20120229: What's Wrong with this Solution?

Refer to the set of solution written in the board.
Identify as many error that you can spot and pen them in the comments.


After discussion:

20120224: Submission of REPLIES to Australian Mathematics Competition 2012

The following have not submitted the form:
  • Alexandre Shing
  • Farruq Daniel B Humardany
  • Lau Guan Heng Jose
  • Seah Gui Cong Aloysius
Please submit by next week.

Submission of REPLIES to Australian Mathematics Competition 2012

The following have not submitted the returns.
Please do so, latest by tomorrow 24 February 2012 (Friday).
  • Achutha d/o Karuppiah
  • Chiam Chuen
  • Khor Ethan
  • Koh Guo Feng
  • Kota Kiran Chand
  • Ng Keen Yung
  • Tan Shi Jie
  • Tham Chun Leong

Commutative Law & Associative Law of Addition & Multiplication

Commutative Law of Addition
Given that 4 + 5 = 9 and 5 + 4 = 9
Therefore, 4 + 5 = 5 + 4
The order of adding any two numbers does not affect the result.
This is the commutative law of addition.

Associative Law of Addition
We can add three numbers together in two different ways:
1st way: 2 + 3 + 5
= 2 + (3 + 5)
= 2 + 8
= 10

2nd way: 2 + 3 + 5
= (2 + 3) + 5
= 5 + 5
= 10
The order of grouping the numbers together does not affect the answer.
This property is called the associative law of addition,

Commutative Law of Multiplication
Given that 2 x 6 = 12 and 6 x 2 = 12
Therefore, 2 x 6 = 6 x 2
The multiplication of numbers follows the commutative law.

Associative Law of Multiplication
Since 2 x (3 x 4) = 2 x 12, resulting 24
and (2 x 3) x 4 = 6 x 4, resulting 24
Multiplication is therefore associative.

Real Numbers (Activity) Which Tribe do I belong to?

The solution is available at the GoogleSite > Mathematics > Class page


Homework not submitted (updated 18 Feb)

Chapter 2: Real Numbers

The following has not submitted Homework 1a:
  • Lim Zhongzhi
  • Ng Keen Yung

Chap 2: Real Numbers - Story Marathon at FaceBook

"Numbers" is part of our everyday life! It comes in different forms - Positive & Negative; Integers, Decimals, Fractions, and they can be "Irrational"!

In this story marathon, you will let your imagination run wild! Using Real Numbers, continue the story where the last person has commented. You may comment more than once. Each time, real numbers must be used, in one way or another. Do not limit yourself to only positive integers.

It is going to take place in Facebook > Group: Mathematics in Real Life
You must be a member to be able to comment.
Look for the post on 2012 S1-04 The Princess & REAL NUMBERS

This story marathon will run till Term 1 Week 10 before we consolidate it as a full story to share with others :)

Homework (17 Feb)

Attempt the following on the topic: Real Numbers
  • Homework 1b
  • Worksheet 1

For those of you who have not watched the videoclips on "Real Numbers in Operation",
please watch them to understand the concepts behind the Addition and Subtraction of Integers.

Then you link it back to the technique we discuss in class:
(1) By looking at the numerical value, identify the larger one.
(2) Adopt the sign of this number (+ or -)
(3) If both numbers have the same sign, we'll add the numerical values. If both numbers have different signs, then we'll subtract the numerical values.

Chap 2: Real Numbers - Investigative Activity on Recurring Decimals

Dear Students

The NUMBERS file for the activity has been uploaded to the GoogleSite (in your class page).
You may download to check against what you have done in the class.

During lesson, you should have indicated in your notebook:
(1) Which are the fractions that will result a recurring decimal
(2) How to write a recurring decimal




Points to Ponder:
Are the following recurring decimals?

If they are recurring decimals, how would you write them?
  • 0.0212112111211112111112111111...
  • 1.2031203120312031...
  • 30.0029292929292...

Chap 2: Real Numbers - Introduction of the Relationships

In the previous lessons, we discussed the relationship between the different types of numbers, and came up with a Venn Diagram to represent their relationships :)

We have also started exploring the "Recurring Decimals" using NUMBERS.
What is your observation amongst the fractions? 1/2, 1/3, 1/4, ... 1/50
Are there some characteristics of the denominators that you could tell if the number is going to be a terminating decimal, recurring decimal, or a non-terminating (& non-recurring) decimal?

What's happening next...
  • Concept behind the addition and subtraction of Real Numbers - Introduction of Zero Pairs
  • http://sst2012-s104maths.blogspot.com/p/real-numbers-in-operation.html

Chap 1: Worksheet 3 Q8c - Using Algebra to Explain

Gentle Reminder... Level Test on 13 Feb 2012 (Monday)

Please remember to bring along with you a working calculator.

As pointed out in class, no homework is assigned over the weekend as you should be preparing for the level tests with the hand-outs that were returned to you.

As advised during the lesson, you should have done the corrections to the Homework copies, by making reference to the solutions put up in the GoogleSite.

In your file, you should have the following for your revision:
  • Diagnostic Test (Factors & Multiples)
  • Worksheet 1
  • Homework 1(a)
  • Homework 1(b)
  • Worksheet 2
  • Homework 2(a)
  • Homework 2(b)
  • Homework 2(c)
  • Worksheet 3
  • Homework 3(a)
  • Homework 3(b)
  • Homework 3(c)
  • Formative Assessment

Homework not submitted (updated 7 Feb 2012)

The following have not submitted homework:

Homework 3(b) Chiam Chuen

Homework 3(c): Tan Shi Jie

Homework 2(b): Chiam Chuen, Kota Kiran
Homework 2(c): Chiam Chuen, Kota Kiran

Maths Level Test 13 February (Monday)

Duration: 1 hour

Chapter 1: Factors and Multiples
- page 1 to page 22 (entire chapter)
- Make reference to all the Worksheets and Homework assigned under this chapter

Chapter 2: Real Numbers - Calculator use only
- page 47 to page 49

Calculator is allowed.

6 AM Quiz: Factors & Multiples



Answers to QUIZ Word Problems #1 to #5

1. 14 tables in each row
  • Use square root
2. 15625 cubes
  • 1. Convert the lengths to common unit (i.e. cm)
  • 2. Find the number of small cubes that can be lined up along the side.
  • 150/6 = 25 cubes per side
  • No. of cubes = 25^3 = 15625
3. 14352 cubes
  • 1. Find HCF, hence the common factor of no. of cubes could be lined up along the sides.
  • 2. Calculate the no. of cubes for each side by dividing the length by the 'length of the smaller cube'.
  • 3. Hence the total number of cubes.
  • HCF of 312, 184, 128 is 8
    No. of cubes by the length = 39
    No. of cubes by the breadth = 23
    No. of cubes by the height = 16
    Total no. of cubes = 14352
4. 64 m
  • 1. Find area of the triangle
  • 2. Using the area, find the length of square
  • 3. Find perimeter
  • Area of triangle = 256
    Length of square = sqrt(256) = 16
    Perimeter = 64
5. Date: 15 April 2011
  • 1. Find LCM
  • 2. Count from the day after 1 Jan 2011
  • LCM of 8, 13 = 104Jan = 31-1 = 30 days (reason being both planes took off on 1 Jan, so we start counting from 2 Jan); Feb = 28 days; Mar = 31 daysTotal = 89 days (short of 15 days)

Chap 2: Real Numbers - Investigative Activity (I) Addition of Numbers

In this investigative activity, you are going to add integers of different combinations:
  • positive and negative integers
  • negative and negative integers
Observe patterns amongst the answers generated.
Draw up a 'rule' that would guide us when we add integers (especially when it involves negative integers).

Vocabulary List: Numerical Part. Sign. Positive. Negative. Difference. Sum. Same.

You are going to work in pairs or threes.

1. One of you will download the file "Chapter 2 Investigative Activity - Addition and Product.numbers" (from GoogleSite: 01 Mathematics). Another will display the blog post so that you could enter your discussion into the Comments.



2. Refer to the worksheet "Addition of Numbers":
  • (a) Enter formula to find the value of "a + b" of the first set of integers (i.e. 10 + (-1)). The spreadsheet will compute the value automatically for you.
  • (b) Copy the formula to the rest of the cells below; also to the next column.

3. Discuss the patterns you observe between the addition of integers:
  • (a) What happens when a positive integer + a negative integer (given that the positive number has a greater numerical value)?
  • (b) What happens when a positive integer + a negative integer (given that the positive number has a smaller numerical value)?
  • (c) What happens when a negative integer + a negative integer? How similar or different it is when compared the sum of two positive numbers?
4. Pen the observations down in the Comments. Suggest a rule that would help one when adding two integers.

5. Sign off the Comments with the name(s) of both of you.

Chap 2: Real Numbers - Investigative Activity (II) Product of Integers

In this investigative activity, you are going to multiply integers of different combinations:
  • positive and positive integers
  • positive and negative integers
  • negative and negative integers
Observe patterns amongst the answers generated.
Draw up a 'rule' that would guide us when we multiply integers (especially when it involves negative integers).

Vocabulary List: Numerical Part. Sign. Positive. Negative. Product.

You are going to work in pairs or threes.

1. One of you will download the file "Chapter 2 Investigative Activity - Addition and Product.numbers" (from GoogleSite: 01 Mathematics). Another will display the blog post so that you could enter your discussion into the Comments.




2. Refer to the worksheet "Product of Numbers":
  • (a) Enter formula to find the value of "a x b" of the first set of numbers (i.e. (-4) x (-4)).
  • Press ENTER and the spreadsheet will compute the value automatically.
  • (b) We are going to tell the spreadsheet to use the row of numbers in Row 2 and Column B for computation.
  • At the formula bar, click at C2 and select (C$2) absolute row. The spreadsheet will use the numbers in Row 2 for calculation.

  • At the formula bar, click at B3 and select ($B3) absolute column. The spreadsheet will use the numbers in Column B for calculation.
  • (c) To copy the formula, select cell B3, place the cursor at the bottom right corner. It will turn to a cross-hair. Now drag it to cover the entire area to be computed.
3. Discuss the patterns you observe between the product of integers:
  • (a) What happens when a positive integer x a negative integer (given that the positive number has a greater numerical value)?
  • (b) What happens when a positive integer x a negative integer (given that the positive number has a smaller numerical value)?
  • (c) What happens when a negative integer x a negative integer? How similar or different it is when compared the product two positive numbers?
4. Pen the observations down in the Comments. Suggest a rule that would help one when adding two numbers.

5. Sign off the Comments with the name(s) of both of you.

Maths Olympiad Selection Test

Information pertaining to the Selection Test is now available at the Student Blog.

Homework (2 Feb)

Worksheet 3, on Square Roots & Cube Roots is issued today.
This is part of your preparation for the Level Test in Week 7.
Please try them and we shall discuss this on next Tuesday when we meet.

A 6AM Quiz has been scheduled this Saturday, as part of your preparation for the level test. This is optional; however, it's a good opportunity to test your own understanding :)

Remember to explore NUMBERS as it will be used in the Investigative activity next Tuesday.

eTextbook: Activation Code (updated 6 Feb)

Dear Students

A digital copy of the Maths textbook is available.

For those of you who bought the learning device through NCS, it has been already been installed in your device, except those who bought Macbook Air*.

Use Spotlight to search for iBook.
You will be prompted to enter the serial number. Enter 22169 (which is compulsory) and the second number is either 31718 OR 19607
  • For those who bought the Macbook Air and did not buy the learning device through NCS, please see Mr Lim at the HelpDesk to help install the softcopy of the textbook.
  • Suggestion: Make an appointment in the mornng with Mr Lim before morning assembly or during recess.





Note: Some of you pointed out that there's problem accessing the eTextbook. We are checking out with the vendor. Will update all once we get the update on the access and the serial number.

Homework (1 Feb)

There is no homework for the day.

Please remember to submit:
- WORKSHEET 2 in the last Maths lesson of this week
- WORKSHEET 3 in the first Maths lesson of next week

Group 1

BY SHIJIE, JIAWEN,QIANZHE,ACHUTHA and ZHONGZHI

Chap 2: Number Puzzle (by Group 5)

Group 2;Gabriel,Keen,Sarah,Guofeng,Subramamaniyan

chapter 2 number puzzle (Group 4)

Chap 2: Number Puzzle (by Group 3)

Chap 2: Number Puzzle

You are going to arrange the number cards in ascending order.

Take a picture of the final arrangement.
One person in the Group will post it in the blog with
  • Subject Title: Chap 2: Number Puzzle (by Group.....)
  • Insert a label: Real Numbers
After it is posted, each member of the group will go to "Comment", to describe how the group solved the problem, such that it can serve as an advice to anyone given the same puzzle.

Chap 2: Real Numbers - Negative Numbers

Group 1:
http://www.blogger.com/img/blank.gif

Group 2:

http://www.blogger.com/img/blank.gifhttp://www.blogger.com/img/blank.gif
Group 3:


Group 4:


Group 5: