Thursday, 26 January 2017

[Menu] 26 Jan 2017: Number Lines & Real Numbers

1. Number Line 
  • How to represent real numbers on a number line (e.g. n ≥ 10)
  • Under what circumstances that it is not possible to draw a number line
  • You may check your answer to the worksheet, "02 Real Numbers - Number Lines (Class Activity)" in the GoogleSite.
  • Formative Quiz 1
2. Real Numbers 
  • The concept of "Difference": Larger number - Smaller number
  • Illustrations to find the difference of numbers (involving negative numbers)
  • Zero Pair concept
  • Addition and Subtraction of numbers - Concept and Technique
  • Finding Roots of Positive and Negative numbers (perfect squares & cubes)
3. Just for Fun

  • It's time to get familiar with your calculator.
  • Click at the post, Calculator Skills 02: Calculator Talks!, to access a fun activity with calculator. You can have fun and earn group points at the same time, too :)
4. Preparation for next lesson on 4 operations

Complete the Alternative Assessment 1 Practice as soon as you could, and submit via the Google Classroom. (Login Required)
Deadline: 31 January 2017 (Tuesday)

You are strongly encouraged to complete the task as soon as possible so that feedback can be given to you before you embark on the actual Alternative Assessment end of next week.

You can earn points for your group for 'early bird' submission:
  • Submit on 26 Jan (Thu): 10 points
  • Submit on 27 Jan (Fri): 5 points
  • Submit on 28 Jan & 29 Jan (Sat & Sun): 3 points

Textbook 1

Attempt the following questions in your workbook.
You are to post your answers (with working clearly presented) in the Google Classroom

Exercise 2A (p31)
Intermediate: Q6, Q7

Exercise 2B (p38)
Intermediate: Q3 - You are expected to show the steps clearly. Do not skip steps.
Advanced: Q6, Q8

Estimated duration: 30 min
Deadline: 27 January 2017 (Friday), 2359

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".

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

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

In preparation for the next two lessons that would focus on the operations of numbers...

Watch the collection of lesson clips at the Khan Academy to better understand the concepts of addition and subtraction of negative numbers (in particular, explanation with the use of number line)


Calculator Skills 02: Calculator Talks!

Let's key the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 into the calculator. Look at what's displayed on the calculator output screen. Turn the calculator upside-down. Do they look like any letters in the alphabet?

For example: The digit 0 becomes O, 1 becomes I, 2 becomes Z, 3 becomes E, 4 becomes h, 5 becomes S, 6 becomes g, 7 becomes L, 8 becomes B, and 9 becomes G.

 Let's try the following:
  • enter 6.2
  • multiply this by itself
  • add 0.23
  • divide by 50
Turn the calculator upside down, and you have a friendly greeting!

Let's see what we have for breakfast:
  • multiply this by 1000
  • divide the result by 6
  • throw away the part to the right of the decimal (what is the TECHNICAL term for this???)
  • subtract 3 from the result. Mmm! Delicious! 
  • But be sure to throw the ( 68 x 68 - 7 ) x 5 x 5 x 5 + 220 in the trash!
Let's see if you could figure out the secret code below :)
  • Does the ( 19 + 19 - 1 ) x 19 + 2 x 3 x 5 have (47 x 47 + 10 x 10 ) x 5 x 5 - 3 x 3 or (47 x 10 + 47 x 10 + 47 x 10 + 47 x 10 - 1) x 3 ? or lay 7 x (800 + 9)?
  • Is there one in your neighbourhood 1 / 50 ?
  • What about the 2 x 13 x 13 ?
  • Or the 3 x 3 x 3 x 3 x 101 - 3000?
  • The (50 x 50 x 3 + 1) x 6 - (50 x 50 x 4)?

(Of course, the plural of (50 x 50 x 3 + 1) x 6 - (50 x 50 x 4) is (8 - 1) x 8 x ( 8 x ( 8 x (8 + 1 + 1) - 1 ) - 1 ), isn't it.)

Now, create a secret code that and post it in the Padlet!

Each unique expression resulting in word will worth...

  • Expressions involving +, -, x, ÷ will gain the 3 points
  • Expressions involving squares, cubes and roots will gain 1 bonus point (on top of 3 points)
  • Expressions phrase made up of 3 or more words will gain 10 points
Remember to add your name and group number to the title of the post.

Made with Padlet

The above is an interesting way to use arithmetic to 'code' secret messages.

Do you know...


Tuesday, 24 January 2017

[Menu] 24 Jan 2017 (Tuesday)

Today, we went through

  • Discussed the deciding factors - when to use HCF and LCM with the problems
  • 6 AM Quiz - The Calculator Mystery (as an introduction to the Unit 02: Real Numbers)
  • Brief - Alternative Assessment 1 (AA1) Practice 
  • Homework: You are strongly encouraged to finish the task before this Friday (27 Jan 2017)
  • Introduction to Number Lines
  • Homework: Worksheet on Number Lines (softcopy available in GoogleSite)

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 :)

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

Saturday, 21 January 2017

Friday, 20 January 2017

[Menu] 20 Jan 2017 (Friday)

1. Understanding the question and strategy behind the following task:
2. Revisit: Finding HCF and LCM using index notation method (both numerical and algebraic expressions)

3. Completed discussion of task: [For Discussion] HCF, LCM, Perfect Square/ Cube

  • The following have not submitted the class work yet:
    • 2 FOO LIN HUI 
    • 14 LOKE YI MING 
5. Getting ready for next topic:
  • Go through Chapters 3 and 2

Something NEW!

(Fortnightly) 6 A.M. Quiz
Starting from this Saturday, a Quiz will be posted in the Blog at 6 A.M. on a Saturday morning.
The early birds may start the day with a Quiz question. All responses will contribute points to your group :)

  • Early Bird points (correct responses received before 7 am): 5 points
  • Any correct responses received by 9 am: 3 points
  • Any correct responses received by end of Saturday: 1 point

The quiz will remain in the blog for future discussions.

Things to accomplish:

1. Complete Assignment 1.2 (Individual)

  • This was assigned on yesterday (19 Jan 2017, Thursday).
    • You may refer to the worksheet in GoogleSite (if you could not find it)
  • Deadline: Next Tuesday (to be submitted in class)

2. Complete Word Problems for HCF and LCM: Divide and Conquer (Group effort)

3. Complete the 3 questions in Google Classroom (Individual)

  • This was assigned on yesterday (19 Jan 2017, Thursday).
  • Deadline: Today (20 Jan 2017, 2359)
  • Last check on Today, 1500h, the following have not attempted the task.
    • PS: George - pls check your submission. You might have missed out a step.

[Homework 20170120] Task: Divide & Conquer

Estimated duration: 10 minutes per question

As briefed in the class,
  • Within your group, you will decide among yourselves who is going to take charge of which ONE question.
  • In total, there are 7 questions. If your group has fewer than 7 members, you may leave one question unattempted. However, that would mean your group is likely to lose out in the group points.
1. Attempt the question on your Maths workbook. Your working must be clear as points are awarded to working and concluding statements.
For easy reference in future, indicate the Workbook page and Question number.

2. Take a photo that shows your working clearly.
Upload the photo to the slide that your group is assigned to.
Remember to indicate your name.

On another note, you are strongly encouraged to attempt all the questions for your own practice, and to be familiar with how the techniques/ methods are applied in various contexts.

Deadline: 23 January 2017 (Monday) 1200h.

Click HERE to open the slides file


Click HERE to open the slides file


Click HERE to open the slides file

Click HERE to open the slides file

[Homework] What's the deciding Factor? HCF or LCM

Click HERE to view responses

Thursday, 19 January 2017

[Class Discussion] Roots: When the condition changes...

[All Roads Lead to Rome] Highest Common Factor

Find the highest common factor (HCF) of the following numbers: 216, 36 and 135

Method 1: Listing

Method 2: Combined division

Method 3: Through reasoning

Method 4: Circle Common Factors
> Which part of this set of working (presentation) needs to be improved?

Method 5: Using Index Notation

> What's wrong with this set of working?

[All Roads Lead to Rome] Lowest Common Multiple

Find the lowest common multiple (LCM) of the following numbers: 216, 36 and 135

Method 1: Listing

> Which part of the working needs to be improved?

Method 2: Circle Common Factors

> What's wrong with this presentation?

Method 3: Long Combined Division

> Which part of the working needs to be improved?

Method 4: Using Index Notation
> Which part of this working is not correctly presented?

[For Discussion] HCF, LCM, Perfect Square/ Cube

Source: Workbook (p7) Question 31 (Advanced)

Attempt the following question in your notebook.

Tuesday, 17 January 2017

[Menu] 17 Jan 2017 (Tuesday)

1. Application of Prime Factorisation

2. "Perfect Numbers" and Roots

Things to do - Homework

1. Activities in the blog (to be completed by 17 January 2017, 2359h)
2. For submission on Wednesday, 18 January 2017 (in class)
  • Assignment 1.1 
    • Complete the remaining question, Q3 on the handout
  • Workbook 1 (p6) Q26
    • To be done on writing paper, staple behind Assignment 1.1
    • Copy question before you attempt to answer with complete working.

Finding Cube Root... What's wrong with this working?

Question: Find the cube root of 13824

Read the working carefully.
  • Highlight area(s) that you think is incomplete
  • Identify an 'critical' mistake - because of the way the working is presented

Food for Thought (1) Pondering over "m" and "n"

Click HERE to see responses

Food for Thought (2) Pondering over PRIMES

Click HERE to see responses

Friday, 13 January 2017

[Menu] 13 Jan 2017 (Friday)

1. Introduction of Number Family
2. Prime Numbers - What is it?
3 Return of Diagnostic Activity, and quick discussion of answers

Things to do - Homework

1. Go through the blog post that summarises the Number Family

2. Watch the short clips on the procedures to carry out Prime Factorisation of a number before doing the assignment. There are two written examples included in the same blog post.

  • Watch it. Doing it: Prime Factorisation
  • Assignment 1.1: Attempt Q1, Q2, Q4, Q5, Q6 
    • Q2 to be done on writing papers with SST letterhead. Label the question and parts clearly.
      • You may choose to use ladder method or factor tree
    • Do not attempt Q3 yet
  • To be submitted on Wednesday (18 Jan 2017) during lesson
  • Estimated duration: 40 minutes

3. Diagnostic activity for HCF and LCM - Techniques
  • Click HERE to see details
  • To be submitted by Monday (16 Jan 2017) 2359h via Google Classroom
  • Estimated duration: 20 minutes

An Introduction: The Number Family

Before we start discussing the different types of numbers, we learn the different types of numbers, and their relationship. We will discuss further when we work on Unit 02.

The relationship between the numbers system is as follows:

Amongst the 4 types of numbers:
  • NATURAL NUMBERS is the smallest of all - starts from 1, followed by 2, 3, 4, 5, ... basically, it's positive integers
  • INTEGERS is made up by negative integers (-1, -2, -3, .... ), zero (0) and positive integers (1, 2, 3, ...)
  • RATIONAL NUMBERS are numbers that can be expressed as a fraction a/b such that both a and b are integers and b is non-zero. Integers and natural numbers are rational numbers since we can express them with denominator = 1.
  • REAL NUMBERS are numbers include natural numbers, integers and rational numbers. It also includes numbers that cannot be expressed as a fraction, e.g. pi, square root of 2
Note: Whole numbers and Complex numbers are not mentioned above.

Attempt the following exercise to check your understanding

Click HERE to view responses

Watching it. Doing it: Prime Factorisation

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

More examples

Example 1:

Example 2:

Diagnostic Activity for next lesson

The objective of the task is to find out the techniques you know.

Find the highest common factor (HCF) and lowest common multiple (LCM) of the following numbers: 216, 36 and 135

On a single sheet of paper, find the above in as many ways as you know.
Divide the page into 2 halves - one part for HCF and the other half for LCM.
Indicate clearly - subheadings.

Take a photo of your work and submit to the Google Classroom (The task will be assigned).
Deadline: by Monday 16 January 2017

Thursday, 12 January 2017

[Menu] 12 Jan 2017 (Thursday)

1. Diagnostic Test (1)
2. Diagnostic Activity - Unit 01: Primes, HCF and LCM

Things to do:

1. Sieve of Eratosthenes
2. Calculator Skills 01

Things to bring for next lesson:
1. Study notes
2. Maths Notebook (A4)

Sieve of Eratosthenes

To be completed by 12 January 2017 (Thursday), 2359

Reference: Study Notes (p2)

Click HERE to access the applet.

As you follow the steps to use the applet to 'sieve' the prime numbers.

Why is this method considered the most efficient method to find prime numbers?

Click HERE to view the responses (in the next lesson)

Calculator Skills 01

To be completed by 12 January 2017 (Thursday), 2359

Click HERE to view your submission. We shall check the answers in the next lesson.

Wednesday, 11 January 2017

Tuesday, 10 January 2017

Pre-Lesson Activity: Mathematics is about...

Enter as many words as possible that describes what you know about Mathematics since your first encounter with the subject.

Friday, 6 January 2017

[Preparation] Term 1 Week 2

Dear S1-01

Please take note of the following, in preparation of the Maths lessons starting next week.

1. Diagnostic Test

You will be sitting for the diagnostic test for the subject on Thursday (12 Jan 2017)
The purpose of this test is to gauge your understanding of various mathematical concepts, for the teachers to pace the lessons.

What will be tested?
  • What you already know
  • What you would be learning in this academic year
Other important information
  • Duration: 50 minutes
  • Electronic calculator is allowed to evaluate explicit numerical expressions; however, clear and systematic working is expected as omission of essential working will result in loss of marks
  • Answer all questions in INK.

2. Reading

To prepare your for next two weeks, you should start reading the following
  • Maths Textbook 1: Chapter 1 Primes, Highest Common Factor and Lowest Common Multiple
  • Maths Textbook 1: Chapter 3 Approximation and Estimation