writing numbers in scientific notation.

8. Distribute to students the Scientific Notation in the Real World Activity Sheets. (See Associated File.) Tell students to complete the table consisting of several examples of instances where extremely large or small numbers occur. Instruct students to work with a partner and write the missing equivalent forms using knowledge of rational numbers and scientific notation. Hold a class discussion at the conclusion of the activity allowing students to check their own papers for accuracy and make corrections as deemed necessary using the Scientific Notation in the Real World Activity Sheet Answer Key provided in the associated file.

9. Tell students one of the most common places to encounter scientific notation is in matters dealing with science. Some examples are:
a) Scientists utilize scientific notation in measurement of quantities to express the number in a way that gives an indication of its precision.
b) Chemistry deals with tremendously large and small numbers that makes it extremely difficult to keep up with all of the zeros without the use of scientific notation.
c) Flights into space have explored territories beyond our wildest imaginations.

So, what better place is there to explore the use of scientific notation than to take a look at the events surrounding a walk on the moon! The Apollo program became the backbone of the American space program. Tell students: So, let’s explore a trip to the moon!

10. Distribute All for a Walk on the Moon Problem Solving practice sheets to students. This is a good group activity because it requires a large degree of reading. If students are working in groups, create a way that they can be partnered or grouped effectively. Instruct group members to first read each problem silently; then, select one group member to read the problem aloud. Allow students to collaborate, discussing possible answers, before reaching consensus.

11. When students complete the problem-solving sheet, allow time to discuss the various occupations that go hand-in-hand with the problem solving. This continues to reinforce the math connection between mathematics and the world of work. Look for students’ responses such as astronomer, NASA engineer, astronaut, computer operator (data entry), scientist/researcher, etc.

12. Inform students to begin formulating ideas for their own original math problems. For homework, students produce hand-written rough drafts of original math problems correlated to their chosen career fields as much as possible. Students consult with parents, friends, or relatives for thoughts and ideas. Emphasize to students the importance of completing this assignment. The activities of the following day are contingent on their being prepared with the hand-written rough draft!

13. Distribute and discuss Guidelines for Original Math Problem handout so students will fully understand the expectations. Inform students this is the criteria they will use in peer reviewing each other’s math problems.

14. Use the Example of Created Math Problem Transparency found in the associated file to demonstrate an example of a math problem related to the world of work with the grading criteria.

15. While students are completing the problem-solving practice sheets, collect students’ folders. The added documents of today’s lesson include the Warm-Up Activity #4, the Scientific Notation in the Real World activity sheet, and All for a Walk on the Moon Problem Solving practice sheets.

16. Collect students’ All for a Walk on the Moon Problem Solving sheets at the end of the class period to be returned the following day. Check students’ problem solving skills using the Scientific Notation Problem Solving Answer Key found in the associated file.* Identify any students struggling with the problem solving due to the inadequacy of understanding decimals, exponents, or their relationship to scientific notation. Attach additional practice work sheets as needed to the scientific notation problem solving activity sheets and return to students the next day to take home for extra practice.

*Note: If deemed necessary, adapt the checklist provided in the associated file of Rising and Falling Fractions to record the results for scientific notation.

#### Assessments

This assessment aligns with the part of the standard only dealing with scientific notation in real-world situations.

Students understand concrete and symbolic representations of scientific notation in real-world situations represented in a variety of equivalent forms and the relative size of integers as demonstrated on the All for a Walk on the Moon Problem Solving practice sheet. (See Associated File.)

Students analyze and evaluate the information from the text within the real world math problems presented for solving. Students demonstrate understanding by correctly solving the problems. Students are formatively assessed using the answer key provided in the associated file. Vocabulary is embedded throughout the unit plan allowing students to refine vocabulary for interpersonal, academic and workplace situations.

Irrational numbers and complex numbers are not addressed or assessed in this lesson.

#### Extensions

This is Lesson 9 of 10 in the unit The Math Connection addressing [When Are We Ever Going to USE This MATH?]

The Beacon Unit Plan associated with this lesson can be viewed by clicking on the link located at the top of this page or by using the following URL: http://www.beaconlearningcenter.com/search/details.asp?item=2947. Once you select the unit’s link, scroll to the bottom of the unit plan page to find the section, “Associated Files.” This section contains links to the Unit Plan Overview, Diagnostic and Summative Assessments, and other associated files (if any).

Scientific Notation in Everyday Life
Question Corner and Discussion Area

Largest Possible Number
Question Corner and Discussion Area

Why Use Scientific Notation?
Scientific Notation

Explanation and Scientific Notation Generator
Scientific Notation

A History of Speed
Voyage to the Milky Way

The Six Apollo Landings
Apollo Missions

Travel on the Moon
The Apollo Lunar Roving Vehicle

When Are We Ever Going to USE This Math?
The Math Connection