1. Least Common Multiple (LCM):

The least common multiple of a group of numbers is the smallest positive integer which is divisible by all the numbers in the group.

The multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, …

The multiple of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, …

24 and 48 are the first two common multiples of 6 and 8. Since 24 is the least of all common multiples, we say the least common multiple (LCM) of 6 and 8 is 24.

2. Methods to find LCM

• Using prime factorization. LCM is obtained by multiplying the highest power of each prime factor of the given numbers. Teaching on whiteboard in the class.
• Continuous division. Teaching on whiteboard in the class.
• Venn diagram. Teaching on whiteboard in the class.

3. Why LCM?

• adding, subtracting, or comparing vulgar fractions, it is useful to find the least common multiple of the denominators, often called the lowest common denominator, because each of the fractions can be expressed as a fraction with this denominator. Ex. 1/15 + 1/18 + 1/21
• Word problems: Teaching on whiteboard in the class

4. Home Work:

• Handout: two pages
• Workbook:
  • page 2: 7
  • Page 3: 13, 15(a), 15(b)(ii), 17(a), 17(b)(ii)
  • Page 4: 23
  • Page 5: 24

1. Greatest Common Factor (GCF): the largest common factor of a group of numbers is the largest positive integer that can divide all the numbers in the group.

The factors of 18: 1, 2, 3, 6, 9, 18

The factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

1, 2, 3, and 6 are called the common factors of 18 and 24. The largest of these common factors is 6. Thus, 6 is the greatest common factor of 18 and 24.

HCF: the highest common factor, same as GCF

GCD: the greatest common divisor, same as GCF

Relatively Prime or Mutually Prime: when two numbers, such as 15 and 16, have no common factors greater than 1, their GCF = 1 and the numbers are said to be relatively prime, or mutually prime.

2. Methods to find GCF

• Using prime factorization. GCF is obtained by multiplying the lowest power of each common factor of the given numbers. Teaching on whiteboard in the class.
• Continuous division. Teaching on whiteboard in the class.
• Venn diagram. Teaching on whiteboard in the class.

3. Why GCF?

• Reduce a fraction to its lowest terms: 18/48 = (18 / 6) / (48 /6) = ⅜
• Algebra, GCF of the coefficients: 18x*x + 48x = 6x(3x + 8)
• Word problems: Teaching on whiteboard in the class

4. Home Work:

• Handout: one page
• Workbook:
  • page 2: 6, 10(a), 10(b), 11
  • Page 3: 12, 14, 15(a), 15(b)(i), 17(a), 17(b)(i)
  • Page 4: 21, 22
  • Page 5: 26, 27, 28, 29(b)

1. Factors: the number 12 can be expressed as the product of two smaller whole numbers as follow:

12 = 1 x 12

12 = 2 x 6

12 = 3 x 4

1, 2, 3, 4, 6, and 12 are called factors of 12. We say that 12 is divisible by each of its factors.

2. Multiplies: when a number is multiplied by a non-zero whole number, we get multiple of the number:

The multiple of 3 are: 3×1, 3×2, 3×3, 3×4, 3×5, …

That is: 3, 6, 9, 12, 15, …

The multiple of 4 are: 4×1, 4×2, 4×3, 4×4, 4×5, …

That is: 4, 8, 12, 16, 20, …

3. Link between factors and multiplies:

Recall 3 and 4 are factors of 12. Interestingly, 12 is a multiple of both 3 and 4. The number 12 is a multiple of each of its factors 1, 2, 3, 4, 6, and 12.

4. Prime number, composite number, prime factor

• Prime number: a prime number is a whole number greater than 1 that has only two factors. 1 and itself. 2, 3, 5, 7, 11, 13, 17, 19, …
• Composite number: a composite number is a whole number greater than 1 that has more than two factors.
• Prime factor: a prime number that is a factor of a composite number is called a prime factor of the composite number.

5. Prime factorization methods:

• Factor tree: teaching on whiteboard in the class
• Continuous division: teaching on whiteboard in the class
• divisibility: https://www.khanacademy.org/math/pre-algebra/pre-algebra-factors-multiples/pre-algebra-divisibility-tests/v/divisibility-tests-for-2-3-4-5-6-9-10

6. Exponential notation:

Squared, cubed, fourth power, … teaching on whiteboard in the class

7. Home Work:

• Handout: three pages
• Workbook page 1: 1, 2, 3, 4, 5

Dear NCLS Math 6A parents,

Welcome to a new NCLS school year! My name is Li Zhen, the teacher for Math 6A class at Newton Chinese School. I am excited to meet your children this coming Sunday afternoon!

First thing first: each student needs to set up a gmail account and please email me his/her gmail address so I can share my Google Classroom with him/her. Please do so no later than the end of day on Friday , 9/11/2020.

What does each student need to bring to the first class? Pencils and/or pens; three note books — one for taking notes in class and class work and two for homework; and most importantly, a Can-Do Attitude.

I’d like to have regular communication with students, parents and my wonderful and very capable Teaching Assistants Jessie Wang. You can find a lot of information on my blog and you can find out what we have learned in the class on any given Sunday, and what the homework is for that week:

http://blog.newtonchineseschool.org/zhenli/

Please feel free to email me or call me (in evenings) to talk about your concerns, things like the materials we have covered in class; home work load; or just chat like parents. My older daughter has graduated from college, and my younger daughter would be a sophomore at Harvard University this fall. Here is my contact info:

Li Zhen Phone: 617-785-6137 email: math_lizhen@yahoo.com

In the past, we had some 4th graders, 5th graders and mostly 6th graders in class. We’ll get to know each other in the first class. A great group of beautiful children for sure, and they are at the perfect age to learn basic math skills, and most importantly, to shape up their problem-solving abilities. It is my deep belief that every child is smart, every child can learn and every child will exceed our expectations! My ultimate goal is, to encourage and to help our students to develop the love of (the beauty of ) math and the confidence of solving many problems in real world.

With that in mind, I will give a lot of homework this year, not only do I believe the students can do it, but also because this is the only way that they can master a certain skill by practicing a lot. In addition to the class handouts and the exercise in the Work Book, I also encourage the students to try some Math Contest problems each week, for fun and challenge.  If the load is too much for a student, the latter can be optional.

My TA will take attendance and correct all the homework. Quiz and exams are given on a regular basis. The students’ progress and grades will be recorded in each class. Final report will be distributed to each family.

It’s a privilege to work with your child, and I thank you for that!

(PS. Please come to the classroom on the first day, or at the very least, reply to this email that you have read and been fully aware of our course load.)

Thank you very much!

Li Zhen