BASIC EDUCATION ASSISTANCE FOR MINDANAO LEARNING GUIDE FIRST YEAR - MATHEMATICS I ALGEBRAIC EXPRESSIONS — SCIENTIFIC NOTATION

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BASIC EDUCATION ASSISTANCE FOR MINDANAO

FIRST YEAR - MATHEMATICS I (ELEMENTARY ALGEBRA)

ALGEBRAIC EXPRESSIONS

MODULE 5 : SCIENTIFIC NOTATION

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given by the author(s) or the BEAM Project Management Unit and the source must

be clearly acknowledged.

REYNANTE A. SOLITARIO

Secondary Mathematics Specialist - Region XI

Basic Education Assistance for Mindanao, RELC, Quirino Avenue, Davao City

Produced by the Materials Development Center, Region XI

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BASIC EDUCATION ASSISTANCE FOR MINDANAO LEARNING GUIDE

FIRST YEAR - MATHEMATICS I

ALGEBRAIC EXPRESSIONS — SCIENTIFIC NOTATION

Mind Map

Stages of Learning

The following stages have been identified as optimal in this unit. It should be noted that the stages do not represent individual lessons. Rather, they are a series of stages over one or more lessons and indicate the suggested steps in the development of the targeted competencies and in the achievement of the stated objectives.

INTRODUCTION

There are numerous problems and situations in the study of science and mathematics that make use of the exponents. Some of these are the approximate distances and measures of heavenly bodies, the growth of bacteria, and the measures of microscopic body cells and substances.

The problems presented here are mainly applications of science which relate to the comprehension of the the laws of exponents. For example, the diameter of a normal red blood cell is about 0.00077 cm and that if the largest type of white blood cell, the

monocyte, is about 0.0019 cm. How can these be expressed in scientific notation? What is then a scientific notation?

This module will help answer such questions.

Activating Prior Learning

Background or purpose

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Strategy

Cross Algebraic Expressions Puzzle. A unique version of a cross number/word puzzle. This activity enhances the analytical thinking of the students and aims to tap their their logical and mathematical intelligence.

Activity

Let the students solve and answer the cross expression puzzle with a partner. After which, call volunteers to show solutions on the board. It is good if the the format of the puzzle is written in a flip chart aside from the the activity sheets provided for them.

Refer to Activity Sheet 1.

Formative Assessment

The students will answer the following questions:

1. Did you find it easy or difficult for you to complete the cross expression puzzle? Why? 2. What are the different laws of exponents? Describe each law.

Roundup

Students were able to conclude that expressions containing exponents can easily be simplified with the use the different laws of exponents.

Setting the Context

It would be interesting for the students to know the following facts wherein some of the questions contain very large and very small numbers, and in the end, they will be able to express these in scientific notation.

Present the following to the students and let them think and make an educated guess about these questions. Ask them to match Column A with Column B.

COLUMN A COLUMN B

1. Do you know this number, 300,000,000 m/sec? A. mass of the Earth

2. Do you recognize this number, 0.000 000 000 753 kg.? B. diameter of hydrogen atom

3. Can you give what this number, 0.000 000 01 cm

represents C. speed of light

4. Guess what this number represents, 150 000 000 km? D. mass of a dust particle

5. This number, 5 975 000 000 000 000 000 000 kg. is

the E. approximate distance of the Earth to the Sun

Basic Education Assistance for Mindanao

Learning Guide, July 2007 4

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Questions:

1. Which are large and small numbers?

2. Is it possible to express those numbers in a different way? How? Express those numbers in a simplest way.

Learning Activity Sequence

Background or purpose

Students will be able to express very large and very small numbers into scientific notation and vice versa conveniently and precisely.

Short Discussion

This time, we will discuss the use of scientific notation, also referred to as exponential notation. This notation is based on powers of base number 10. The general format looks something like this:

a x 10n, where 1 ≤ a < 10 and n is an integer.

This is read as “a times 10 raised to the nth power, where a is a number greater than 1 but less than 10.”

To express standard numbers into scientific notation:

1. Locate the decimal and move it either right or left so that there is only one non-zero digit to its left.

2. The resulting placement of the decimal will produce the

a

part of the standard scientific notational expression.

3. Count the number of places that you had to move the decimal to satisfy step 1 above.

4. If it is to the left as it will be for numbers greater than 10, that number of positions will equal to n in the general expression.

Example:

How do we change the number, 23419 in standard scientific notation?

1. Position the decimal so that there is only one non-zero digit to its left. In this case we end up with

2.3419

2. Count the number of positions we had to move the decimal to the left and that will be n.

3. Combine the results of step 1 and 2 above for the standard form:

So we have: 2.3149 x 104

To express numbers written in a scientific notation into standard form:

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Example:

How do we place the number, 5.6237 x 103 i_{n standard scientific notation?}

1. Determine the exponent of 10 — in this case it is 3. This is the number of places we move the decimal place to the right.

2. Move the decimal places to the right 3 places.

So we have: 5623.7

Scientific Notations can be multiplied or divided.

The general format for multiplying using scientific notation is as follows:

(a x 10x) (b x 10y) = (a)(b) x 10 x+y

1. First, multiply the a and b numbers together and express an answer.

2. Secondly, multiply the exponential parts together by ADDING the exponents together. 3. Finally, multiply the two results for your final answer.

For Example:

(2.134 x 102) (7.81 x 106) = (2.134 x 3.81) x 102+6 = 8.13054 x 108

To divide scientific notations:

1. Perform the division on the a and b numbers.

2. Perform the division on the exponential parts by subtracting the exponent in the lower number from the exponent in the upper number.

3. Multiply the two results together. For Example:

(6.74 x 10-2) ÷ (3.45 x 108) = (6.74 ÷ 3.45) x 10-2-8 = 1.9536232 x 10 -10

Strategy

Cooperative Learning. This strategy aims to enhance the group work skills of the students in working a common task.

Activity

Divide the class into groups of four (4). Distribute the materials needed in every group and let them perform the following tasks. See Activity Sheet 2.

Formative Assessment

The students will answer the following questions:

1. Is it easy for you to make a solar system? What did your group do before completing the solar system?

2. How to change numbers in standard form into scientific notations? What is the scientific notation of one quadrillion?

Roundup

Students were able to appreciate that scientific notation is a convenient way to express very large and very small numbers. They understood that a number is expressed in scientific notation when it is written in the form, a x 10n, where 1 ≤ a < 10 and n is an integer.

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Check for Understanding of the topic or skill

Background or purpose

The students will write standard numbers into scientific notation and vice versa.

Strategy

Provision of Cooperative Learning to tap students' interpersonal intelligence and to develop their higher order thinking skills.

Activity

Group the students having five (5) members in a team to perform the following activities on scientific notation.

Refer to Activity Sheet 3.

Formative Assessment

Guide Questions:

1. How to obtain the product of two numbers expressed in scientific notations? 2. How to divide numbers in scientific notations?

Roundup

Students made the following generalizations:

• To multiply scientific notations, find the product between numbers a and b, multiply

the exponential parts together by adding the exponents and finally, multiply the two results for the final answer.

• To divide scientific notations, perform the division on the a and b numbers, divide the

exponential parts by subtracting the exponent in the lower number from the exponent in the upper number and multiply the results together expressed in a scientific notation.

Practice and Application

Background or purpose

Students will apply their knowledge on scientific notation to perform the activity presented in this stage.

Strategy

Round Table Discussion. A group activity to prepare for discussion. The activity presented will enhance their analytical thinking and to tap their verbal/linguistic and mathematical intelligence.

Activity

Divide the class into five groups and give each group one problem to solve applying the concept on scientific notation.

In groups, students write down their thoughts and solutions. Pass the paper around the group. As each person reads the solutions, they initial if they agree or leave blank if they do not. When paper returns to owner, he/she reads ideas and review own solutions to present a discussion among members using new and different ideas.

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1. R. Millikan, a physicist, found out in his oil drop experiment that 1 electron unit (e.u.) is equal to 1.602 x 10-19 coulomb. How many coulombs are there in 105 e.u.? 2. A meter is equal to 1 000 000 microns. Blue lights has a wavelength of 4.7 x 10-1

micron. Express this wavelength in meters.

3. The diameter of a red blood cell is about 0.00075 cm. The diameter of a white blood cell is about 0.0015 cm. Which has a bigger diameter and how many times is it bigger?

4. The D line or yellow line of the metal sodium has a wavelength of 5.89 x 10-7. If one (1) millimicron equals 1 x 10-9 meter, express the wavelength of the D line in millimicrons.

5. Alpha Centauri is 4.3 light years from Earth. Express this distance in kilometers in scientific notation. (A light year is 5.9 x 1012 km)

Formative Assessment

Given the following facts, make your own word problem applying the concept on scientific notation. You may write these in a cartolina/flip chart.

Learning Guide, July 2007 8

INTERESTING FACTS:

1. 5.975 X 1021_{is the mass of the Earth.}

2. The diameter of a giant star is 2 800 000 000 km. 3. A quintillion contains 18 zeros.

4. The mass of a dust particle is 0.000 000 000 753 kg. 5. The world's population today is estimated to be 6.5 billion. 6. The estimated population of the Philippines as of July 2003 is about 87,857,473.

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Roundup

Real life problems on scientific notations can be solved by applying the rules in multiplying and dividing numbers expressed in standard notational form.

Closure

Background or purpose

Students will use the different terms applied in scientific notation to compose a song.

Strategy

Song Composition. A strategy to enhance students' musical and bodily/kinesthetic intelligence.

Activity

Divide the class into groups of eight (8) and let each group compose a song (folksong, love song, rap, pop, or nursery). The lyrics of the song should contain words used in scientific

INTERESTING FACTS:

1. 5.975 X 1021_{is the mass of the Earth.}

2. The diameter of a giant star is 2 800 000 000 km. 3. A quintillion contains 18 zeros.

4. The mass of a dust particle is 0.000 000 000 753 kg. 5. The world's population today is estimated to be 6.5 billion. 6. The estimated population of the Philippines as of July 2003 is about 87,857,473.

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notation, but the tune must be adopted from the original. After which, make a choreography out of your composition and present it among the other groups.

Formative Assessment

Scoring Rubrics for group's performance. (Assessment Tool 1 for Teacher)

Roundup

Students were able to appreciate the significance of the scientific notation and the effort they had shown while composing the song.

Teacher Evaluation

(To be completed by the teacher using this Teacher’s Guide) The ways I will evaluate the success of my teaching this unit are:

1. 2.

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ACTIVITY SHEET 1

“CROSS ALGEBRAIC EXPRESSIONS PUZZLE”

Objective:

To simplify exponential notations applying the different laws of exponents and to complete the cross-expression puzzle.

Directions:

Simplify the following expressions below to complete the grid. Make sure that in every box contains number (either one or 2-digit) or could be a variable (with or without exponent).

1 8

2 3 9

10

4

12 11

5 13 6

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WORKSHEET

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ACTIVITY SHEET 2

“DO IT IN SPACE!”

Objective:

To make a creative and attractive solar system and be able to express the distance of the planets to the sun in scientific notations.

Materials:

Yarn (assorted colors), flip charts, marking pens, glue, art papers (assorted colors), scissors, Activity Sheet # 2, and crayons

Directions:

Divide the class into groups of four (4). Distribute the materials needed in every group and let them perform the following tasks.

1. Make your own attractive solar system utilizing the materials provided. Make sure to follow the correct chronological positions of the sun and the planets.

Here's a sample for you: (The teacher may use other sample of a solar system)

2. Given the facts about the nine planets, show using the yarn the distance of each planet directly to the sun. Present the distances of each planet to the sun in scientific notation.

For Example:

9.29571 x 107

Sun

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Measures of the Planets: Larger Scale Model

Planet Diameter in Miles Diameter in Scientific

Notation

Distance to the Sun

in Miles Distance in Scientific Notation

Mercury 3 032 35,983,610

Venus 7 521 67,232,360

Earth 7 926 92,957,100

Mars 4 222 141,635,300

Jupiter 88 846 483,632,000

Saturn 74 898 888,188,000

Uranus 31 763 1,783,950,000

Neptune 30 778 2,798,842,000

Pluto 1 413 3,674,491,000

3. After which, complete the table above wherein you are asked to express the diameter of each planet into scientific notation and the distance as well.

4. When everyone is through, present your output to the class as well as the completed table on “Measures of the Planets”.

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ACTIVITY SHEET 3.1

“What's the Equivalent?”

Objective: Write numbers in scientific notation and vice versa. Complete the tables below. Materials: flip chart, marking pens and masking tape

Table 1

Number Equivalent in Scientific Notation

84 266

665.8

7.44 x 103

98 322

5.49 x 104

Table 2

Number Equivalent in Scientific Notation

0.0000041

2.09 x 10-6

0.000000000000792

5.86 x 10-5

0.1

Guide Questions:

1. What kind of numbers are those in Column 1?

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ACTIVITY SHEET 3.2

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Objective: To multiply and divide numbers in scientific notation. Complete the two tables below.

Table 1

Factors Product

(2 x 103)(3 x 104) 6 x 107

(3 x 103)(1 x10-5)

(8.1 x 10-3)(1.2 x 10-5)

(9.1 x 109)(0.632 x 10-7)

(0.0078 x 102)(45.1 x 10-3)

Table 2

Given Quotient

1.32 x108

1.2x 102

8 x10−6

4 x10−2

0.045 x 102 1.07 x103

9.2 x 10−7

4.6x 10−1

Guide Questions:

1. How to obtain the product of two numbers expressed in scientific notations? 2. How to divide numbers in scientific notations?

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ASSESSMENT TOOL FOR TEACHER

Scoring Rubric

for Group Performance on Song Composition and

Presentation

Criteria

Score Point 3

Score Point 2

Score Point 1

Organization of

Presentation Clearly organized all the way through; well-structured and presented in logical sequence

Somewhat structured; little organization; disjointed sequence

No organization evident; presentation is out of logical order

Use of Mathematical Terminology

Lots of mathematical terminology correctly used

Some mathematical terminology not correctly used

No mathematical terminology used

Use and Variety of Formations/ Choreography

Excellent choreography Little variety of choreography