This is the last teaching lesson for this semester, we finish off Chapter 14 for Algebraic Manipulations.

Today we talked about simplifying algebraic fractions, fractions whose numerator and denominator are both polynomials — such expression is called rational expression. We can eliminate the common factors. We talk about how to solve equations with algebraic fractions — such equation is called rational equation. One important thing to remember when solving a rational equation is that any solution cannot make any denominator zero.

We talk about identity equations where it is true for all values for the variable involved.

We will have a review next week, followed by a final exam in two weeks (last day of school).

Homework:

Page 148, #20 – 22, 26 – 32.

We go over polynomial addition, subtraction, multiplication, and division.

For addition and subtraction, it is important to remember to combine the terms with the same degrees. For example, you cannot combine a 2x^2 term with 3x term.

For multiplication, remember to multiply every term in one polynomial with every term in the other, then add them all up.

For division, we use the vertical form to do the division. We talk about the relationship between the divident, the divisor, the quotient, and the remainder.

Homework:

Chapter 14 homework: #1 – #17.

We cover the topics in Statistics II, averages.

While we commonly use the term “average” to mean the “arithmetic mean” in statistical sense, there are other kinds of averages in statistics.

We call the data scores, and the frequency is a term used to indicate the number of times a particular score occurs. We can use a frequency table to represent data, and use a histogram to represent the table.

Apart from the arithmetic mean or just mean, which is the sum of all scores divided by number of scores, we also have:

* Mode. which is the score that occurs most often in a distribution;

* Median, which is the middle score in the list (if the list has even number of scores, the median is the average of the middle two scores).

Homework:

Page 137: #1 – #12

Math contest results are out. We have several students who won:

Richard Chang: 1st place, 5th grade

Yuheng Dong: 2nd place, 6th grade

Aaron Zhang, 3rd place, 7th grade

Congratulations!

We cover reading and drawing of pie chart, line graphs, and pictograms. This is part of Statistics I.

Again, these are topics students feel intuitive and straight forward.

With the extra time, we go over some more of the math contest results.

Homework:

Page 130: #1, 2, 3, 6, 7, 9, 13, 14

Plan change.

School has decided to have a school wide math contest on 4/28/2013 and all Math class students will take part in this contest. As such, we have decided to use the contest in place of the midterm exam.

So, we didn’t have the exam today. Instead we finish the chapter on transformations.

Up to now the three kinds of transformations we have talked about, Reflection, Rotation, and Translation, all do not change the figure’s shape and size. They are called rigid transformation. Today we talk about enlargement where the shape remains but the size changes. And an enlargement transformation can increase (when the scale fact is bigger than 1) and reduce (when the scale factor is less than 1) the size. And there must be a center of enlargement.

Lastly, we talked about the combination of multiple transformations and how to identify each transformation involved and fully describe it.

Homework:

Page 122: #14, #15, #17, #18, #19, #20.

This is our midterm review day, as we will have the midterm exam next Sunday (4/7/2013).

Please go over your homework for this semester to prepare for the exam.

Homework:

Page 102, Test paper 4; page 126, test paper 5

We start with measurement for spheres. Two important formulae to remember:

Volume of a sphere with radius r is: 4/3 pi r^3

Surface area of a sphere with radius of r is: 4 pi r^2

We then talk about areas of similar figures and volumes of similar solids.

In general, if the ratio of the corresponding lengths of two similar figures is a / b, then the ratio of their areas is ( a / b )^2.

And if the ratio of the corresponding lengths of two similar solids is a / b, then:

• the ratio of their volumes is ( a / b )^3;
• the ratio of their total surface areas is ( a / b )^2.

Knowing the above formulae, as well as the ones we learned last time, allows us to make various calculations in terms of finding the area or volume of some real world objects.

Homework:

Page 97: 42, 43, 44, 46, 49, 52, 53, 56, 59, 61