Students will be expected to demonstrate an understanding of factors of whole numbers by determining...

78
math 10 plus chapter 3 Ms. Albarico Nanchang No. 2 High School

TAGS:

Transcript of Students will be expected to demonstrate an understanding of factors of whole numbers by determining...

Page 1: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

math 10 plus

chapter 3

Ms. Albarico

Nanchang No. 2 High School

Page 2: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

TABLE OF CONTENTS  3.1 Factors and Multiples of Whole

Number3.2 Perfect Squares, Perfect Cubes, and Their Roots3.3 Common Factors of a Polynomial3.4 Math Lab: Modelling Trinomials as Binomial Products3.5 Polynomials of the Form x2+ bx + c3.6 Polynomials of the Form ax2+ bx + c3.7 Multiplying Polynomials3.8 Factoring Special Polynomials

Page 3: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

3.1 & 3.2 Curriculum Outcome

Students will be expected to demonstrate an understanding of

factors of whole numbers by determining the prime factors, greatest common factor, least

common multiple, square root, and cube root.

Page 4: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

3.1 & 3.2 Specific Outcomes

Determine the prime factors of a whole number. Explain why the numbers 0 and 1 have no prime factors. Determine, using a variety of strategies, the greatest

common factor or least common multiple of a set of whole numbers, and explain the process.

Determine, concretely, whether a given whole number is a perfect square, a perfect cube, or neither.

Determine, using a variety of strategies, the square root of a perfect square, and explain the process.

Determine, using a variety of strategies, the cube root of a perfect cube, and explain the process.

Solve problems that involve prime factors, greatest common factors, least common multiples, square roots, or cube roots.

Page 5: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Lesson 3.1

Page 6: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

PRIME FACTORIZATION

The prime factorization of a

natural number is the number

written as a product of itsprime factors.

Page 7: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Prime Factorization Quiz Online Prime Factorization Lecture  

http://e-learningforkids.org/Courses/EN/M1103/
http://e-learningforkids.org/Courses/EN/M1103/
Page 8: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Example 1

Determining the Prime Factors of a Whole Number

Page 9: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Determining the Prime Factors of a Whole Number

Example 1

Page 10: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

GREATEST COMMON FACTOR

The greatest commonfactor of two or more

numbers is the greatestfactor the numbers have in

common.

Page 11: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Greatest Common Factor Quiz Online

Greatest Common Factor Activity

Greatest Common Factor Module

http://www.oswego.org/ocsd-web/match/dragflip.asp?filename=slanegcf
http://www.glencoe.com/sites/common_assets/mathematics/mc1/cim/chapter_04/M1_06/M1_06_dev_100.html
http://e-learningforkids.org/Courses/EN/M1104/
Page 12: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Determining the Greatest Common Factor

Example 2

Page 13: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Determining the Greatest Common Factor

Example 2

Page 14: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Determining the Greatest Common Factor

Example 2

Page 15: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

LEAST COMMON MULTIPLE

The least common multiple of two or more

numbers is the least number that is divisible by each

number.

Page 16: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Least Common Multiple Game HG

Least Common Multiple Module

Least Common Multiple Game SB

http://www.sheppardsoftware.com/mathgames/fractions/LeastCommonMultiple.htm
http://e-learningforkids.org/Courses/EN/M1105/
http://www.sheppardsoftware.com/mathgames/fractions/LeastCommonMultiple.htm
Page 17: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Determining the Least Common Multiple

Example 3

Page 18: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Determining the Least Common Multiple

Example 3

Page 19: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Solving Problems that Involve Greatest Common Factorand Least Common Multiple

Example 4

Page 20: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Solving Problems that Involve Greatest Common Factorand Least Common Multiple

Example 4

Page 21: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Solving Problems that Involve Greatest Common Factorand Least Common Multiple

Example 4

Page 22: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Solving Problems that Involve Greatest Common Factorand Least Common Multiple

Example 4

Page 23: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Solving Problems that Involve Greatest Common Factorand Least Common Multiple

Example 4

Page 24: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

PRACTICE EXERCISES

Answer # 3-11(classwork)13-22 (homework) on

pages 140-141.

Page 25: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Lesson 3.2

Page 26: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Key Terms

Index - Radicand - Radical -

Page 27: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Key Terms

Page 28: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

PERFECT SQUARE

Any whole number that can be represented as the area of a square with a whole number side length is a perfect square.

The side length of the square is the square root of the area of the square.

Page 29: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

PERFECT SQUARE

Page 30: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Calculator Command

SQUARE ROOT

Press 2nd then x2

Page 31: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Example 1

Determining the Square Root of a Whole Number

Page 32: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Example 1

Determining the Square Root of a Whole Number

Page 33: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

PERFECT CUBE

Any whole number that can be represented as the volume of a cube with a whole number edge length is a perfect cube.

The edge length of the cube is the cube root of the volume of the cube.

Page 34: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

PERFECT CUBE

Page 35: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Calculator Command

CUBE ROOT

Press math then choose #4

Page 36: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Example 2

Determining the Cube Root of a Whole Number

Page 37: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Example 2

Determining the Cube Root of a Whole Number

Page 38: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Example3

Using Roots to Solve a Problem

Page 39: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Practice Exercises

Answer # 4-18 on pages 146-147.

Page 40: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Practice Exercises

Page 41: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.
Page 42: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.
Page 43: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Checkpoint!

Draw the diagram in your notebook on page 148.

Homework!

Answer ASSESS YOUR UNDERTSANDING questions 1-10 in your notebook on page 149.

Page 44: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

EXTRA LESSON – CUBE ROOT

Page 45: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Objective: You will be able to determine if a number is a perfect cube and to find the

cube root of a number that is a perfect cube.

Page 46: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Remember

A cube is a three dimensional prism with 6 square faces; so all sides are congruent and all angles are right angles.

Perfect Cubes and Cube Roots

Page 47: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Squares and Cubes:Similarities- All sides congruent- All angles 90 degrees

Differences:- Square is 2 dimensional- Cube is 3 dimensional that number’s

square root.

Perfect Cubes and Cube Roots

Page 48: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Remember

A number is a perfect square if you can take that many 1 x 1 unit squares and form them into a square. The side length of the square you form is that number’s square root.

Perfect Cubes and Cube Roots

Page 49: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

A number is a perfect cube if you can take that many 1 x 1 x 1 unit cubes and form them into a cube. The side length of the cube you form is that number’s cube root.is that number’s square root.

Perfect Cubes and Cube Roots

Page 50: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Is 8 a perfect cube?that number’s square root.

Perfect Cubes and Cube Roots

Page 51: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

that.

Perfect Cubes and Cube Roots

Page 52: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

that.

Perfect Cubes and Cube Roots

Page 53: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

8 is a perfect cube and its cube root is 2

Perfect Cubes and Cube Roots

Page 54: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Is 5 a perfect cube?

Perfect Cubes and Cube Roots

Page 55: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Is 5 a perfect cube?

Perfect Cubes and Cube Roots

Page 56: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Three Dimensions

Perfect Cube

Volume

Perfect Cubes and Cube Roots

Page 57: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Perfect Cube: 8 Cube Root 2

Volume: 8 units3 Side Length: 2 units

Perfect Cubes and Cube Roots

Page 58: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Perfect Cubes and Cube Roots

Side Length

Volume Operation

Volume Perfect Cube

2 units

2 x 2 x 2 8 units3 8

Page 59: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Perfect Cube: Cube Root

Volume: units3 Side Length: units

Perfect Cubes and Cube Roots

Page 60: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Perfect Cubes and Cube Roots

Side Length

Volume Operation

Volume Perfect Cube

1 unit 1 x 1 x 1 1 units3 1

2 units

2 x 2 x 2 8 units3 8

Page 61: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Perfect Cube: Cube Root

Volume: units3 Side Length: units

Perfect Cubes and Cube Roots

Page 62: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Perfect Cubes and Cube Roots

Side Length

Volume Operation

Volume Perfect Cube

1 unit 13 1 units3 1

2 units

23 8 units3 8

3 units

33 27 units3 27

Page 63: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Perfect Cubes and Cube Roots

Side Length

Volume Operation

Volume Perfect Cube

1 unit 13 1 units3 1

2 units

23 8 units3 8

3 units

33 27 units3 27

4 units

Page 64: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Perfect Cubes and Cube Roots

Side Length

Volume Operation

Volume Perfect Cube

1 unit 13 1 units3 1

2 units

23 8 units3 8

3 units

33 27 units3 27

4 units

43

Page 65: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Perfect Cubes and Cube Roots

Side Length

Volume Operation

Volume Perfect Cube

1 unit 13 1 units3 1

2 units

23 8 units3 8

3 units

33 27 units3 27

4 units

43 64 units3

Page 66: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Perfect Cubes and Cube Roots

Side Length

Volume Operation

Volume Perfect Cube

1 unit 13 1 units3 1

2 units

23 8 units3 8

3 units

33 27 units3 27

4 units

43 64 units3 64

Page 67: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Perfect Cubes and Cube Roots

Side Length

Volume Operation

Volume Perfect Cube

1 unit 13 1 units3 1

2 units

23 8 units3 8

3 units

33 27 units3 27

4 units

43 64 units3 64

S units

S3 S3 units3 S3

Page 68: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Perfect Cubes and Cube Roots

Side Length of cube

Volume Operation

Volume of cube

Perfect Cube

1 unit 13 1 units3 1

2 units 23 8 units3 8

3 units 33 27 units3

27

4 units 43 64 units3

64

S units S3 S3 units3 S3

10 units

Page 69: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Perfect Cubes and Cube Roots

Side Length of cube

Volume Operation

Volume of cube

Perfect Cube

1 unit 13 1 units3 1

2 units 23 8 units3 8

3 units 33 27 units3

27

4 units 43 64 units3

64

S units S3 S3 units3 S3

10 units

103

Page 70: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Perfect Cubes and Cube Roots

Side Length of cube

Volume Operation

Volume of cube

Perfect Cube

1 unit 13 1 units3 1

2 units 23 8 units3 8

3 units 33 27 units3

27

4 units 43 64 units3

64

S units S3 S3 units3 S3

10 units

103 1000 u3

Page 71: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Perfect Cubes and Cube Roots

Side Length of cube

Volume Operation

Volume of cube

Perfect Cube

1 unit 13 1 units3 1

2 units 23 8 units3 8

3 units 33 27 units3

27

4 units 43 64 units3

64

S units S3 S3 units3 S3

10 units

103 1000 u3 1000

Page 72: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Square Root

Perfect Cubes and Cube Roots

Page 73: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Square Root Cube Root

Perfect Cubes and Cube Roots

Page 74: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Square Root Cube Root

Perfect Cubes and Cube Roots

Page 75: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Square Root Cube Root

Perfect Cubes and Cube Roots

Page 76: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Practice

Perfect Cubes and Cube Roots

Page 77: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Practice

Is 827 a perfect cube?

Perfect Cubes and Cube Roots

Page 78: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.

Conclusion: You can now determine if a number is a perfect cube and find the cube

root of a number that is a perfect cube.


Home - Sebring Local Schools · Greatest Common Factor List the common factors. Circle the greatest common factor. Lesson COMMON CORE STANDARD CC.6.NS.4 Compute fluently with multi-digit

Home - Sebring Local Schools · Greatest Common Factor List the common factors. Circle the greatest common factor. Lesson COMMON CORE STANDARD CC.6.NS.4 Compute fluently with multi-digit

Level 1 Business Studies 1.1 - AS90837 Demonstrate an understanding of internal factors of a small business.

Level 1 Business Studies 1.1 - AS90837 Demonstrate an understanding of internal factors of a small business.

FACTORS AND GREATEST COMMON FACTORS A PRIME NUMBER is a whole number, greater than 1, whose only factors are 1 and itself. A COMPOSITE NUMBER is a whole.

FACTORS AND GREATEST COMMON FACTORS A PRIME NUMBER is a whole number, greater than 1, whose only factors are 1 and itself. A COMPOSITE NUMBER is a whole.

CorrectionKey=A Factors and Multiples MODULE 2...Understanding Common Factors The greatest common factor (GCF) of two numbers is the greatest factor shared by those numbers. A florist

CorrectionKey=A Factors and Multiples MODULE 2...Understanding Common Factors The greatest common factor (GCF) of two numbers is the greatest factor shared by those numbers. A florist

Factors and Multiples Chapter Questionscontent.njctl.org/courses/math/6th-grade-math/... · Factors and Multiples Chapter Review Multiple Choice Questions 83) Find the Greatest Common

Factors and Multiples Chapter Questionscontent.njctl.org/courses/math/6th-grade-math/... · Factors and Multiples Chapter Review Multiple Choice Questions 83) Find the Greatest Common

Tuesday, Sept 3 Lesson 1.1 Greatest Common Factors.

Tuesday, Sept 3 Lesson 1.1 Greatest Common Factors.

Over-expression of the epidermis-specific HD-ZIP IV transcription … · 2010/7/6  · factors. Our data demonstrate that, in addition to AP2/EREBP and MYB type transcription factors,

Over-expression of the epidermis-specific HD-ZIP IV transcription … · 2010/7/6  · factors. Our data demonstrate that, in addition to AP2/EREBP and MYB type transcription factors,

Multiples, Factors, Primes and Composites - Assessment Task · 2009. 11. 2. · In this assessment task, students will be asked to demonstrate their understanding of multiples, factors,

Multiples, Factors, Primes and Composites - Assessment Task · 2009. 11. 2. · In this assessment task, students will be asked to demonstrate their understanding of multiples, factors,

World War I Looms p. 352. Deadly Social Factors Invite War Four factors led the Imperialist European Powers, in 1914, into one of the greatest, most destructive.

World War I Looms p. 352. Deadly Social Factors Invite War Four factors led the Imperialist European Powers, in 1914, into one of the greatest, most destructive.

Chapter 7 Factors and Greatest Common Factors Ms. Fisher.

Chapter 7 Factors and Greatest Common Factors Ms. Fisher.

Factors and Multiples MODULE 2 - WELCOME TO MATH€¦ · Understanding Common Factors The greatest common factor (GCF) of two numbers is the greatest factor shared by those numbers.

Factors and Multiples MODULE 2 - WELCOME TO MATH€¦ · Understanding Common Factors The greatest common factor (GCF) of two numbers is the greatest factor shared by those numbers.

Merit · 2018. 4. 9. · Achievement with Merit Demonstrate in-depth understanding of how a large business responds to external factors. Achievement with Excellence Demonstrate comprehensive

Merit · 2018. 4. 9. · Achievement with Merit Demonstrate in-depth understanding of how a large business responds to external factors. Achievement with Excellence Demonstrate comprehensive

Greatest common factors ( gcf ) & least common multiples (lcm)

Greatest common factors ( gcf ) & least common multiples (lcm)

Greatest Common Factor. The greatest common factor (GCF) is the product of the prime factors both numbers have in common. Or It is the largest number.

Greatest Common Factor. The greatest common factor (GCF) is the product of the prime factors both numbers have in common. Or It is the largest number.

EoC ReviewPractice: The greatest common factor is 4. 3,@, 6, 9, 12, 18, 36 Circle the common factors. Example: I-Ina tn e greatest 8, 16 common a List the factors of each number.

EoC ReviewPractice: The greatest common factor is 4. 3,@, 6, 9, 12, 18, 36 Circle the common factors. Example: I-Ina tn e greatest 8, 16 common a List the factors of each number.

The Greatest Barriers for Women of Color Business …...The Greatest Barriers for Women of Color Business Owners 2 of 3 Increasing education and relevant work experience are also factors

The Greatest Barriers for Women of Color Business …...The Greatest Barriers for Women of Color Business Owners 2 of 3 Increasing education and relevant work experience are also factors

1 The purpose of this presentation is to demonstrate factors ...

1 The purpose of this presentation is to demonstrate factors ...

ECONOMIC SYSTEMS. Demonstrate an understanding of economic systems and the factors that influence them. Describe the economic relationship between.

ECONOMIC SYSTEMS. Demonstrate an understanding of economic systems and the factors that influence them. Describe the economic relationship between.

1.1 Factoring Review Greatest Common Factors of a Polynomial...1.1 - Factoring Review Greatest Common Factors of a Polynomial Example 1 – Factor 2a) 4 +14 b) − 2− 34c) 27 +36

1.1 Factoring Review Greatest Common Factors of a Polynomial...1.1 - Factoring Review Greatest Common Factors of a Polynomial Example 1 – Factor 2a) 4 +14 b) − 2− 34c) 27 +36

Factors Greatest Common Factorsmrsdempseysmathsite.weebly.com/uploads/2/3/7/4/... · The first step in factoring is to determine its greatest monomial factor. If there is a greatest

Factors Greatest Common Factorsmrsdempseysmathsite.weebly.com/uploads/2/3/7/4/... · The first step in factoring is to determine its greatest monomial factor. If there is a greatest