Math 6A, Lesson 2, Fall 2018, 9/16/2018

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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)


Math 6A, Lesson 1, Fall 2018, 9/9/2018

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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:

6. Exponential notation:

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

7. Home Work:

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


Letter to Math 6A Class Parents 9/7/2018

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Letter to Math 6A Class Parents 9/7/2018

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 on this coming Sunday afternoon!

First thing first: what does each student need to bring to 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 would like to have regular communication with students, parents and my two wonderful and very capable Teaching Assistants Iris Yang and Karen Li. You can find a lot 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:

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 is a senior at Newton South High School. Here is my contact info:

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 believe that every child is smart, and 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 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 heavy for a student, the latter can be optional.

My TAs will take attendance and correct all the homework, quiz and exam are given on regular base. The students’ progress and grades will be recorded in each class. Final report will be distributed to each family.

It is a privilege working with your child, and I thank you for that!

Thank you!

Li Zhen

Math 6A, Lesson 16, Spring 2018, 6/17/2018

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Go over Final Exam, and class celebration party.  All of our students have worked very hard and have made so much progress. I’m so proud of you! Have a great summer!


Math 6A, Lesson 15, Final Exam Spring 2018, 6/10/2018

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Final Exam Spring 2018, 6/10/2018

Math 6A, Lesson 14, Spring 2018, 6/3/2018

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1. Perpendicular Bisectors and Angle Bisectors

  • Use of compass: center, radius, pin leg, and drawing leg
  • To draw a circle
  • To mark off or copy a line segment
  • How to draw a perpendicular bisector of a line segment?
  • Any point on the perpendicular bisector of a line segment is equidistant from the two  end points of the segment.

2. Angle Bisectors

  • A ray AZ divides <BAC into two equal angles, <BAZ and <CAZ. The ray is called the angle bisector of <ABC
  • How to draw an angle bisector?
  • Any point on the angle bisector of an angle is equidistant from the two sides of the angle.

3. Class work

  • Construct/draw circles, triangles, angles, equal line segments
  • construct /draw perpendicular bisectors of line segments
  • construct/draw angle bisectors of angles

4. Classification of Triangles

  • The number of equal sides in the triangle: scalene triangle – no equal sides; isosceles triangle – two equal sides; equilateral triangles – three equal sides
  • The type of angles of the triangle: acute-angled triangle – all angles are acute; right-angled triangle – one of the angles is a right angle; obtuse-angled triangle – one of the angles is an obtuse angle
  • Is an equilateral triangle also an isosceles triangle?
  • Is it Possible to draw a triangle with more than one obtuse angle?
  • Can a scalene triangle be an acute-angled, right-angled or obtuse-angled triangle?
  • All the three angles in a scalene triangle are different size
  • The angles opposite the equal sides of an isosceles triangle are equal
  • All the three angles in an equilateral triangle are equal in size

5. Quadrilaterals

  • A closed plane figure with four straight sides joined by four vertices is called a quadrilateral
  • Vertices, diagonals
  • Properties of special quadrilaterals
  • Parallelogram: 2 pairs of parallel and equal opposite sides
  • Rectangle: all angles are right angles
  • Rhombus: all sides are equal, diagonals are perpendicular to each other
  • Square: all sides are equal, all angles are right angles
  • Trapezoid: 1 pair of parallel sides

6. Home Work:

  • Handout:
    • Two pages
  • Workbook:
    • Page 48-50: 12, 13, 14,15,16


Math 6A, Lesson 13, Spring 2018, 5/20/2018

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1. Discount

  • Discount = Marked price – Selling price
  • Percentage discount = ( Discount / Marked_price) x 100%
  • Selling price = (100% – Discount %) x Marked_price

2. Sales Tax and Income Tax

  • Tax = Tax_rate x Cost
  • Income_tax = Tax_rate x Income
  • Income: wage (hourly-paid), salary (annual basis)

3. Compound Discount

  • Each successive discount is based on the price after the previous discount

4. Points, Line and Planes

  • Point: has position; has no size
  • Line: has an infinite number of points; has no width; can be determined by two points; can be straight or curved
  • Ray: a part of a line with one endpoint
  • Endpoint
  • Line segment: a part of a line between two end points; has length
  • Plane: a flat surface; has no thickness
  • Parallel lines: two lines on the same plane do not intersect (meet or cut)
  • Perpendicular (lines) to each other: two lines intersect at right angle
  • Foot of the perpendicular

5. Types of angles

  • Acute angle: angle < 90 degree
  • Right angle: angle = 90 degree
  • Obtuse angle: 90 degree < angle < 180 degree
  • Reflex angle: 180 degree < angle < 360 degree

6. Complementary, supplementary, and adjacent angles

  • Complementary angles: the sum of two angles is 90 degree
  • Supplementary angles: the sum of two angels is 180 degree
  • Adjacent angles: two angles share a common side and a common vertex but do not overlap

7. Properties of Angles

  • The sum of adjacent angles on a straight line is 180 degree
  • The sum of all angles at a point is 360 degree
  • Vertically opposite angles: when two lines intersect, the vertically opposite angles are equal

8. Home Work:

  • Handout:
    • Three pages
  • Workbook:
    • Page 45: 1, 2, 3
    • Page 46: 4, 5

Math 6A, Lesson 12, Spring 2018, 5/13/2018

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1. Reverse Percentage

  • In a box, 15% of the balls are green. If there are 54 green balls, find the number of balls in the box.
  • In the library, the fine for not returning a book on loan is 125% of the price of the book. If the fine for a book that was not returned was $90, find the price of the book.

2. Percentage increase

  • Increase = Increased_value – Original_value
  • Percentage increase = ( Increase/ Original_value) x 100%
  • Increased_value = (100% + Increase %) x Original_value

3. Percentage decrease

  • Decrease = Original_value – Decreased_value
  • Percentage decrease = (Decrease / Original_value) x 100%
  • Decreased_value = (100% – Decrease %) x Original_value

4. Home Work:

  • Handout:
    • Three pages
  • Workbook:
    • Page 40: 8, 9, 10, 11


Math 6A, Lesson 11, Spring 2018, 5/6/2018

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1. Percentage: a percentage is a fraction with 100 as the denominator

  • Meaning of percentage: “per cent” means “by the hundred” or divided by one hundred. The term “percentage” is derived from the Latin per centum, meaning “per hundred”.

38% = 38/100 = 0.38

100% = 100/100 = 1

0% = 0/100 = 0

  • Decimals, percentages and fractions and how to express a number in each form
  • Express one quantity as a percentage of another
  • Compare quantities using percentage
  • Word problems involving percentage

2. Home Work:

  • Handout:
    • Two pages
  • Workbook:
    • Page 39: 1, 2, 3, 4, 5
    • Page 40: 6, 7


Math 6A, Lesson 10, Spring 2018, 4/29/2018

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Exam on ratio, rate, average rate, speed, uniform/constant speed and average speed, and Conversion of units.