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

Go over the Final Exam, online kahoot! run by our TAs and class celebration party – share your story and your thoughts.  All of our students have worked very hard and have made so much progress. I’m so proud of you! It has been an unprecedented pandemic year, and I’m SO VERY PROUD of each and every one of my students, for sticking around, for your curiosity and your grit!  Keep up your good work in the summer and years beyond. Wish you and your family a healthy and safe summer! Please come to room 216 to visit me in Fall 2021. I shall have some special treat for each student. I love you all!

Stay hungry. Stay foolish. – Steve Jobs

Final Exam Spring 2021, 6/13/2021. The exam will cover all the materials we have learned in Spring 2021 term, namely chapter 5 to chapter 8.
http://blog.newtonchineseschool.org/zhenli/course-info/

You can access each  lesson summary here:http://blog.newtonchineseschool.org/zhenli/
http://blog.newtonchineseschool.org/zhenli/page/2/

Exam will be posted Saturday night in Google Classroom. Please print out all the pages before class.

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

1. No Quiz about percentage today

2. Discount

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

3. Sales Tax and Income Tax

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

4. Compound Discount

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

5. 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

6. 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

7. 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

8. 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

9. Home Work:

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

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 ( End_value, or New_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 ( End_value, or New_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

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

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