Section 1:

1. Quiz on negative number, addition and subtraction of integers

2. Multiplication, division and combined operations of integers:.

• If two numbers have the same sign, their product/quotient is positive
• If two numbers have opposite signs, their product/quotient is negative
• Any integer multiplies 0, the product is 0: a x 0 = 0
• 0/a = 0, given a !=0
• a/0 is undefined
• How about 0/0? https://www.khanacademy.org/math/algebra/introduction-to-algebra/division-by-zero/v/undefined-and-indeterminate
• Combined operation: PEMDAS

3. Rational numbers: rational numbers are numbers that can be expressed in the form of a/b, where a and b are integers, and b != 0

4. Addition, subtraction, multiplication and division of rational numbers

5. Home Work:

• Handout: three pages
• Workbook:
  • page 8: 6, 8, 9, 10, 11
  • page 10: 18, 19, 20, 21, 22, 23

Section 2:

1. Quiz next week

2. Real numbers and use of calculators:.

• Rational number: can be expressed as a decimal by dividing the numerator of the rational number by its denominator
• Terminating decimal: has a finite number of digits: ⅜, 5/16
• Repeating decimal: 9/11, 7/11
• Irrational number: non-terminating and non-repeating decimals
• Use of calculators

3. Rounding numbers to decimal places

• Mark the cut-off point after the desired place value
• Rule of rounding up: the first digit after the cut-off point,  is >=5
• Rule of rounding don: the first digit after the cut-off point, is  < 5
• Nearest 10, 100, 1000, one million, …
• Nearest tenth, hundredth, or thousandth, …
• 1 decimal place, two decimal places, 3 decimal places, …

4. Home Work:

• Handout: two pages
• Workbook:
  • page 11: 24, 25, 26, 27, 28, 29
  • page 12-13: 30, 31, 32, 33, 34, 35, 36

Section 1:

1. Opposite Numbers (additive inverse): is a number that when added to a given number yields 0. The opposite number for any number x is -x. Note that x may be positive or negative.

(-5) + 5 = 0

x + (-x) = 0

On the number line, the numbers 5 and -5 are located at the same distance from zero. We say that the numbers 5 and -5 are opposites. We can also say that -5 is opposite to 5, and 5 is opposite to -5 on the number line.

2. Addition of integers:

• Addition of a positive number is taken as a movement to the RIGHT of the number line
• Addition of a negative number is taken as a movement to the LEFT of the number line

(-3) + 4

2 + 3

(-1) + (-3)

2 + (-5)

0 + (-4)

3. Rule for addition:

• If the signs of the integers being added are the same, the sum has the same sign as the integers and we add the absolute values of the integers

For any a > 0, and b > 0,

a + b = a + b;        3 + 5 = 8

(-a) + (-b) = -(a+b);         (-3) + (-5) = – (3 + 5) = -8

• If the signs of the integers being added are different,, the sum takes the sign of the integer with the greater absolute value and we find the difference of the absolute values of the integers.

For any a > 0, and b > 0,

a + (-b) = +(a – b) if a >=b;        9 + (-6) = +(9 – 6) = +3 = 3

a + (-b) = – (b -a) if b > a;         15 + (-20) = -(20 -15) = -5

-a + b = -(a – b) if a >= b;         -18 + 12 = -(18 -12) = -6

-a + b = +(b -a) if b > a;          -23 + 27 = +(27 – 23) = +4 = 4

4. Home Work:

• Handout: one page
• Workbook: page 7: 4

Section 2:

1. (Not today) Quiz on negative number and addition of integers

2. Subtraction of integers:.subtraction is the reverse process of addition. Using a number line:

• Subtraction of a positive number is taken as a movement to the LEFT of the number line
• Subtraction of a negative number is taken as a movement to the RIGHT of the number line

(-3)  – 4

2 –  3

(-1) –  (-3)

2 –  (-5)

0 – (-4)

3. Rule for subtraction: to subtract integers, we change the sign of the integer being subtracted and add them together according to the rule for addition of integers.

For any integers a, and,b,

a – b = a + (-b)

4. Absolute value of the difference:

For any integers a, and,b,

|a – b| = |b – a|

5. Home Work:

• Handout: two pages
• Workbook:
  • page 8: 7
  • page 9: 17
  • page 10: 20

1. Negative Numbers: we often across quantities that have opposite directions or meanings. For example,  traveling due east and west, the rise and fall in price, profit and loss, and being above or below sea level. When we assign a certain meaning of quantity to be positive, a value of the quantity that has the  opposite meaning may be considered as negative and is represented with a “-” sign.

• Positive numbers: 1, 2, 3, 0.8, ⅜, …
• Negative numbers: -1, -2, -3, -⅔, -0.0025, …
• Meanings of positive and negative numbers: teaching on whiteboard in the class.

2. The (horizontal) number line:

How to draw a number line:

• Draw a line, and mark the zero point on it;
• Choose a unit length, e.g., 1 cm, to mark the points 1, 2, 3, … at equal unit intervals on the right of 0, and the points -1, -2, -3, … on the left of 0;
• Draw an arrow at each end.

Inequality signs:

• > greater than
• < less than
• >= greater or equal
• <= less than or equal

On a horizontal number line:

• All the positive numbers are to the right of 0
• All the negative numbers are to the left of 0
• Numbers are arranged in ascending (increasing) order from left to right
• Every number is smaller than any number on its right and greater than any number on its left

3. Absolute Value: the absolute value of a number is the distance that number is from 0 on the number line. Both 3 and -3 are the same distance from 0. The absolute value of a number is never negative.

|3| = 3, or |x| = x if x >= 0

|-3| = 3, or |x| = -x if x < 0

4. Home Work:

• Handout: two pages
• Workbook 7A: page 7: 1, 2, 3, 5

Dear NCLS Math 7 students and parents,

Welcome to a new NCLS school year! My name is Li Zhen, the instructor for Math 7 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 Saturday , 9/11/2021.

What does each student need to bring to the first class? Computer and internet connection; 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 is a sophomore at Harvard University this fall. Here is my contact info:

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

This year, we have some 4th graders, 6th graders and mostly 7th 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 the 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.

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