Food for Thought: Rational Numbers on a Number Line?

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Enter your response to the following in "Comments". 

(2-to-3 Activity) Number Lines - Common Errors

Are these errors obvious to you?



Compare this with what you have done...

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Now, it's your TURN....

Click HERE to access the form.

Introduction: Real Numbers - How deep is deep?

Class Discussion:

What is the distance between the two extremes (in metres)?

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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/

[Homework] 22 January - Consolidation & Preparation

A summary of homework assigned:

1. Google Classroom 

• [HW2] Selected Questions from Textbook Chapter 1
• Focus: Prime Numbers, HCF, LCM
• Estimated duration: 30 minutes
• Follow instructions; refer to template
• To be submitted on 29 January 2020 (WED) during Maths lesson

2. Maths Blog/ Padlet

• Review Exercise 1 from Workbook Chapter 1
• This is to consolidate what you learnt in Chapter 1
• Read the instructions in the post below
• Estimated duration (for 2 questions): 10 minutes
• Complete before 27 January 2020 virtually

3. Preparation for next Chapter

You do not need to do all before the next lesson... do pace yourself to do the following in the next 2 weeks

• Read up textbook Chapter 2
• Refer to SLS materials 
• Watch the clips in the Blog page

4. For those who have not attempted the following - please complete the following for discussion on WED:

• [HW] HCF and LCM - What's the deciding factor?

[HW] Workbook Chap 1 Review Exercise 1 (p15-p17) - 2 Questions of your choice

This is an exercise to consolidate what you learnt in this chapter (to-date).

Pace yourself to do these questions in the workbook.
It may take up to 2 hours if you were to complete the entire exercise.

Advice: Review and revise what you learnt in this topic (go through the notes) and blog posts. 

As a contributing member of the class, you will submit answers to 2 questions (your choice) to the padlet before next MONDAY (27 Jan). With this, we can learn from each other how we approach certain questions and present our answers. You may also ask questions or provide feedback to your peers. (remember to observe 4Rs here).

Feedback will be provided to you after the public holidays.

LINK

Quick Check: Highest Common Factor

Attempt the task in your Maths Notebook.
It should take less than 5 minutes.

LINK

[Summarising] Techniques to find HCF, LCM

These 2 clips summarises how we can find HCF and LCM of 2 or more numbers

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Clip 1: Observe what are the factors 'circled' in each case

When we look for Highest common factor, technically, we are looking for the 'lowest' power.
For the Lowest common multiple, technically, we multiply the prime factors with the highest power.


Clip 2: Some of us learnt to find the HCF and LCM using the division method.
The clip attempts to show how these 2 methods (i.e. Long Division method and Index Notation Method) are related to each other - the same thinking behind, though the representation looks different.

Quick Check: Lowest Common Multiple

Attempt the task in your Maths Notebook.
It should take less than 5 minutes.

LINK

Challenging Question: Roots

Submitted on behalf of FELIX ZHU SING HAN 


[Checked: 21 Jan 2020]
Working needs greater clarity - need to show how you systematically work from the given number.

[Prime Factorisation] Watching it. Doing it

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

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There are 2 methods to do this:

(a) Repeated Division

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(b) Factor Tree

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More examples

Example 1:

Example 2:

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Challenging Question: Roots

[Checked: 21 Jan 2020]

Should not apply estimation as it will introduce greater error margin.

The method is you take the last digit of the number, 9870

Which is 0

Then ignore the last 3 numbers.

Which leads us to number 9.

The closest cube number is 8.

The root of 8 is 2

Put 2 in front of 0, which was the last digit of 9870.

Thus the answer is 20

(estimated)

[Homework] 17 January - Consolidation

A summary of the Homework assigned today:

1. Read the feedback given to the Prime Factorisation Exercise (Padlet)

2. Attempt the written work assigned in the Google Classroom (refer to template for presentation)

3. Attempt the post below - which checks your understanding of the concepts learnt this week.

• [HW] Taking a closer look at Factors & Multiples

4. Attempt the post below - that gets us to think about the application of HCF and LCM (which we will go further and deeper in the next lesson)

• [HW] HCF and LCM - What's the deciding factor?

5. [Optional] Challenging Question

Attempt the following challenging that question worths "-3" points if it is correctly answered with clear and proper presentation.
Post your answer as a blog post with heading "Challenging Question: Roots" 

[HW] HCF and LCM - What's the deciding factor?

The task will take approximately 10 minutes to complete.
To be completed by 20 January 2020 Monday (5pm)

LINK










Click HERE to view responses

[HW] Taking a closer look at Factors & Multiples

The task will take approximately 20 minutes to complete.
To be completed by 20 January 2020 Monday (5pm)

LINK to form

[HW] Prime Factorisation (using LONG DIVISION method)

Complete the task before 5pm TODAY so that feedback could be given to you before the next lesson.
Estimated time: 5 minutes

LINK

[HW] Prime Numbers and non-Prime Numbers

TASK 1: Attempt the activity in Textbook 1A 
Estimated time: 10 minutes

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Task 2: Why NOT PRIME?
Estimated time: 5 min

Click HERE to attempt the task





Click HERE to view submission

[Going a bit beyond...] Sieve of Eratosthenes

In search of PRIME Numbers.... using technology

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Reference: Textbook (p4)

You are going to use an applet to help you surface all the prime numbers between 1 to 100.
Click HERE to access the applet.

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

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

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Enter your thoughts in COMMENTS
Remember to sign off with your Group number
- A reasonably well-explained answer can contribute to "-2" to class time :)

Quick Glimpse: The Number System

Below is a very much simplified representation of the various number families and their relationships. We will discuss further when we start the topic on Real Numbers.

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Broadly...
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.

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[Extension] Going Beyond Real... Imaginary Numbers

Today, we discussed the Real Number System, which the relationship of the families of numbers can be represented in a Venn Diagram.

What's beyond the REAL Number system?

The Imaginary Numbers! [which is not in the "O" level syllabus]
Some of you may be interested to find out more about this...
This will shade some light to the 'mysteries' when we start to discuss "Roots" of numbers

[Preparation] Unit 1 Primes, HCF, LCM, Number Systems

Resources in SLS of the following topics have been assigned to you (from 14 Jan to 31 Jan)

With reference to the Scheme of Work (refer to Google Classroom),

• Pace yourself when you attempt the topics 
• Do not attempt all in one go
• You can also use the resources as a summary or recap after the lesson/ topic, too. 

If you spot any error in the answers to the QUIZ, you can screenshot the error, explain why the answer is incorrect and email to me.

How would I contribute to how my Maths classroom look like...

Read the MISSION in the Padlet carefully.
This is to be completed before the next lesson.

LINK

TED 1: Is math discovered or invented? - Jeff Dekofsky

What is "Mathematics" to you? 
What do you associate "Mathematics" with? 
Share your thoughts in "Comments"

TED 2: Math is the hidden secret to understanding the world by| Roger Antonsen

Listen to the passionate sharing about the existence of this "Language". 
What kind of "Mathematics" do you see in your everyday encounter? 
Describe in a couple of sentences in "Comments".

TED 3: Why Can't You Divide by Zero?

Have you wonder why we do not "divide" any number by Zero?