2011, 28 April: Home Joy... (for today and the weekend)

1. Algebra Worksheet 3: Attempt the worksheet
For those who are able to finish and submit by this week, please pass the worksheet to Abhi tomorrow before dismissal.
For those who need more time to do, please hand in by next Tuesday before morning assembly.


2. Preparation for Common Test - Quizzes
Short quizzes (5min) will be conducted next week for 3 topics:
(i) Tuesday (TCS, 5 min): Chap 1 - Factors and Multiples
(ii) Wednesday (during lesson, 5 min): Chap 2 - Real Numbers
(iii) Thursday (during lesson, 5 min): Chap 3 - Approximation & Estimation

3. An Assignment worksheet will be issued tomorrow.
Deadline - next Tuesday (3 May)

S1 Mathematics Common Test

Sec 1 Mathematics Common Test is going to take place on 11 May 2011.

Topics to be tested include...
  • Chap 1: Factors & Multiples
  • Chap 2: Real Numbers
  • Chap 3: Approximation and Estimation
  • Chap 4: Algebra
  • Chap 5: Algebraic Manipulation (without factorisation)
  • Chap 16: Data Handling
Duration: 1 h 30 minutes
Calculator is allowed.

2011, 25 April: Home Joy... (for today and tomorrow)

In the stapled set of handouts, attempt the 1st set of worksheets (4 pages).
~ Finish the questions that were not discussed.

Those who know how to do the 2nd set of worksheet, you may attempt that, too.

Follow-up of 13 April (Stem-and-Leaf Task): Which part of the Singapore Island has the best air quality?

Claim 1: Air Quality in the eastern part of Singapore is always better than the western part of the island

To investigate this, we are going to compare the quality of air (PSI) in the eastern and western parts of the island. To make comparison for one month is not enough since the air quality varies over the different months in a year (e.g. the wind direction varies in different times of the year).

First, we compare the air quality in the month of October.
  • In both zones, the modes do not stand out significantly amongst other days (east with 3 occurences only while the 7 modes identified in the west zone had only 2 occurences). Hence, mode will not be refered to, in this case.
  • By comparing the mean, mean PSI for east zone is lower than that of the west. Both zones have 'outliers' (95 and 96 for east and west zones respectively). With reference to the mean, quality of air in east zone is better than that in the west.
  • With reference to median, it shows that the east 15 days with PSI less than 33 while the west has less (its median is 38, and it has 11 days enjoying air quality below 33 in the same month)
Hence, based on October 2010's data, quality of air in the east is better than that in the west.

Next, to check for 'consistency' by taking comparing the PSI values in March 2011:
  • Comparing the mode, it was 20 at the east (with 5 occurences), which is better than the mode PSI value of the west.
  • Both zones have the same median, 26
  • Comparing the mean, the east enjoyed better air quality (25.5 compared to 28.6), with no outliers.
Hence, based on March 2011's data, quality of air in the east is better than that in the west.

Using the data from the 2 months, we are able to conclude that air quality in the eastern part of Singapore is better than the western part of the island.




Claim 2: Air Quality has worsen over the years

 The comparison is carried out by comparing the overall PSI values of the same months between 2 years (which are 5 years apart).

Comparing the data for the month of October in 2005 and 2010:
  • Both Mean and Median values show that air quality in 2005 is better than that in 2010
  • By comparing the median, in 2005, 15 days enjoy air quality that are 36 and below whereas in 2010, it was reduced to 10 days. 
  • Moreover, in October 2010, there were 4 days with PSI value 80 and above, which in turn contributed to the higher PSI value.
 Next, comparing the data for the month of March in 2005 and 2010
  • All 3 averages: Mean, Median and Mode PSI values recorded in 2005 were much hihger than than those recorded in 2010. 
  • From the stem-and-leaft diagram, it was clear that more than 50% of the values are above 50. 
  • Hence, air quality in 2005 is worst off than that in 2010. 
Therefore, using these 2 sets of data, we are unable to conclude that the air quality has worsened over the years.

Chapter 5: Algebra - Can you tell where has gone wrong?

Textbook (p89)

Julie says that
3a² + 2a + 5a² = 10a³
and
7b x 5b² x 6 = 210b
Do you agree with Julie? If not, what are the mistakes in her algebraic manipulations?

Enter your responses under Comments.

Complete this for Monday's (25 April) discussion

Chapter 5 Algebraic Manipulation



....

Chapter 5: Algebra... Different "Faces" of Algebra (I)

Write an algebraic expression that has 3 terms involving variables p and q.


Based on what's posted in the comments:
(i) The following are algebraic expressions comprising of 3 terms involving variables p and q:
  • 4p+4q+4pq  
  • 3q + 6p - 5p  
  • 100p+p x 300q-q
  • px2+p^2-pq 
  • 111p+11q-10px3 
(ii) The following are algebraic expressions with less than 3 terms involving p and q:
  •  p+q
  •  p-q
  • p×2p+pq
  • 5px2p-q
  • 4p x 2q^2 - 2p^2 
  • (p+p)/3qx2p
  • p^2 x q^5 - pq  
  • (p+q)*2p/3q  
  • p^5 x q^9 - p
  • p^10 x q^2 - pq 
  • 162p + 8p/2q x 83q  
  • pxq 
  • p^2*3q÷pq
  • [99p+(-200000q)]^86pq 
(iii) The following are NOT algebraic expression:
  • 7p*2q+8q=10p+2p*q 
Can you figure out what distinguishes (i), (ii) and (iii)?

Chapter 5: Algebra... Different "Faces" of Algebra (II)

The total length of 4 roads is (3x - 1) km. What are the possible lengths of the 4 roads in kilometres?

e.g. The length of the 4 roads are: x km, x km, x-7 km, 6 km
Check: x + x + (x - 7) + 6 = 3x - 1 

~~~~~~~~~~~~~~~~~~```
Based on your posting in the comments:
The following are correct...
  • 2x, x, x + 2, 1- x
  • 0.5x , x, x, 0.5x - 1 
  • 0.25x, 0.75x, 1.25x, 0.75x-1 
  • x, x, x-8, 7
  • 0.25x , 0.75x, 1, x-2
  • 0.75x, 0.25x - 1, 1.5x, 0.5x
  • x-1, x, 4/6 x, 2/6 x 
In class (21 April),  we discussed that these lengths are only valid if "x" satisfies some condition.
e.g 1: In the example of lengths, x, x, x-8 and 7
values of x must be greater than 8, otherwise x-8 would not be valid (in this context)
e.g. 2: In the example of lengths, 0.25x, 0.75x, 1 and x-2
values of x must be at greater than 2, otherwise x-2 would not be valid (in this context)
~~~~~~~~~~~~~~~~
What's wrong with the following?
  • 2x-1, 0.5x, 0.25x, 0.25
  • 0.5x, 0.5x, 0.5x-1, 1.5x 
  •  xx, x, (-1)
  • 2x, 0.5x, 0.5x, -1
  • 8, 4x, -x, -7
In class (21 April), we discussed where goes wrong with this lengths:
  • The sum might not have added up to the given expression, 3x - 1
  • The context (as length of road is a positive number)

Chapter 5: Algebra... Different "Faces" of Algebra (III)

The perimeter of a rectangle is (6x + 5y) cm.
Suggest 2 possible dimensions of the rectangle.

e.g.
Length of rectangle = 2x + 2y cm
Breadth of rectangle = x + 0.5y cm
Check:
Perimeter = 2 (2x + 2y) + 2 (x + 0.5y) cm
= 4x + 4y + 2x + y cm
= 6x + 5y cm

Chap 16: Assignment 1 Answers

Question 1
(a) Pets
(b) Discrete. They are countable.
(d) 30%
(e) 15%

Question 2
(a) Phone Calls
(b) 48%
(c) 2
(d) Outlier

Question 3
(a) Minimum value =2
(b) Maximum value = 62
(c) 16
(d) 5
(e) 17.1% (as required in the instructions)

Question4
(a)  Stem-and-Left Diagram
Stem | Leaf
0 | 9
1 | 8
2 | 0 0 2 4 5 5 5 6 8 8 8 8 9
3 | 0 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 8 9
4 | 0 1 2 2 3 4 5 6 8 9
5 | 0

Key: 1|8 represents 18 marks

(b) In the stem-and-leaf diagram, data are grouped and all the original data are shown.
(c) Highest score is 50 while lowest score is 9
(d) 24.4% (3 SF)

Air quality in Singapore in Oct 2010 (East & West)

 Key: 2|0 represents 20

East:
Mode: 20
Median: 31
Mean: 35.42 (2dp)

West:
Mode: 27, 28, 32, 34, 40, 44
Median:37.5
Mean:40.72(2dp)

Our group concludes that the quality of the air is better in the East than the West.

iTurtle 1A (Jia Qi, Sandy, Jonathan)

Order of the onions-March 2005 and March 2010 PSI

March2005
Mean 51.19 (4S.F)
Mode 54,59
Median 51

March 2010
Mean 38.45(4S.F)
Mode 39
Median 39
Conclusion : We think that the air quality in March 2005 is better than March 2010
Group members:Owen ,Gladys,Nina




Order of the Onions Stem and Leaf Diagram (PSI)



October 2005
Mode: 28, 46
Mean: 38.0 (3 SF)
Median: 34

October 2010
Mode: 39
Mean: 44.8 (3 SF)
Median: 40

Our conclusion is that the air quality in October 2005 is better than October 2010. The air quality has worsened over the years.
By: Ryan, Ruoyu, Jiajun

Sogurt (2a) -Overall Air Quality in October 2005 and October 2010 (2b) -Overall Air Quality in March 2005 and March 2010

 (2a)

Names of group members: Mavis, Yi de, Toby
October 2005 Key-> 5I2 = 25

October 2005: Mean-> 36.7(1 D.P)
             Median-> 34
           Mode-> 29  

October 2010 Key-> 4I0 = 40
Mean-> 42.1 (1 D.P)
Median-> 40
Mode-> 29

Our group's conclusion is that the overall air quality in October (2005) was better than that of October (2010).

(2b)

                                                       2005                                    2010  
Names of group members : Mark, Kai En, Matthew
March 2005 Key-> 1I3 = 31

March 2005:  Mean-> 49
       Mode-> 51
          Median-> 49

March 2010 Key-> 3I4 = 34

March 2010:  Mean-> 37.8 (1 D.P)
        Mode-> 39
          Median->39

Our group's conclusion is that the overall air quality in March (2010) is worse than that of March (2005).

CNShine Stem and Leaf Diagram

1A
East's Mode:20 and 30
West's Mode:22
East's Median:30
West's Median:37
West's Mean:34.9(3 S.F)
East's Mean:41.1(3 S.F)
We conclude that the quality of air is better in East than in the West
based on the median of both locations.
1B
East's Mode:20 and 30
West Mode:22
East's Median:26
West's Median:16
East Mean:23.4(3 S.F)
West Mean:27.8(3 S.F)
We can conclude that the air quality in West is better than in the East
based on the median of both locations.

HOME PLAY: End-of-Term 2 Week 4

(1) Stem-and-Leaf Diagram Task
(2) Ace-Learning Tasks
  • 2 Quizzes have been assigned
    • The following have not attempted: Dot Diagrams & Stem-and-Leaf Diagrams (updated 15 April, 2011 5 am) - The Quizzes have been re-assigned to you. Complete them by 15 April 2355h
      • ISHANI SAHA  
      • LEE QIAN HUI
      • WANG YI CHIEH  
      • MARK TAY HAO YANG
  • Complete the quizzes by end-of-today 2355h
(3) Assignment
  • Attempt all questions
  • Deadline: 19 April 2011 (Thursday)

13 April (Dot DiagramTask): Hottest month in Singapore 2010

In a travel guide about Singapore, it was highlighted that "The temperature hovers around a diurnal range of a minimum of 23 °C (73.4 °F) and a maximum of 31 °C (87.8 °F). June is the hottest month of the year in Singapore, followed by May."

However, in 2010, February was reported to be the driest month. 


Let's do a comparison using the dot diagram, to compare the temperature in February 2010 and June 2010.

Below is the dot diagram that represents the maximum temperature of each day recorded in June 2010.
What are the mode, mean and median temperature of June 2010?



Now, it's your turn to look at the data in February 2010:

You can access the history of the Singapore weather at the Weather Underground website: http://www.wunderground.com/
  • Click at tab: LOCAL WEATHER > HISTORY DATA
    • Enter LOCATION: Singapore > DATE: February, 2010
      • Select MONTHLY Display
In your Maths Notebook, write down the following:
  • Title: Dot Diagram February 2010 Maximum Temperature (Actual)
    • Draw the dot diagram
    • Write down the number of data points you have
    • From the diagram, identify the mode and median
    • What is the mean temperature of the month

    13 April (Stem-and-Leaf Task): Which part of the Singapore Island has the best air quality?

    Singapore is a garden city with trees planted all over the island to create a green belt that 'regulates' the quality of air in the Singapore island in a 'natural' manner. However, there would be a few days in a year where the quality of the air is affected by the forest fires in the nearby countries:

    Reported in the ChannelNewsAsia.com website:
    http://www.channelnewsasia.com/stories/singaporelocalnews/view/1087523/1/.html


    http://www.channelnewsasia.com/stories/singaporelocalnews/view/1088509/1/.html


    PSI stands for 'Pollutant Standards Index'. It is an index developed by the United States Environmental Protection Agency (USEPA) to provide accurate, timely and easily understandable information about daily levels of air pollution.

    Click HERE to access the 24-hour PSI readings for Singapore.

    Every year, the quality of air in Singapore in months like October is badly affected by forest fires, when compared to other months (when we heard little about such instances taking place in the nearby region).

    An estate agent claims that no matter how "polluted" the air is, "Air quality in the eastern part of Singapore is always better than that in the western part of the island." Therefore the price of housing properties at East Coast area is higher than those in Boon Lay.

    On the other hand, residents who lived in Singapore over the past 5 years claim that the air quality has worsened over the years, especially in the month of October.

    We are going to analyse the data available at the Singapore National Environment Agency (NEA) to help us find out whether the claims are justifiable.


    Groups 1A & 1B:
    Focus on the first claim "Air quality in the eastern part of Singapore is always better than that in the western part of the island."
    • You are going to make comparison between 2 sets of data: PSI values for October 2010 and March 2011.
      • October 2010 data: Compare the PSI values in the east and PSI values in the west
        • Illustrate the data using a stem-and-leaf diagram
        • Identify the mode and median PSI value in each area
        • Compute the mean PSI value in each area
        • Compare the data between the eastern and the western parts of the island. What can you conclude about the quality of air between the 2 areas in the month of October?
      • March 2011 data: Compare the PSI values in the east and PSI values in the west
        • Illustrate the data using a stem-and-leaf diagram
        • Identify the mode and median PSI value in each area
        • Compute the mean PSI value in each area
        • Compare the data between the eastern and the western parts of the island. What can you conclude about the quality of air between the 2 areas in the month of October?
    Groups 2A & 2B:
    Focus on the second claim "Air quality has worsened over the years, especially in the month of October"
    • You are going to make comparison between 2 sets of data: PSI values for 2005 and 2010.
      • October 2005 & 2010 data: Compare the overall PSI values for both years
        • Illustrate the data using a stem-and-leaf diagram
        • Identify the mode and median PSI value for each year
        • Compute the mean PSI value for each year
        • Compare the data between 2 years. What can you conclude about the quality of air between the 2 years in the month of October?
      • March 2005 & 2010 data: Compare the overall PSI values for both years
        • Illustrate the data using a stem-and-leaf diagram 
        • Identify the mode and median PSI value for each year
        • Compute the mean PSI value for each year
        • Compare the data between 2 years. What can you conclude about the quality of air between the 2 years in the month of March? 
    Instructions to complete the work
    • Each group is divided into 2 sub-groups, with 2-3 members handling each part.
    • In your sub-group
      • You will draw up the Stem-and-Leaf diagram on the A3 paper provided [5 min]
      • Pen down the mean, median and mode below each set of data for the ease of comparison [5 min]
      • Compare the data to come up with a conclusion about the quality of air. Pen down your conclusion on the paper [5 min]
    • Compare the data and averages between the 2 sheets of data [5 min]
      • What can you conclude and say about the 'claim'? Does your data show that the claim is justifiable?
    • One spokesperson to be appointed to share the findings [5 min] 

    • The leader will post photos of the A3 sheets, together with the group's conclusion in the Maths blog
      • Post title: (Group Name) Air Quality in the East is better than the West?
      • In the post: 
        • Include names of the members
        • Photos of your work
        • Conclusion
      • Labels: Data-Handling, stem-and-leaf-diag
      • Submit by the end of today

      Preparation for Lesson on 13 April 2011

      We are going to learn 2 new graphical representations:
      (1) Stem-and-Leaf Diagrams
      (2) Dot Diagrams


      For Stem-and-Leaf Diagrams
      • Video Lessons
        • Introduction
        • Example 1
        • Example 2
        • Example 3
      For Dot Diagrams
      • Dot Diagrams and Examples 1 & 2
      • Example 3
      • Example 4

      7 April 2011: Tasks for the Day

      What we did yesterday:
      • How to present data in a Frequency Table?
      • How to draw information out from the Frequency Table?
      ~~~~~~~~~~~~~~~~~~~~~~~~~~
      What are we going to do today?

      Task 1[5 min]: Review the Homework ~ S1-01's use of Learning Device after class

      Task 2 [30 min]: Mean, Median & Mode
      • (a) An Introduction to learn what are they? [Do in AceLearning]
      • (b) A Summary of what they are. Applying what you know in a class problem. [Post under comments]
      Task 3 [10 min]: Explain what you understand by median [Post under comments]

      Task 4 [Remaining time]: Homework
      Continue with the Handout questions (photocopied from textbook/workbook).
      • Question 7: A survey investigates the number of hours that a person surfs the Internet....
      • Question 8: In a factory, the lifetime of each of 30 dry batteries...

      7 April 2011: Tasks for the Day (Follow-up) - Task 2

      MEAN Question 4


      MEAN Question 5
      MEDIAN Question 1

      MEDIAN Question 5

      MEDIAN Question 10


      7 April (Task 1) Chap 16: Review of Homework

      Task was given on 6 April 2011 (Wednesday):

      (1) Use of learning device after class
      Recently, some parents expressed their concerns over their children spending long hours with their learning device after class. To verify the situation situation, a survey was conducted in classes to gather some preliminary information.

      Below shows the number of hours S1-01 students spent with their learning devices (or home computer) after class. 
      Note that there are only 22 data points because Matthew was absent.


      If findings by the school shows that students who spend more than 9 hours with the learning device need to be 'counselled', how many percent of the class would be involved?

      What you should have done in your notebook:

      1. Present the set of raw data in a frequency table:


      2. Percentage of students involved to be counselled:
      Number of students who spend more than 9 hours with the learning device = 2
      Percentage = 9.1% (correct to 2 significant figures)

      (2) Ace Learning Quiz "Chap 16: Histogram Quiz 2"
      The following have not attempted the Quiz at the Ace Learning
      1. Shawn Kit
      2. Gladys
      3. Lovy
      4. Yi De
      5. Ishani
      6. Qian Hui
      7. Mark
      8. Toby
      For the above, the quiz has been 're-opened' until today 7 April 2355h.

      Matthew: 
      Please find out from your group members what was discussed in class on Wednesday and attempt the Quiz in Ace Learning.

      7 April (Task 2a) Chap 16: Mean, Median & Mode - An Introduction

      "AVERAGE" is one of the ways we describe any data set that we have.

      Here, we are going to learn 3 types of Averages - MEAN, MEDIAN, MODE
      They are sometimes known (more broadly as) Measures of Central Tendency
      ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
      Let's go through the following in the AceLearning Portal:
      • Under "Secondary 1 Express Elementary Mathematics", select "Statistics"
      • Click at "Measures of Central Tendency"

      • Click at 1. The Mean
        • View the Introduction
        • Attempt the Quiz: Chap 16 Mean
      • Click at 2. The Median
        • View the Introduction
        • Attempt the Quiz: Chap 16: Median
      • Click at 3. The Mode
        • View the Introduction 
        • Attempt the Quiz: Chap 16: Mode 
        Do not rush through the quiz. It is an attempt to see how much you understand each of these sub-topics.
        Note that you are given one chance to re-attempt the quiz question(s).

        7 April (Task 2b) Chap 16: Mean, Median & Mode - Let's see if I Understand...

        This is a summary of the 3 types of Averages:
        ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

        Measures of Central Tendency or Averages

        Arithmetic Mean
        • The arithmetic mean of a set of numbers is the sum of numbers divided by the number of numbers in the set : Mean = sum of the numbers/number of numbers
        • It is most the reliable measure provided there are no extreme values in the data because all the values in the data are used in calculating.
        • Whenever the set of data contains extreme values, the median or mode would probably be more reliable because they are not influenced by extreme values.
        Mode
        • The number which occurs most frequently in a set of numbers
        • It is most useful in business planning as a measure of popularity that reflects central tendency or opinion.
        Median
        • May be preferred as a measure of central tendency for describing economic, sociological and educational data.
        • The median is popular in the study of social sciences because much of the data in the social sciences contain extreme values, in the set of household incomes.
        • Median for an odd number of numbers is the middle number when the numbers are arranged in order of magnitude (i.e. ascending/descending order)
        • Median for an even number of numbers is the mean of the two middle numbers when the numbers are arranged in order of magnitude
        ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
        YOUR TASK
        Let's use the 3 types of averages to describe the set of data about the use of learning device after class.




        Answer the following under Comments. Label the parts clearly.


        1. Mean
        (a) Describe how you would find the mean number of hours spend with the learning device after class.
        (b) Compute the mean

        2. Mode
        (a) Describe how do you determine the mode of the data.
        (b) What is the median number of hours?


        3. Median
        (a) Describe what must you do with the data before you can find the median.
        (b) What is the median number of hours?

        Remember to sign off with your name. 

        7 April (Task 3) Chap 16: Mean, Median & Mode - Why use Median here?

        The heading of this article (14 February 2011) says, "S'pore households' median monthly income rises"


        Source: channelnewsasia.com ~ http://www.channelnewsasia.com/stories/singaporelocalnews/view/1110600/1/.html

        The journalist used the term "median". However, not everyone understands what 'median' means. For example, your grandparent might not remember what it means.

        Explain, in your own words (between 50 to 100 words) what the first 3 paragraphs try to say (about the median). You may include some numbers to help you illustrate your point.

        2011, 4 April: Home Joy... (for today and tomorrow)

        1. Complete the following (if you have not done so...)

        2. Handout: Chap 16 Data Handling

        Read Chapter 16.2 p163-p165 before attempting the following questions

        1. 1st sheet: Basic Practice No. 1 & No.2 - Construct the Frequency Table beside the set of raw data.

        2. 2nd sheet: Maths@Work No. 6 - Construct the Frequency Table beside the set of raw data.

        We shall discuss the rest of the answers on Wednesday.

        3. Quiz

        • There will be a One-Question Quiz on Wednesday related to Histogram. 

        • Calculator is required.

        4. eLearning task (cont'd)


        Please make sure that you have the 2 charts ready by Wednesday for discussion.