Download Week 3 math 3 I. Lesson /Unit Overview A. Topic: Exponents and

Week 3 math 3
I. Lesson /Unit Overview
A. Topic: Exponents and scientific notation
B. Skills Targeted
 Reading for mathematical understanding.

Apply concrete mathematic and problem solving strategies to real-life problems involving
Exponents and scientific notation

Create designs/drawings as tools to find word problem solutions.

TI-30xs usage calculator usage
C. Materials/Handouts
 TI-30xs calculator
 Math 3 packet pages 202-220
 Exponent rules and practice handouts
 Math aids: http://www.mathwarehouse.com/radical-equation/how-to-solve-radicalequations.php
 Copy site to browser to show scientific notation usage http://htwins.net/scale2/
 GED formula sheet
 Calculator basic and practice
https://mnliteracy.org/sites/default/files/attachments/ged_scientific_calculator_tutorial.pdf
D. Learning Standards
P3.1: Interpret and apply whole number and benchmark fraction patterns and expressions involving all
four basic operations.
b) Identify part of an expression using mathematical terms (for example, product and quotient)
d) Rewrite repeated multiplication using exponents and vice versa. For example: 25 =
(2)(2)(2)(2)(2)
P4.2: Write and solve equations and inequalities emphasizing proportional reasoning and linear
equations dealing with rational numbers.
e) Apply properties of operations to solve multi-step equations and converting between forms
as appropriate to aid fluent computation.
i.) Use square/cube root symbols to represent solutions to equations of the form x 2 = p and
x3 = p, where p is a positive rational number.
E. Suggested timeline
 Four periods
II. Lesson Objectives
 Over the next four class periods, students will apply concrete problem solving skills,
designs/drawings to analyze and solve Exponents and scientific notation story problems with
the use of GED formula sheet and TI-30xs calculator.
 Develop strategies to solve and check solutions.
 Students will demonstrate learned skills by progressively solving increasing multiple step
problems.
lll. Lesson Plan
Session 1, 2, 3, 4
A. Preparation
1. Review
 How to use Ti30sx calculator
https://mnliteracy.org/sites/default/files/attachments/ged_scientific_calculator_tutorial.pdf
2. Introduce topic (hook).
 What are Exponents? Have you ever seen them?
 Introduce vocabulary for this unit: Exponents and scientific notation
3. Objective:
 Solve simple and complex real-world Exponents and scientific notation word problems using
diagrams/drawings, from science and business.
 Using the Texas instrument TI 30 SX calculator, and GED formula sheet as primary solution
tools.
 Suggested time - four class periods
B. Presentation
4. Modeling
 Demonstrate the first step in solving Exponents and scientific notation type word problems:
Understanding the problem (analyzing question)
a) What do you want to answer?
b) What information is provided?
c) What step(s) will you take that will guide you to the solution?
d) What tools will you use?
d) Does my answer make sense and how do I check it?
C. Practice
5. Check for Understanding
 Instructor will pose questions to students pertaining to the presentation.
(Example: Give some examples of real-life usage of Exponents and scientific notation.)
6. Guided Practice
 Instructor will guide students in solving Math 3 packet problems pages 212- 214, 202-210, 216 222 (exponent rule and practice).
D. Performance
7. Application/independent practice/assessment
 Students will practice learned skills by solving problems from worksheet
Regentsprep: http://www.regentsprep.org/regents/math/algtrig/ate10/radmodelprac.htm
 Exponent rules and practice handout
 Students will be tested with end of Unit, ten question quiz on Exponents and scientific notation
word/story problems. See below.
Informational material
Name:__________________________________________________Date:____________
Area of a square word problems (Practice /Homework/quiz)
1. Find the area of a square of side 27 cm.
2. Find the area of a square of side 35 m.
3. The length of the side of a square is 25 cm. Find the area.
4. Length of a side of a square field is 275 m. What will be cost of levelling the field at a rate of 10 cent per
square meter?
5. The side length of a square is 1/6 cm.
Find its area.
6 . A squ a r e ga r d en wit h a sid e le n gt h of 1 50 m h as a squ are swimmin g p o o l in t h e
ve r y ce n t er with a sid e len gth of 2 5 m. Calcu lat e t h e are a of th e gard en .
Area of a square word problems (Practice/quiz) ANSWER SHEET
1. Find the area of a square of side 27 cm.
Area of a square = length × length
A = 27 × 27 sq. cm. = 729 sq. cm.
2. Find the area of a square of side 35 m.
Area of a square = length × length
A = 35 × 35 sq. m. = 1225 sq. m.
3. The length of the side of a square is 25 cm. Find the area.
Length of the side of a square = 25 cm
Area of the square = Side × Side
A = 25 cm × 25 cm = 625 cm2
4. Length of a side of a square field is 275 m. What will be cost of levelling the field at a rate of 10 cent
per square meter?
Length of the square field = 275 m
Area of the square field = side × side
A = 275 m × 275 m = 75625 m2
Cost of levelling the field = 75625 m2 × $0.10 = $ 7562.50
5. The side length of a square is 1/6 cm.
Find its area.
(1/6 cm.) (1/6 cm.) = 1/36 cm.2
6 . A sq u ar e gard e n with a sid e le n gt h o f 15 0 m h as a squ are swimmin g p oo l in the
ve r y ce n t er wit h a sid e len gth of 2 5 m. Calcu lat e t h e are a of th e gard en .
A r ea g a r d e n – Ar ea p o o l = A r ea o f gar d en ; A P = 25 2 = 6 25 m² ;
A g =1 5 0 2 = 2 25 0 0; Area o f gar d en = 2 25 00 − 62 5 = 2 18 7 5 m²
Concept of powers (exponents):
A power contains two parts exponent and base.
We know 2 × 2 × 2 × 2 = 24, where 2 is called the base and 4 is called the power or exponent or index of 2.
Examples on evaluating powers (exponents):
1. Evaluate each expression:
(a.) 54.
Solution:
54 = 5 ∙ 5 ∙ 5 ∙ 5
→ Use 5 as a factor 4 times.
= 625
→ Multiply.
(b.) (-3)3.
Solution:
(-3)3= (-3) ∙ (-3) ∙ (-3)
→ Use -3 as a factor 3 times.
= -27
→ Multiply.
(c.) -72.
Solution:
-72
= - (72)
= -(7 ∙ 7)
= - (49)
→ The power is only for 7 not for negative 7
→ Use 7 as a factor 2 times.
→ Multiply.
(d.) (2/5)3
Solution:
(2/5)3
= (2/5) ∙ (2/5) ∙ (2/5)
= 8/125
→ Use 2/5 as a factor 3 times.
→ Multiply the fractions
Writing Powers (exponents)
2. Write each number as the power of a given base:
(a.) 16; base 2
Solution:
16; base 2
Express 16 as an exponential form where base is 2
The product of four 2’s is 16.
Therefore, 16 = 2 ∙ 2 ∙ 2 ∙ 2 = 24
(b.) 81; base -3
Solution:
81; base -3
Express 81 as an exponential form where base is -3
The product of four (-3)’s is 81.
Therefore, 81 = (-3) ∙ (-3) ∙ (-3) ∙ (-3) = (-3)4
(c.) -343; base -7
Solution:
-343; base -7
Express -343 as an exponential form where base is -7
The product of three (-7)’s is -343.
Therefore, -343 = (-7) ∙ (-7) ∙ (-7) = (-7)3
Reference: www.math-only-math.com
Scientific notation (also referred to as "standard form" or "standard index form") is a way of writing
numbers that are too big or too small to be conveniently written in decimal form. Scientific notation has a
number of useful properties and is commonly used in calculators and by scientists, mathematicians and
engineers.
Decimal notation Scientific notation
2
2×100
300
3×102
4,321.768
4.321768×103
−53,000
−5.3×104
6,720,000,000
6.72×109
0.2
2×10−1
0.000 000 007
7×10−9
51
5.1 X101
In scientific notation all numbers are written in the form
a × 10b
(a times ten raised to the power of b), where the exponent b is an integer, and the coefficient a is any real
number Decimal floating point is a computer arithmetic system closely related to scientific notation.
Name ______________________________ Date___________________
Review Exponents and Scientific Notation
Switch these numbers into standard form.
1) 7.8 103
2) 9.14 10 7


4) 1.54 105

5) 4.68 104
7) 6.89 10 2



6) 6.18 10 5
9) 6.7 103
8) 4.67 10 3

11) 9.68 104
10) 6.15 10 3

12) 3.17 10 5

Switch these numbers into Scientific Notation accurate to 2 decimal places.
13) 0.0001759





3) 6.58 10 6
14) 165,400

16) 0.000618
15) 94,762

18) 61,349
17) 0.00005


19) 15,674,106



22) 18,964,526

21) 0.0000068
20) 12,834
For problems 25 – 30, evaluatethe exponent.
25) 2 2

27) 6 2

29) 32
28) (3) 2

31) (4) 3


26) 32


24) 5,841
23) 0.00075
30) 5 3

33) 6 3
32) (9) 2


For problems 31 – 39, expand, but do not evaluate the following.
35) 7 4
34) (5) 6



38) 15 4
37) 12 5

36) 4 8

39) (20) 6

Name __ANSWER KEY_______________ Period_______ Date___________________
Review Exponents and Scientific Notation
Switch these numbers into standard form.
1) 7.8 103
2) 9.14 10 7
0.0078

91, 400, 000

4) 1.54 105

7) 6.89 10 2
618, 000

9) 6.7 103
8) 4.67 10 3
689
4, 670

0.0067

11) 9.68 104
10) 6.15 10 3
0.00615

6) 6.18 10 5
0.000468


6, 580, 000
5) 4.68 104
0.0000154

3) 6.58 10 6
12) 3.17 10 5
0.000968

317, 000

Switch these numbers into Scientific Notation accurate to 2 decimal places.
13) 0.0001759
14) 165,400
15) 94,762
1.76  10 4

1.65  10 5

16) 0.000618

18) 61,349
17) 0.00005
6.18  10 4
6.13  10 4
5.00  10 5


19) 15,674,106


21) 0.0000068
20) 12,834
6.80  10 6
1.28  10 4
1.57  10 7


22) 18,964,526
24) 5,841
23) 0.00075
7.50  10 4
1.90  10 7

9.48  10 4

5.84  10 4

For problems 25 – 30, evaluate the exponent.
25) 2 2
26) 32
4

27) 6 2
9
36


29) 32
28) (3) 2
9
30) 5 3
-9
125


31) (4) 3
33) 6 3
32) (9) 2
-64


81
-216


For problems 31 – 39, expand, but do not evaluate the following.
35) 7 4
34) (5) 6


38) 15 4
37) 12 5
 1 15  15  15  15
12  12  12  12  12

4 4 4 4 4 4 4 4
 1 7  7  7  7
(5)( 5)( 5)( 5)( 5)( 5)

36) 4 8

39) (20) 6
(20)( 20)( 20)( 20)( 20)( 20)

Scientific Notation Word Problems Practice
1) The nearest star to us, Alpha Centauri, is 4.3 light years away. A light year is 5, 865,696,000,000 miles. (This is why we use
light years as a measurement of distance, guys. Space is big.) How far away is Alpha Centauri in miles? Express in scientific
notation round to nearest 100000th.
2. Americans eat an average of 1,200,000,000 pounds of hamburger each year. Assuming that each hamburger is a quarterpounder, how many hamburgers do Americans eat each year? Express your answer in scientific notation.
3.
Red blood cells are only 4 x 10-5 of an inch wide. In the human body, there are about 2.5 x 1013 blood cells in the human
body. If they were lined up side to side, for how many feet would our blood cells line up?
4.
If the Earth is 4.54 billion (billion = 1,000,000,000) years old and you believe in reincarnation, and the average life span is
70 years old, how many lives have you lived? Express your answer in both standard and scientific notation.
5.
The average number of words spoken by men each day is 10,000 words and the average number of words spoken by
women each day is 25,000 words. If the population of the Earth is 6 billion (billion = 1,000,000,000) people and
approximately half are men and half are women, each day how many more words are spoken by women.
Scientific Notation Word Problems Practice ANSWERS
1. The nearest star to us, Alpha Centauri, is 4.3 light years away. A light year is 5, 865,696,000,000 miles.
(This is why we use light years as a measurement of distance, guys. Space is big.) How far away is Alpha
Centauri in miles? Express in scientific notation round to nearest 100000th.
(4.3)(5, 865,696,000,000) = 2.52224928 x 1013 = 2.522250 x 1013
2. Americans eat an average of 1,200,000,000 pounds of hamburger each year. Assuming that each
hamburger is a quarter-pounder, how many hamburgers do Americans eat each year? Express your
answer in scientific notation.
(1,200,000,000)(.25) = 3x 108
3. Red blood cells are only 4 x 10-5 of an inch wide. In the human body, there are about 2.5 x 10 13 blood
cells in the human body. If they were lined up side to side, for how many feet would our blood cells
line up?
(4 x 10-5)(2.5 x 1013) = 1x109
4. If the Earth is 4.54 billion (billion = 1,000,000,000) years old and you believe in reincarnation, and the
average life span is 70 years old, how many lives have you lived? Express your answer in both standard
and scientific notation.
Std. = 64,285,714.29
64285714.29 = 6.428571429 x 107
5. The average number of words spoken by men each day is 10,000 words and the average number of
words spoken by women each day is 25,000 words. If the population of the Earth is 6 billion (billion =
1,000,000,000) people and approximately half are men and half are women, each day how many more
words are spoken by women.
(25,000 - 10,000)(6 x 109) = 9 x1013
Name_______________________________________________Date:__________
Powers, Exponents and Scientific Notation Quiz (notes can not be used)
Please use Calculators and show all work where needed (30 minutes time).
1) If light travels 6.71×108miles in one hour. How many miles will it travel 1minute?
Answer must be in Scientific notation.
2) Change to expanded form for the value of 18
3) What is the product of 107 x 1012? Answer in Exponential form
4) What is the cube root of X3?
5) What is the quotient of X3 and X3?
6) How far is a million inches in miles? (There are 5280 feet in 1 mile.)
Round answer to nearest tenth.
7) There are 3.949 × 106 miles of roads in the United States, If, on average, 1.2 × 102 cars went over each
mile of road per day, how many miles would be driven each day in the United States? Round answer to
nearest whole number. Answer must be in Scientific notation.
8) The cube root of 118 in between what two numbers?
9) Convert to standard form from scientific notation 3.42 x 10- 4
10) The Koch Brothers are claimed to be worth $4,500,000,000. Write their wealth in scientific notation.
Answer must be in Scientific notation.
Extra Credit
McDonald’s has sold more than a billion (1,000,000,000) hamburgers. If it were possible to eat a hamburger
every minute of every day (day and night) without stopping, how many years would it take to eat a billion
hamburgers? Answer must be in Scientific notation.
ANSWERS
Powers, Exponents and Scientific notation (notes can not be used) Please use Calculators and show all work
(30 minutes time)
1) If light travels 6.71×10^8miles in one hour. How many miles will it travel 1minute?
6.71×108miles ÷ 6. X 10 1 = 1.11 x 107
2) Change to expanded form for the value of 1^8 = 1x1x1x1x1x1x1x1
3) What is the product of 10^7 x 10^12? =10x19
4) What is the cube root of X ^3? = X
5) What is the quotient of X^3 and X^3? = 1
6) How far is a million inches in miles? (There are 5280 feet in 1 mile.)
Round answer to nearest tenth.
1,000,000 in. ÷ 12 in./ft. = 83333 ft. ÷ 5280ft. /mi = 15.8 mi.
7) There are 3.949 × 106 miles of roads in the United States, If, on average, 1.2 × 102 cars went over each mile
of road per day, how many miles would be driven each day in the United States? Round answer to nearest
whole number.
(3.949 x106) ÷ (1.2 x102) = 3 x104
8) The cube root of 118 in between what two numbers? 4 and 5
9) Convert to standard form from scientific notation 3.42 x 10 - 4 = 0.000342
10) The Koch Brothers claimed to be worth $4,500,000,000. Write their wealth in scientific notation. 4.5 x 109
Extra Credit
McDonald’s has sold more than a billion (1,000,000,000) hamburgers. If it were possible to eat a hamburger
every minute of every day (day and night) without stopping, how many years would it take to eat a billion
Hamburgers ?
60 mins. = 1hr. 60 mins./hr. x 24 hr./day = 1440 mins./day (1 day) X 365day/yr = 525600 mins./(1 yr.)
1 x 10 9 (hamburgers) ÷ 5.256 x 105 (mins. in a year) = .1903 x 104 = 1.903 x103 (yrs.)