Thursday, 28 January 2016

28 Jan: Homework and Preparation for T1W5

Homework

Attempt the following assignments:

Assignment 2.1 - Introduction to Numbers
Assignment 2.2 - Addition and Subtraction of Integers
Assignment 2.3 - Multiplication and Division of Integers

Assignments 2.4 & 2.5 - 4 Operations for Rational Numbers (Decimals and Fractions)
Note: We'll discuss these 2 assignments on Monday.

Note: 
  • Assignments 2.1 to 2.3: To be submitted on Monday (1 February 2016)
  • Assignments 2.4 & 2.5: To be submitted on Wednesday (3 February 2016)


Food for Thought: Rational Numbers on a Number Line?



Enter your response to the following in "Comments". 


Introduction: Real Numbers - How deep is deep?

This activity was discussed in class.
You may want to click at the hyperlink to find out more about the "Challenger Deep".
Source: http://www.deepseachallenge.com/the-expedition/mariana-trench/



Note: Use Google to convert the height/ depth from "feet" to "metres"


28 Jan: Flipped Learning for next lesson(s) on Operations of Numbers (II)

Watch the collection of lesson clips at the Khan Academy to better understand the concepts of multiplication and division of (positive & negative) numbers) that would answer to some of your questions like, why do we get a negative number when we multiply a positive number and negative number?







Tuesday, 26 January 2016

26 Jan 2016: Preparation for Next Lesson

1. Watch the following video clips at Unit 2: Real Numbers (refer to tab above)
  • Operations of Numbers [8 clips] - Pay attention to "Zero Pairs"
  • Properties of Operations [2 clips]
2. Attempt Workbook (p11) Q3, 5, 6, 7 - in the workbook for discussion in the next lesson

3. Homework: Assignment 2.1

The Family Tree



Click HERE to view responses

AFTER NOTE:



Sunday, 24 January 2016

What did some of you say... When to Use - HCF and LCM?

With reference to the Quiz that the class has attempted, click HERE to view the responses.

Good tips suggested by some of you...

By Alex [Group 1]:
HCF is usually used when we are packing things into boxes. LCM is used when we want to see when we next meet(the number given in the question is usually smaller than the answer)

By Elise [Group 3]:
For HCF, its whether the question asks for the greatest number of etc etc, while for LCM its whether the question asks for the least number of etc etc.

By Peng Kiang [Group 4]:
If it is separation, it is highest common factor. If each party has a separate timing and they ask for a time they will collide, we use lowest common multiple.

By Daniel [Group 4]:
The highest common factor is used to make the number of things in a group equal. The lowest common multiple is used to find out when numbers are equal after multiplying them.

HCF and LCM: Is this TipSheet Useful?

Some teachers had a discussion about when to use HCF and LCM. Here's one suggestion by the teacher named "Funny".
  • Do you agree with what she suggested? 
  • Are those pointers useful? 
Share under "Comments" if you have other insights on this :)

Note: 
In overseas context, Highest Common Factor (HCF) is also known as Greatest Common Factor (GCF)


Saturday, 23 January 2016

Introduction to Unit 02: Real Numbers

Watch the following clip for a preview of what we will be doing in the next few lessons.


23 Jan 2016 Gentle Reminder & Preparation for T1W4 lessons

Dear S1-01


(A) Homework
Remember to complete Assignment 1.2 for submission on Monday (25 Jan).
This task was assigned during lesson on Thursday (21 Jan).

* You can send me an email if you encounter problem when doing the question.
However, you need to be specific which area you are not sure so that we can focus on addressing the gap.


(B) Consolidation of Unit 01
We are completing Unit 01 Primes, HCF and LCM on Monday.

On your own, attempt the following questions from your Maths Workbook:

  • Q15, Q16, Q17, Q18, Q19, Q27, Q28
  • Do these questions on writing papers. 
  • You may check answers from the back of the workbook
  • We will make reference to these questions when we revise the unit for the level test


(C) Getting Ready for Unit 02
You should start reading up Unit 02 Real Numbers in your text book.


Thursday, 21 January 2016

Divisibility of Numbers



Summarising: Prime Factorisation (Classwork 1.2.5)

Classwork 1.2.5





To recap... how to obtain factors of a number in a systematic manner


To do more practice at the "Khan Academy" website, click HERE.



After note: (after lesson on 21 January 2016 Thursday)

Jonathan found the method to find out the number of factors without having listing the factors.
Click HERE to access the site.


Summarising: Squares, Cubes & Roots (Classwork 1.4.3)


Tier A
Question 1:




Question 2:



Tier B
Question 3




Question 4




Tier C
Question 5






Wednesday, 20 January 2016

20 Jan 2016: Things to get ready for tomorrow's lesson

Note: Today's Maths lesson is replaced by ICT Lesson (by Mr Jonathan Chua). Maths lesson will resume tomorrow (for Periods 1 & 2)


Homework assigned on 19 Jan (Tuesday):



You should complete the following before we meet tomorrow (for discussion)

  • Classwork 1.2.5 (p4) Q1, Q2, Q3
  • Classwork 1.4.3 (p5 & p6) Q1, Q2, Q3, Q4, Q5

HCF: Different Routes Converged (Summary)

We learnt that there are several ways that we can use to find HCF of numbers.

Question: Find the HCF of 40, 36 and 24

Here are the various methods used by some of you:

Method 1: Listing - this is the simplest way to do; however, you risk missing out numbers as you test the given number with different factors. This method could be time-consuming when you are handling large mumbers


Method 2: Listing pairs of factors. When systematically carried out, the highest common factor could be easily surfaced. This method could be time consuming as you are 'obliged' to list down all the pairs in order to find the largest factor common amongst the given numbers.


Method 3: Using "grouped' repeated division. This is one of the faster methods. Remember to apply the "prime factorisation" protocol, i.e. start with the smallest prime number.


Method 4 (Preferred) & Method 5 (Preferred): Carry out the prime factorisation for each number. Express the product of these factors in index notation. Express in index notation and surface factors that are common across the numbers. The product of these factors will give the HCF of the numbers.

Method 4

Method 5



Making Connections











Tuesday, 19 January 2016

[For those who missed the briefing] Mathematics Talent Development Programme (TDP)

Dear S1-01

Some of you might have missed the TDP briefing yesterday (18 January 2016) due to the ongoing CCA trials.

For those who are still keen to attend the TDP, please meet Mr Jason Ingham at the Math room next Monday 25 January 2016 at 1540 hours for further details if you are interested.

Click HERE to access the announcement in the GoogleSite

When to use - HCF and LCM - to solve the problem?

This is a 10 minute quiz where you are to decide which technique/ method to be applied in each situation. Think carefully, check your answers (for consistency) before submitting your answers. You are required to describe how you make your decision.
[This task is compulsory]


Click HERE to view the responses

Highest Common Factor... in real world

Lowest Common Multiples... in real world

Monday, 18 January 2016

Food for Thought: Is it even or odd?

A number's prime factorisation is
23 X 32 X 52
Is the number even or odd? Explain your reasoning.
Name four other factors of this number, other than 2, 3 and 5.


Find the unknown....

Find the smallest possible value of n if the number A is a perfect cube, given that


Hence, find the cube root of A.

Friday, 15 January 2016

[Invitation] Mathematics Talent Development Programme (TDP)

The Mathematics department will be organising a meeting on next Monday 18 Jan 2016 at 4pm, to brief students on the Mathematics TDP.

For those of you who enjoy Mathematics and wish to pursue it at a higher level (e.g. to represent SST in competitions), you are strongly encouraged to attend the info session to find out more about the programme and involvement.

Please meet Mr Jason Ingham at the Math room (Block B, Level 3, near Staff Work Room) for further details if you are interested. 

Note: The same announcement is made at the Googlesite.


Thursday, 14 January 2016

14 Jan 2016: Key things we do today...

What we did/ discussed today:
  • Revisit what a prime number and a composite number is.
  • We looked closer to the presentation of working when carrying out prime factorisation using each method.
  • How to tell, from the index notation, if a number is a perfect square or not; which could be extended to others (e.g. perfect cubes)
  • How prime factorisation could be used to find square root of a number, which could be extended to other "roots"
Things to follow-up:

Homework

Assignment 1.1
  • Complete the questions (Tier A, Tier B, Tier C) in the spaces provided.
  • You may attempt Tier B and Tier C in writing papers, and staple at the back of the handout (Assignment 1.1)
  • Deadline for submission: Monday 17 January 2016 [in class]

[Some of you say....] Describe the relationship between "Perfect Square" and "Square Root".

Here are some responses we get when you were asked the relationship between square roots and perfect squares (in the Topic survey).

Food for Thought...
Based on what you have learnt today, what are your thoughts to these initial comments?

  • Is there any misconceptions/ mistakes in these comments?
  • Is there one that provides a complete explanation of the relationship?


What you say... #1

What you say... #2

What you say... #3

Error Analysis

Read the question and answers carefully.

Can you tell what is wrong with the answer presentation?



Questions you asked (13 Jan)...

Here are questions that some of you asked:


Question 1

Afternote

  • A mixed number cannot be an even number because it does not satisfy the condition that any even, when divided by 2 will not leave any remainder.
  • FOLLOW-UP
    • Explain if a mixed number could be an odd number? 
    • Enter your response in comments. The first complete & well thought-through response will get 5 points for the group


Question 2


Afternote:
  • Examples of applications are finding the LCM and HCF of numbers, to find roots of numbers.

Wednesday, 13 January 2016

13 Jan 2016: Key things we do today...

We did the following today:
  • As a follow-up of the activity, "What are your observations?", Pythagoras Theorem is introduced. Do find out more about the relationship of the triplets in relation to right-angled triangles
  • Symbol of Natural Number
  • Understanding "Factorisation" - it is about breaking down of composite numbers
  • Two different methods to factorise a number - Factor Tree & Repeated Division; and one good practice when doing prime factorisation.
  • What is Prime Number? Its "characteristic"
  • Expressing a composite number in index notation
Remember to...

Finding PRIMES: Sieve of Eratosthesnes

Click HERE to access the interactive version of the Sieve of Eratosthesnes.



Prime Factorisation - Doing it...

Prime factorisation is the process of expressing a composite number as the product of prime factors.

There are 2 methods to do this:

(a) Repeated Division






(b) Factor Tree

Click HERE to view the illustrations


(




About Primes - True or False?

IMPORTANT:






As at 14 January, 4.50 am, the following had not submitted the response:

18NGO EU GENE - GROUP 3


25YU YI LUCAS - GROUP 4


Click HERE to view responses

Tuesday, 12 January 2016

12 Jan 2016: Key things we do today...

1. Introduction to the Mathematical Framework 

2. Reminder to go through and adopt some of the good practices from
3. Continue to seek relationship between the numbers in the activity, "What are your observations"

4. Given the handout, examine the methods and pen down your thoughts of the case you are assigned to in "What is it trying to do?"

5. Remember to key bring an A4 Exercise Book (if you have not done so) as your Maths Notebook


What is it trying to do?

There are altogether 5 cases. Each student is given one case to work on.

What you need to do...


1. The same number is 'subjected' to TWO different processes (Method 1 and Method 2).
What do you think... the method is trying to do (in both methods)

2. In each method, attempt to describe how the numbers are organised, and what is the relationship between the numbers.
  • Draw out as much information as possible

Case 1

Case 2

Case 3



Case 4


Case 5



Monday, 11 January 2016

What are your observations?


Draw out as much information as possible from the 3 sets of numbers.
e.g. characteristics these numbers; relationship
  1. 25,  144,  169
  2. 121,  3600,  3721
  3. 49,  576,  625
Key in your observations in Comments


Friday, 1 January 2016

Welcome & Getting Ready


Greetings and welcome to the new year, and new class :)

Before we meet at our first Maths lesson of the year, do take some time to do the following:

1. Accept the invite to the Maths blog with your sst email account.
  • You will be required to participate in activities delivered this platform.
  • Follow the blog so that you are informed of the posts put up
2. Go through various pages (in this blog), in particular - the "Habits of Mind" and "Tips to do well in Maths".
  • These are useful because they are about inculcating good learning habits and self-discipline that are relevant in all contexts (not just Mathematics).

What do you need to bring for your first Maths Lesson
  1. A4 Exercise Book - as your Maths Notebook - for all lessons
  2. A calculator
  3. Maths file (orange arch file): Write your name, register number, class at the spine
Look out for more emails along the way... before we meet in Term 1 Week 2



New Year... Begin with an end in mind


Welcome to an exciting year 2016
Success comes with adequate preparation and as a start do take note of the following.

1. Know the Mathematics Syllabus
  • This is the 4-year syllabus leading the "O" level exam: Elementary Mathematics 4016 (SEAB site)
  • We will not be covering all the topics listed in the syllabus in Sec 1. 
  • The curriculum adopts a spiral approach where selected topics will be revisited and going into depths as we move from year to year.
  • The abridged-scheme of work will be made available by end-January.
2. Using the Relevant Resources
  • SST Maths Notes - It is made available at the GoogleSite > Mathematics 
  • Calculator - It will be verified before the first level test and an "approved SST" sticker will be issued
  • SST Foolscap paper and graph papers (for assignments)
  • ICT Resources
    • Class Maths Blog: Most of the online learning activities will be carried out here
    • GoogleSite > Mathematics: Selected materials will be posted in the respective class pages; Performance Tasks/ Alternative Assessments are posted there.
    • Software: Grapher, Geogebra, Numbers, PhotoBooth, QuickTime Player
3. Assessment for 2016
  • Term 1   Level Test 1 + Alternative Assessment
  • Term 2   Common Test 1 
  • Term 3   Level Test 2 + Alternative Assessment
  • Term 4   End of Year Summative Assessment 
4. Diagnostic/ Summative assessments will be conducted as follows:
  • Diagnostic Assessment: Beginning of new topic - to assess prerequisite knowledge and linkages to new knowledge
  • Summative Assessment: End of topic - to assess level of understanding and competency
5. Daily learning and monitoring platforms
  • Class work -  in the form of online activities and practice questions
  • Assignment - to be done on printed handouts or SST foolscap papers
  • All classwork to be completed within designated time
6. Character is Destiny
    Your destiny should begin with your daily routines
    A.   Be Present
    B.   Listen without Prejudice and One conversation at a time
    C.   Be Socially Aware (we are after all living in a gregarious community)
    D.   Manage your impulses
    E.   Know that the choice that you have chosen has its own consequences