Thursday, 25 February 2016

Consolidating Lesson 1: Algebra - Simple Manipulation


1. Do the following on a sheet of writing paper

  • Write your name, register number, class and group number on the heading of the paper
  • Write the title, Algebra - Simple Manipulation

2. Copy the question carefully and label it neatly by the side

Remember to
(1) Show all steps clearly. No not skip any step.
(2) Neat and proper presentation of working is important. 

  • The working must show your train of thought.
  • Do not break down the working into parts. 

(3) Leave a line after each question

Maximum duration for Q1 and Q2: 10 minutes

Maximum duration for Q5: 5 minutes

Afternote (posted on 26 February 2016, Friday)

Click HERE to view the "Working and Answers" by Matthew Liang.

Wednesday, 24 February 2016

Support Programme (S1-01) Unit 03 - Approximation & Estimation

The following are to attend the Support Programme on Unit 03: Approximation & Estimation:
  • Date: 25 February 2016 (Thursday)
  • Time: 4 pm to 4.30 pm [max: 30 min]
  • Venue: S1-01 classroom
  • Things to bring: Maths Workbook

You may turn up for the session if you would like to take the opportunity to clarify your doubts on the Unit 03: Approximation & Estimation.
Do bring your workbook along for the discussion.

24 Feb: Things we accomplished and Getting Ready for the Next Lesson

In the first two lessons of this week (Monday & Wednesday (today)):
  • We discussed several questions in the Maths blog and used Paul's Wheel of Reasoning to check the assumptions when making decisions (e.g. whether one expression is greater/ equal/ less than another expression)
  • On Substitution type of questions, we should carry out the steps systematically (step by step): 
  • Answers in Lesson 1 (p5) were checked and discussed
  • The class identified 3 questions in Assignment 4.1 for discussion before submitting it.

Preparation for next lessons (Thursday, Periods 1 & 2)

(A) Lesson: Algebra
  • We will be discussing Lesson 2: Simplifying Algebraic expressions (involving 4 operations).
  • Go through Study Notes (Lesson 2) and attempt Assignment 4.2 (for discussion)
  • At the end of the lesson, you should be able to answer the challenging questions:
(B) Revision
Bring your marked assignments, as well as the 2014 S1 Level Test 1 question paper.
We will start the revision discussion at the 2nd period.

Saturday, 20 February 2016

6 AM Quiz: Let's Test FIDO out!

In this round of 6 am quiz, you will attempt to uncover the mystery behind Fido's Mind-Reading ability.

Fido claims that he can read our mind.
Click at the following link to test him out!!! :

There are several ways to explain Fido's trick, using mathematical reasoning. 
Make an attempt to use ALGEBRA to explain the "trick"?

Enter your thinking (algorithm) in Comments.
Have Fun!

Wednesday, 17 February 2016

17 Feb: Things we accomplished today and Getting Ready for Next Lesson

We have completed all 4 periods of lessons for the week.

Unit 04: Algebra

  • We discussed the questions in the activity, "Divide and Conquer": I am the Translator
  • You should have checked the answers and taken down notes as we discussed the questions. Please remember to insert the handout in your Maths file.
  • Paul's Wheel of Reasoning was introduced to guide us in questioning our assumptions when we attempt questions
  • Click HERE to read more about Paul's Wheel of Reasoning.
  • We applied this thinking model when we discussed  "Algebra: Which is Larger?"
    • We agreed that there are 3 possibilities: Greater, Smaller, Equal.
    • Please go through the class responses again and see you are able to propose a fuller solution before we meet to continue the discussion next week.
Homework (1) - to complete by Friday (under Comments)
Homework (2) - to complete by next Monday for class discussion
  • Assignment 4.1 

Preparation for next lessons...
More materials will be shared with you over the next two days for preparation.

6 AM QUIZ is making a come-back this Saturday (20 February 2016).
Look out for some fun stuff!

Algebra... Which is larger? (I)

Which is larger in magnitude?
5 + n or  5n

Explain your answer clearly with examples.
Indicate any assumptions made.

Enter your response in Comments.
This question is compulsory.

Algebra... Which is larger? (II)

Jennifer says, "5x2  is always smaller than  (-5x)2. "

Do you agree? Explain your answer. 
Indicate any assumptions made.

Enter your response in Comments.

This question is compulsory.

Algebra... Different "Faces" of Algebra (I)

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

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

Enter your suggested lengths in comments.
You may also enter any assumptions you made to your answers.

Algebra... Different "Faces" of Algebra (II)

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

Length of rectangle = 2x + 2y cm
Breadth of rectangle = x + 0.5y cm
Perimeter = 2 (2x + 2y) + 2 (x + 0.5y) cm
= 4x + 4y + 2x + y cm
= 6x + 5y cm

Enter your suggested dimensions in Comments.
Indicate any assumptions made.

Tuesday, 16 February 2016

Divide & Conquer: I am a Translator

Afternote (updated: 17 Feb, after lesson)

1. We had a discussion on the answers. Notes and answers are updated in the slides (in red).

2. Some of you expressed needed more clarity for selected questions.
Click at the clips to understand how the question is tackled:

Algebra: Equation vs Expression

(I) Algebraic Expressions vs Equations
The following are expressions
  • 3x
  • 5 - 2y
  • p + 2q - 45
  • mn
The following are equations:
  • 2x = 4
  • x + 8 = 20
  • x² = 36
  • 2x + y = 4
Can you tell the difference between an expression and an equation?

(II) Coefficients, Variables and Constants
In the following algebraic expressions:

(a) 6x
  • x is a variable
  • 6 is the coefficient of x
  • There is no constant
(b) 2y + 5
  • y is a variable
  • 2 is the coefficient of y
  • 5 is the constant
(c) 3m + 7n + 9
  • m and n are variables
  • 3 and 7 are coefficients of m and n respectively
  • 9 is the constant
(d) p + 2q - 45
  • p and q are variables
  • 1 and 2 are coefficients of p and q respectively
  • -45 is the constant
(e) 5a - 3b + 1
  • a and b are variables
  • 5 and -3 are coefficients of a and b respectively
  • 1 is the constant
(f) x - y
  • x and y are variables
  • 1 and -1 are coefficients of x and y respectively
  • There is no constant
When given an expression, are you able to pick out the variable(s), coefficient(s) and constant terms?
Click HERE to read more about these...

Algebra: Variables & Constants

For discussion: Click HERE to see the responses

The Blue Elephant @ Work

Here's another interesting challenge... this time, from Mr Dean Ang :)

Are you able to 'crack' the mystery behind this?

Introduction to Algebra... Crystal Ball Gazing...

Could you UNCOVER THE MYSTERY behind the crystal ball?
(in the Algebraic way!)
Submit your explanation under comments...

Monday, 15 February 2016

15 Feb: Things we accomplished today and Getting Ready for Tomorrow

(A) What we did today...
We discussed how to recognise the possible degree of accuracy when given a number.
Several examples were cited

In addition, we discussed:

  • When evaluating an arithmetic expression, we normally round off to 3 significant figures if the answer is non-exact.

(B) Homework 
1. Percentages - Homework

  • We discussed the expectations of the written work, which includes clear and complete working, not dividing the page into 2 columns
  • To be submitted tomorrow 16 February (Tuesday)

2. Attempt the following for discussion Tomorrow:

  • Assignments 3.1 to 3.3
  • It should not take more than 30 minutes to finish the 3 assignments

Amendments to Assignments:

  • Assignment 3.2: Q1 & Q2: Change "Estimate" to "Evaluate"
  • Assignment 3.3: Do not attempt questions from Q8 onwards

(C) Revision Papers
In preparation of the upcoming Level Test (to familiarise you with the expectations), a hardcopy of the 2015 S1 Level Test 1 question paper was issued to all.
Note: Softcopy is available in the GoogleSite (see image below)
  • Attempt the questions on writing papers. 
  • Show all working clearly in ink. Do not divide the page into two columns.
  • Label the working clearly (i.e. Question and parts).
  • Staple the question paper on top of the writing papers.
  • All sheets of papers to have your name, register number and class.
Deadline: Next Monday 22 February 2016

Note: Elrond & Celine - please find out from the classmates the examples we discussed in class.

Saturday, 13 February 2016

Thursday, 11 February 2016

Point to Ponder... Significant Figures

Study Notes: Lesson 2 (p3) 

We shall discuss this in the next lesson...

What are your thoughts?
Share it in Comments.

Let's discuss: What could the extremes be?

Below are two articles (The Straits Times, 10 Feb 2016) where approximated/ estimated figures are used in the reporting.

Wednesday, 10 February 2016

10 Feb: Things we accomplished today and Getting Ready for Tomorrow

1. Introduction to Unit 03: Approximation and Estimation

We discuss...
  • The difference between "Approximation" and "Estimation"
  • The difference between "Rounding off" and "Rounding Up/ Down"
  • When to use "" and how to present the working clearly with the degree of accuracy indicated at the end of the rounded off figure, e.g. 43 (rounded off to the nearest who number)
  • Depending on context, when to use precise/ exact figures and when to use approximated/ estimated figures

2. Getting Ready for Tomorrow

Read through the study notes - Unit 03 Lessons 1 to 2
Watch the video clips to understand the technique to approximate numbers by "Significant Figures"

3. Follow-up of marked assignments

The following are returned to all:
  • Diagnostic Test - do corrections for questions in p1 & p2
  • Assignments 1.1 & 1.2
    • Do corrections
      • GoogleSite - scroll down and refer to folder Unit 01 for suggested solutions
      • Click HERE to view clips that explain Assignment 1.2 Q2 to Q6 
  • Assignments 2.1 to 2.5 - for those who submitted before Lunar New Year holiday - do corrections. Refer to the following:
    • Do corrections
      • GoogleSite - scroll down and refer to folder Unit 02 for suggested solutions

Activity: Choice of Precision - To be EXACT or to APPROXIMATE?

1. Go through newspaper reports.
2. Identify an article that some numbers are cited.
3. Screen capture the article and paste the image in the designated slide (refer to register number).
4. Box-up the number(s) and indicate if it is an exact figure or an approximated/ estimated figure.
5. Explain briefly why the journalist chose to use this precision.
6. Remember to cite the source.

Examples of reliable sources: The Straits Times; Today Online

Guess My Age

Introduction: Why precision matters?

Here's an example when precision matters. Why?

World Record:


World Record Progression: 50 metres freestyle

Introduction: Precision matters - To who?

Read the article, "Nepal in new bid to finally settle Mount Everest height"

About Approximation: Interesting Figures about the Beijing Olympics

Source: My Paper Friday August 8, 2008
Can you tell... which is an exact figure? which is an approximated/ estimated figure?

The "Guessing" Game

  • Visit
  • Choose “Multiply Tens” for Game Type.
  • Score as much as possible within the timeframe of the game.

Monday, 8 February 2016

Operations of Real Numbers: Working - What's not acceptable; How it should look like

Below are examples of working that are not acceptable.

Illustration 1: "Choo-choo train" working
All steps are presented in a single line, continuously.
This is going to be confusing when handling equations.

General guide: No more than one equal sign (=) in each line of working.

Illustration 2: Fragmented working
An arithmetic expression is broken down into parts; and you work on individual parts before putting them together.

As we are handling numbers involving negative numbers, there will be a high tendency to make mistake in the sign when 'putting' the parts together.

General guide: Identify the portion that you intend to work on, copy the remaining components in the arithmetic expression. 

SAMPLE Working

1. Work on the terms within the bracket(s) first
2. While evaluating the square/ cube terms, the remaining terms are copied to the new line
3. "Remove" all brackets before working from left to right.

Wednesday, 3 February 2016

Mathematics Level Test 1

Note: This information is available at the GoogleSite (Maths > Announcement page)

Your Level Test will take place in T1W9.
To help you better prepare for it, here are the details for Mathematics Level Test 1: 
  • Primes, HCF, LCM
    Prime factorisation; index notation.
    LCM, HCF, Perfect Square, Perfect Cube
    HCF (word problem)
    LCM (word problem)
    Square / Square root of real numbers
    Cube / cube root of real numbers
    Integers, Rational & Real Numbers
    Order of real numbers
    Number line, number system, inequality
    Order of operations; Calculator use
    Order of operations (BODMAS)
    Order of operations (error analysis)
    Order of operations (word problem)
    Approximation & EstimationDegree of accuracy; recurring decimal.
    PercentagesWord problem (computation around percentage increase/ decrease)

  • Duration: 60min
  • Marks: 40 marks
  • Venue: Classroom
  • Items needed: Scientific calculator (with SST sticker), writing material, 3 sheets of writing paper

3 Feb: Things we accomplished today and Planning Forward

Dear S1-01
  • You were briefed on three areas (SDL, AA1, Preparation for next topic)
  • We went through Study Notes: Unit 2 Lesson 4 and focused on the strategies when operating on fractions. 
    • It is important for you to master the strategies as they are relevant and applicable to another topic, Algebra. 
  • Complete the "Spot the Error(s)" handout for discussion in the next lesson.
  • You are strongly encouraged to watch the set of video clips (Unit 2 Operation of Numbers (tab above)) to understand and be familiar with the strategies.
  • Challenging Question 2 was issued to the class. This is optional. 
    • You may submit the paper tomorrow as correct answers will contribute to group points.
  • You should submit the corrections for Number Line activity by today (to Maths Rep).
  • You need to submit Assignments 2.1 to 2.5 by the end of tomorrow's lesson.
  • Failure to do so will require you to stay back after school to complete the task on Friday (after the LNY celebration)

For forward planning... [We went through in class... step-by-step]
  • Self-Directed Learning (SDL): Percentages
    • Study notes are issued to you (with Homework indicated at p8)
      • Homework to be submitted on 17 February (Wednesday) (Term 1 Week 7)
    • You were referred to the GoogleSite for the online activities
    • Revision Handout - to be ready for discussion in Term 1 Week 8
    • Online practices will be assigned via AceLearning portal
  • Alternative Assessment 1 (AA1)
    • We went through the information (including useful references) in both the GoogleSite and Google Classroom
    • Deadline: 12 February 2016 (Friday) (Term 1 Week 6) 
    • You have also been informed that there will be penalty for late submission of work
  • Unit 03: Estimation and Approximation
    • This is the next lesson unit.
    • In preparation of the lesson unit, you are strongly encouraged to watch the video clips posted in the AceLearning portal (under this topic)
    • Video clips on specific areas: Significant Figures are now available in the Maths Blog (tab above), do VIEW the clips before we start the topic.

Key Pointers for Operations of Fractions

Study Notes: Lesson 4 (p2)

Activity & Discussion: Spot the Error

Study Notes: Lesson 4: Operations of Fractions

Monday, 1 February 2016

1 Feb: Things to do

Dear S1-01

Today, we went through the number lines assignment.
Several commonly made mistakes were pointed out.

Assignments 2.1 to 2.5
  • We were discussing halfway though
  • We shall continue to discuss the remaining questions tomorrow
Preparation for discussion
  • Study Notes: Unit 2 Lesson 4

Food for Thought: Challenging Question 1 (S1) Real Numbers


  • Group 1: 15 points (5 submissions)
  • Group 2: 6 points (1 submission)
  • Group 3: No submission
  • Group 4: 15 points (3 submissions)

Food for Thought

(A) Do they mean the same thing?