Sorry I could not post handouts for Chapter 2 yet, lots of fractions could not published well once I convert the documents to PDFs.

I will distribute all handouts in class.

Thanks.

 

 

Chapter 1 Factors and Multiples

Numbers: Prime, composite, (integer, natural, whole, decimal, positive, negative, fractions, etc.)

Prime factoris(z)ation

Highest common factors (HCF)

Least common multiple (LCM), why not Highest common multiple

Square, square root, cube, cube root

Class exercises

1. Factors and multiples

18 = 1 x 18 = 2 x 9 = 3 x 6 = 6 x 3 = 9 x 2 = 18 x 1

1, 2, 3, 6, 9, 18 are all factors of 18

18 is a multiple of 1, 2, 3, 6, 9, 18

When 18 is divided by its factors 1, 2, 3, 6, 9, 18, the reminder is 0 à divisible

1. Prime numbers and composite numbers

Prime number: a number which has only two different factors, 1 and the number itself

Examples: 2, 3, 5, 7…

Composite number: a number has more than two different factors

Examples: 4, 6, 8, 10, 15, …

The number 1 is neither a prime number nor a composite number

Goldbach’s Conjecture: Every even number greater than 2 can be expressed as the sum of two prime numbers, verify using the following numbers 16, 36, 64, 98

Two-digit prime numbers with reversed digits: 37 and 73, others?

Twin prime numbers: prime numbers that differ by 2, like 5 and 7, list others?

1. Prime factorization

Decomposition of a composite number into prime factors

Example:               60                                             2 |  252

                              /   \                                              2 | 126

                            2     30                                             3| 63

                                   /   \                                            3| 21

                                 2     15                                               7

                                        /   \
                                       3     5

  So, 60 = 2 x 2 x 3 x 5                                        252 = 2 X 2 X 3 X 3 X 7 = 2² X 3² X 7

1. Index Notation

5 x 5 x 5 is written 5³ and is read 5 cubed or the cube of 5

5 x 5 x 5 x 5 is written as 5⁴ and is read as 5 to the power of 4

a x a x a x a x … x a is written as aⁿ and is read as a to the power of n

 

Exercises: Factorize 100, 125, 147, 216, 225, 360, 567, 648

 

1. Highest common factor (HCF)à Greatest common factor (GCF)

Case Study: How to cover a 30 cm by 36 cm sheet of paper completely with identical SQUARE patterns? Find the side of the largest possible square.

Can we use 1 x 1 square? Or 2 x 2 square?

The factors (prime factorization) of 30: 30 = 2 x 3 x 5

The factors (prime factorization) of 36: 36 = 2² x 3²

So the HCF of 30 and 36 is 2 x 3 = 6, use 6 x 6 sheet to cover the 30 x 36 area

Method 2:     2 | 30  36

                         3| 15  18

                                 5    6

  So the HCF is 2 x 3, there is no common factors between 5 and 6 bigger than 1

 

Exercises: Find HCF of the 60, 180, 210

 

1. Least common multiple (LCM)

Case Study: Using a rectangular pattern measuring 9 cm by 12 cm to form a square, decide how many rectangular patterns needed

The multiples of 9 are 9, 18, 27, 36…,

The multiples of 12 are 12, 24, 36…

The least common multiple of 9 and 12 is 36

 

Class exercises: find LCM of 30 and 36

30 = 2 x 3 x 5

36 = 2² x 3²

Then the lease common multiple of 30 and 36 are 2² x 3² x 5

 

Method 2:   2 | 30  36, then the LCM is 2 x 3 x 5 x 6

                       3| 15  18

                                5    6

 

Exercise: Find LCM of 18, 24, 36

 

1. Squares and square roots, cubes and cube roots

Find positive square root of 784 and 2025, find the cube roots of 512 and 5832

 

1. Workbook Summary and Practice questions: page 1- 3

Newton Chinese Language School

2011- 2012

Class ID 2551: 数学6甲, Math – VI (A)

Teacher: Li, Weidong  李卫东, TA: Han, Lijuan 韩黎娟

Class Room: 312

Time: 3:40 – 5:00 PM

 

Text Book and Work Book: New Elementary Mathematics, Syllabus D, by Low Wai Cheng

Supplemental Materials: Math Contests for Grade 4-8, AMC 8, and others

Classroom Rules: (1) One voice at a time, respect others and listen while others are speaking; (2) Come to class on time with all necessary materials, including homework, workbook and class folder; (3) Positive attitude, active thinking and participation

Course Contents: Numbers, Expressions, Open sentences and Equations, Rate/Ratio/Percentage, Geometry, Polygons, Symmetries and Solid Figures, Area/Perimeter, Volume/Surface/Density, Similarity and Congruence

Homework: Expect 1-2 hours every week

Grading: Homework, Quiz, Mid-term and Final

Contact Information: weidongli_2002@hotmail.com, 617-835-9615, or by appointment

Web Postings: http://blog.newtonchineseschool.org/liweidong/

Calendar: Sept 11, 18, 25 || Oct 2, 16, 23, 30 || Nov 6, 13, 20 || Dec 4, 11, 18 || Jan 8, 15(opt), 22, 29 || Feb 5, 12, 19(opt), 26 || Mar 4, 11, 18, 25 || Apr 1, 15(opt), 22, 29 || May 6, 13, 20 || Jun 3, 10, 17

 

Objectives (Yours, mine and parents):