## Tuesday, 27 June 2017

### [Menu] 27 Junel 2017 (Tuesday)

What we did in class:

• Revisited Perpendicular Bisector, related vocabulary terms and how to label the diagram clearly
• Analyse the diagram to draw out properties related to the line and its perpendicular bisector
• Relate the properties to shapes: Circle, Triangles (equilateral, isosceles triangles), Rhombus, Square, Parallelogram
• Spot the Error (3 questions): To describe, using the correct metalanguage, what was wrong with the way the diagram was constructed
• Angle Bisector: The construction and "seeing" the "invisible" perpendicular bisector
• Sketching the diagram based on information given to aid construction of shape (SDL during holidays)
What we did:
• Construct a regular hexagon with length 5 cm using a ruler and compass (clue: Use a circle).
• This is in preparation of an activity in the next lesson
Things to follow-up:
1. Complete the Spot the Error Tasks if not completed yet.
2. Complete Assignment 1 (2 Questions) [Estimated duration: 30 min] - construct a fully-labelled diagram with pencil - to be submitted in next lesson.
3. Apart from the construction set, bring a pair of scissors and clear tape for an activity in the next lesson.
4. Examples of hologram clips from Youtube:

### Geometrical Construction: Spot the Error (1)

As a group, watch the clip and try to spot as many errors as possible.

### Geometrical Construction: Spot the Error (2)

As a group, watch the clip and try to spot as many errors as possible.

### Geometrical Construction: Spot the Error (3)

As a group, watch the clip and try to spot as many errors as possible.

## Sunday, 21 May 2017

### June Holiday Engagement & Planning ahead

Dear S1-01

We went through the June Holiday Engagement activities in our last lesson this term (17 May 2017, Wednesday). Below is a summary, to be accomplished before Term 3 starts:

1. June Holiday Engagement: Challenger 1 - PISA questions
• As shared during lesson, the set of selected questions aims to challenge us beyond just applying the mathematical skills we already know. The questions require us to apply reasoning skills and articulate our train of thought clearly in the written form, which are competencies that 21st century learners need to develop
• Softcopy of the handout is available in the GoogleSite (Mathematics) for the class
• Suggestion: Do not do all questions in a single attempt. Give your brain a break after half an hour. You may stagger the tasks over a few days. You may attempt the task in any order.
• Recommended duration: approximately 3 to 4 hours.
• Deadline: 23 June 2017 (Friday) – 4th week of June Holidays
2. Geometrical Construction (partial SDL)
• The set of notes was issued on Wednesday (17 May). It is also available at the GoogleSite. Click HERE to access the handouts as well as the video clips.
• We attempted the construction of perpendicular bisector in class (last lesson of the term) and made an attempt to draw out the characteristics of the lines and the properties of the triangles obtained.
• Complete the tasks before the term starts as we will be moving into more complex constructions that build on the skills you learn from this series of self-directed activities.
• You must bring with you the construction set (ruler, set square, compass, protractor and sharp pencil) for lessons when school starts in Term 3.
• The constructions in the handouts should be completed by the end of the holidays.
• Recommended duration: approximately 3 hours.
• Deadline: before 27 June 2017 (Tuesday)

In addition, you were informed that we will be doing the following topics in Term 3
1. Geometrical Construction
2. Functions and Linear Graphs
3. Data Handling (we did part of this topic very briefly when we were preparing for SASMO in April). Click at the link to see post related to MEAN, MEDIAN & MODE.

6 AM Quiz

The quiz will take a break during the June Holidays.
It will return on 24 June 2017

### [SASMO 2016] Congratulations!

Click HERE to access PDF file for the results that is published in its official website.

Silver Award
1. CHRISTABEL LEE
3. FOO LIN HUI
4. XEE ZUN KYE
5. JIA ZEYU
Bronze Award
1. SHARMA SIMRAN
2. WOO SYN TING, SARA
3. HO RUI YANG
4. CHONG YAO KIAT, CORWIN
5. WAN HANAFI BIN WAN MOHAMAD SANI

Some of you may be interested to take part in the upcoming Australian Mathematics Competition (AMC).
• Click HERE to access the post in the Students Blog.

## Thursday, 18 May 2017

### Pythagoras' Theorem - revisited

We discussed about Pythagoras' Theorem when we did "Algebra: Equations" - FORMULA.

Here are an interesting "proof" of Pythagoras' Theorem (using a simple set of Pythagorean triplets:

Source:

### June Holiday Engagement: Challenger 1 - PISA questions

Deadline: 23 June 2017 (Friday), week 4 of June Holidays
Estimated duration to complete the entire task: 3 hours
Suggestion: You may want to stagger your time a attempt a handful of questions in a day.

Refer to the Handout given to you in Term 2 Wee 9.
• Attempt all the questions in the handout.
• You can also find the question booklet in the GoogleSite

## Tuesday, 2 May 2017

### 2 May: Revision

Today's revision focuses on Percentages, Rate & Ratio.

The suggested solution of the worksheet for class discussion is now available at the GoogleSite:

You may wish to refer to your Maths Workbook Units 8 & 9 for look at more scenarios - it is not necessary to practise all the questions, but to understand the context of the question and know how to apply the skills to solve those problem.

## Wednesday, 26 April 2017

### Revision: Ratio, Rate & Speed - Word Problems (Tier C Q5, Q6)

With reference to the revision handout, "Ratio, Rate and Speed: Word Problems",
you are encouraged to post your worked solution (if you have attempted) for Tier C Questions 5 & 6 in the padlets before the next lesson.

## Thursday, 20 April 2017

### Speed: Travelling via different modes

In December, Ms Loh travelled from Takayama via Toyama (in Japan).
There were several means that she could choose: by car, by train or by foot.

(Q1) Given the suggested duration (by Google; search for "distance between Takayama station to Toyama station"), find the average speed by all three means of travelling.

(Q2) What assumption(s) did we make when computing the speeds?

(Q3) At present, only local train runs between the two stations. If shinkansen is available between the two stations, how much time would be saved?
Using the information in the blog post (click HERE) to see more details

## Wednesday, 19 April 2017

### Speed: Every Minute Counts...

Enter your individual response in the comment. Remember to label the parts as given.

(1) Describe clearly how would you approach the question?
(2) What is your final answer (round off to 3 SF if it is non-exact)

Duration: 5 minutes

Suggested Train of Thought...
The following suggestion reduces the 'redundant' working (updated on 23 April 2017)

Step 1: Draw out the info available
Speed of Wolf: 65 km/h
Little Red Riding Hood (LRRH) - start 35 minutes later; catch up after 130 km.

Step 2: Make inference
Since distance travelled by both Wolf and LRRH is the same,
then Wolf would have travelled 130 km.

Thinking:
By finding the time taken by Wolf, we can find the time taken by LRRH to travel the same distance (since she started 35 min later).
With this time, we can find the speed that LRRH travels at.

Step 3: Find time taken by Wolf. This will enable us to find amount of time LRRH has taken.
Distance by wolf = 130 km.
and time taken by Wolf = distance ÷ speed = 130 / 65 = 2 hours

Step 4: Find time taken by LRRH
Remember both Wolf and LRRH travel the same distance,
and LRRH started 35 min later than
Since wolf takes 2 hours to cover a distance of 130 km,
Time taken by LRRH = 2 h - 35 min = 85 min
Convert the time to h, we have 1 5/12 h

Step 5: Find speed that LRRH travels at
Speed = Distance ÷ Time
Speed = 130 km ÷ 1 5/12 h = 91.8 km/h (3 significant figures)

### Q1-Q4: Things to look out for when presenting your solution

The following pointers were suggested by the class that we should take note of when presenting our worked solution, to express our thoughts clearly, hence making our thinking visible to the reader.

Updated (23 April 2017): Group SCORE
Note:
The highlighted mark shows that the team had scored full mark for the question they managed.

### SDL (02) Revision: Rate & Speed (Q1) The Traveller's Route

Instructions
Attempt the task on papers provided.
Remember to label the parts and show your working clearly. Presentation must be clear.

Eunice is driving from Singapore to Malacca, Malaysia.

Eunice is driving from Singapore to Malacca, Malaysia. She leaves Singapore Woodlands checkpoint at 08 30 and travels the first 60 km of the journey at an average speed of 25 m/s and the next 120 km at an average speed of 80 km/h. She stops at Muar for a 30-minute break before continuing the last part of her journey at an average speed of 90 km/h in 35 minutes.

(a) Convert 25 m/s to km/h. [1]
(b) What time does she reach Muar? Give time in the 24h notation. [3]
(c) Find the average speed for its entire journey, giving your answer in km/h. [3]

### SDL (02) Revision: Rate & Speed (Q2) The Singapore Flyer

Instructions
Attempt the task on writing papers.
Remember to label the parts and show your working clearly. Presentation must be clear.

At a height of 165m, Singapore Flyer is one of the world’s largest Giant Observation Wheel and also one of Asia’s biggest tourist attractions.

The diameter of the Singapore Flyer measures at 150 metres, and it travels at an average speed of 0.24 metres per seconds.

(a) Express its average speed in km/h [1]

(b) How long (in minutes) does it take for the flyer to complete one revolution? [2]

(c) The company is promoting the "dining capsule" concept, inviting people to dine in the capsule. If the meal lasts for one hour, how many revolutions would the diner have gone through for his meal? [1]

Circumference of Circle = 2 π r   where r is the radius and use π = 3.142

Sources:

### SDL (02) Revision: Ratio (Q3) Precious Gold

Instructions
Refer to the Handout and attempt the task on writing papers.
Remember to label the parts and show your working clearly. Presentation must be clear.

By mass, Yellow Gold 18K is made up of 75% of Gold (Au), 15% of Silver (Ag) and the remainder is made up of Copper (Cu), by mass.

(a) Find, by mass, Au : Ag : Cu, giving your answer in the simplest form. [1]

(b) A goldsmith is tasked to make a piece of jewellery with Yellow Gold 18K. With 2.25g of Silver, how much of gold and copper would be needed to form the alloy? [2]

(c) If this piece of jewellery is to be melted into liquid alloy
(i) Find is the volume of the alloy. [3]
(ii) Compare the volume with that of a 15g of pure 24 carat gold, which has a greater volume – Yellow Gold 18K or 24 carat gold? [2]

Given that the density of Gold is 19.3 g/cm3, Silver is 10.49 g/cm3 and Copper is 8.92 g/cm3.

Watch the following clip for background info that would help you understand the context of the question better:

Mass, volume and density are related by an equation: density = mass ÷ volume

### SDL (02) Revision: Ratio (Q4) Fresh Lemonade for all

Instructions
Refer to the Handout and attempt the task on writing papers.
Remember to label the parts and show your working clearly. Presentation must be clear.

Ms Lee, the Sports & Wellness teacher, is going to conduct a fresh juice making class in the “Eat Healthy, Live Healthy” week. She is going to teach participants how to make fresh lemonade, with reference to a recipe available at https://www.sunkist.com/recipes/fresh-lemonade/

Find out, from the website, the amount of ingredients that Ms Lee needs to prepare for each participant, enough to make the beverage for 4 servings.

(a) Express the ratio of lemon juice, water and sugar in its simplest form. [2]

(b) If only 10 cups of lemon juice are available, what is the maximum number of participants that Ms Lee can have for the workshop if she needs to ensure every participant has the same amount of ingredients for the workshop? [1]

(c) Based on the constraint she has in (b), how much water and sugar does she need for her workshop? [2]

(d) If Ms Lee wants to prepare enough lemonade for all participants (not including herself), find out from the website how much of each type of ingredients she needs. [1]

## Tuesday, 18 April 2017

### [Menu] 18 April 2017 (Tuesday)

1. We went through the Error Analysis for Summative Quiz 2
The marked quizzes were returned, and suggested solution are available in the GoogleSite.

2. We started the discussion of RATIO (refer to the new set of study notes issued).

3. Homework - assigned at the Google Classroom (Ratio).
Do attempt by today 10 pm (as a review practice)

4. Homework for submission - Inequalities Handout (given on Monday)
- to be submitted tomorrow (19 April 2017)

5. Report to Learning Oasis 1 tomorrow for Maths lesson.
Bring along (1) Study Notes for Ratio (2) Maths Notebook (3) Learning Device (4) Calculator (5) Writing materials

### [Review] Algebra: Factorisation Summative Quiz 2

Report on Friday (21 April 2017) at 1.30 pm to 1.45 pm for a dipstick quiz on factorisation (in S1-01 classroom).
Preparation: Revise "Factorisation"-related materials and watch the clips at the Maths Blog (Algebra (3))

## Monday, 17 April 2017

### Algebra Mind-Map

This is a mind-map to recap what we had learnt for algebra for the past few weeks and months

1. Summary of Algebra - mapping the various subtopics (revision)
[Hao Min - pls post the image in the blog. Thanks.]

2. We completed our discussion on the handout , "Algebra - Factorisation (Consolidation)"
You can find the suggested solution (complete with working) in the GoogleSite
(Maths > S1-01 > Unit 04 Algebra)

3. You did Summative Quiz 2
You can find the suggested solution in the GoogleSite (same section)

4. Preparation for lesson on Tuesday
We will be doing the SDL topic, "Rate, Speed and Ratio".
Do take a bit of time to go through Textbook Chapter 9 if you can.

5. Homework - Inequalities (II)
Below is the working for the example - take note of the presentation.
Your working should be similar - clear and systematic.

## Tuesday, 4 April 2017

Today's lesson focused on "Inequality".

We noted, in particular, the 2nd topical EU:
• The solution of an algebraic inequality may not be unique
and we saw these through examples (see the post below).

We also discussed Study Notes (p3) with arithmetic examples (see post below); and went through p5 of the notes (Example 1 & Exercise 1).

Assignments 81. and 8.2 are given.
Deadline: This FRIDAY (7 April 2017)

AceLearning Assignment is given.

The handout, "In Music, What Does "Allegro" Mean?" (courtesy of Mr Johari) was given.
Objective: For practice and to build up the speed to solve inequalities.

### Inequalities - An Introduction

I think of a number... er... some numbers....?

### Discussion: Equations VS InEqualities

Examine the pairs of working...
• Describe on similarities within each pair of working
• Describe the difference in the answers in each pair of the working

## Monday, 3 April 2017

### Inequalities - An Introduction

(1) What do these symbols mean?

(2) Making connection

Click HERE to see responses

(3) Checking Understanding

Number Sequence: An extension

Note that arithmetic progression is covered in the upper secondary syllabus.
As share in class, this is gently embedded in the topic, Number Sequence when we attempt to generalise patterns using algebraic formulae.

Source: http://keisan.casio.com/exec/system/1223465446
Click HERE to explore

Note: I did not touch on GP during the lesson.

Fibonacci Sequence
We briefly talked about the sequence (and the rabbits!)
You would find the following interesting:
• https://plus.maths.org/content/fibonacci-sequence-brief-introduction
• http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html

## Sunday, 2 April 2017

### [Have Fun] Have you started 'snacking'?

Dear S1-01

You received the following on Friday
(this was distributed to all S1 classes, under the EL Programme).

One of the cards is about financial mathematics - "Save for What you Want"
What's the difference between a "need" and "want"? How would you prioritise them? What are some examples of "needs" and "wants"?

Do you know you can create your own account digitally using a spreadsheet to keep track of your savings and expenditure? Try that out.

## Saturday, 1 April 2017

### Maths SASMO Preparation

Solving Simultaneous equations!
We discussed 2 methods - Elimination method and Substitution method.

Testing your eye powers! Are you able to explain where the misconceptions are for each of these working?

### 6 AM Quiz #06: Algebra or Numeric?

Suggested solution (posted on 2 April 2017)

### SASMO on 5 April 2017 (Wednesday)

Dear S1-01

This is a gentle reminder that the event is going to take place on upcoming Wednesday. Please make alternative arrangements for other appointments or events that happens at the same time, reason being there is NO make-up session for the competition (and there is NO refund if you miss the session).

Instructions (from Mr Chen Jinquan)
Date: 5 April, Wednesday
Time: 2:40pm - 4:30pm
Place: Auditorium
Special Instructions: No calculator allowed

• Writing materials, including PEN and 2B Pencil (or mechanical pencil with 2B lead)
As your last period lesson ends at 2 pm. please remind your teacher in the last period to dismiss the class on time so that you have ample time for lunch.

A calendar invite has been sent to you as a reminder for the event.

All the best :)

## Thursday, 30 March 2017

### Number Patterns & Sequence (Group work) - Submission Status

Group 1: both questions submitted (25 points)
Group 2: both questions submitted (25 points)
Group 3: both questions submitted (30 points)
Group 4: only Q4 submitted (10 points)

## Wednesday, 29 March 2017

### [Menu] 28 & 29 March 2017

28 March 2017 (Tuesday)

(A) During the lesson...
• We made an attempt to link the Pascal Triangle with the expansion of (a + 1)^n
• Coefficients
• You were briefly introduced to the Binomial Expansion (see an earlier post below)
• Simplified version: (a + 1)^n and (a + b)^n
• Note that Binomial Expansion/ Theorem are not tested in Sec 1 (S3 Add Maths syllabus). It is, nevertheless, good to be aware the existence of such theorem that would be very useful when we have to handle expansion of (a + b)^n when n is large.
• Counting strategies
• Multiplication Principle
• Arrangement Principle
• The use of diagrams to organise information to aid visualisation
(B) After lesson (SASMO Preparation)...
• Simultaneous Equations

29 March 2017 (Wednesday)

Number patterns and sequence (Divide and Conquer)

• Group work where each group is divided into two teams to tackle a pair of questions.
• There are two deliverables to be posted in the Google Classroom as a new post.
Complete the remaining 7 questions.
One of the questions will be used as the Summative Assessment Question in lesson on Monday (3 April 2017)

THINGS to bring on THURSDAY: Submit your MATHS File - line them up on the cupboard top.
Hao Min will note down those who have not submitted by tomorrow 3.30 pm, and email to me.

## Tuesday, 28 March 2017

### Linking Pascal Triangle to Binomial Expansion

You can generate the Pascal Triangle in a systematic manner.

After note: Can you spot the error in the above (clue: Check the last 2 lines)

Now, attempt to make a connection between the patterns generated in the Pascal Triangle with the following:

What do you notice?

Can you generalise this pattern?

## Thursday, 23 March 2017

### Speeding up with Algebraic Pizzaz!

All of you would have received the "Pizzazz!"
(courtesy of Mr Johari)

How is this "pizza" going to be useful to you?
By now, you should be pretty familiar with the skills taught for the topic (hence, the mastery).
The key now is your processing speed!

Let's see who's the first to get the pizza delivered!
You may collaborate as a group....  The form will be available in this same post end of today :)

## Wednesday, 22 March 2017

Today's Class Discussion:

1. Word Problems:

I think of a number (n) ...
The product of 2 numbers is 154. If the difference between the two numbers is 3, find the possible values of n
Skill needed:
> Form an equation (you will get a quadratic equation here)
> Reorganise the terms to LHS of the equation
> Factorisation
> Find possible values of n by solving linear equations.
(Source: Mathematics Workbook 2 (p37))

Area of rectangle
What is the area of the small rectangle if the perimeter of the large rectangle is 64 m?

We also discussed, based on context, value of n must be larger than 3 (refer to the dimension given).

2. Finding values of expression

We discussed the following (and the strategy to solve such problem) in class:

1. 2013 S1 Maths Common Test Question 6

2.

3.

3. Formulae

In relation to the formula, Speed = Distance / Time
We spent some time to understand the difference between distance and displacement; speed and velocity.
Reference: Handout Q1

We also discussed the use of Heron's formula to find the area of a triangle when given 3 sides of a triangle.
Reference: Handout Q4

4. Homework

1. Complete the handout on Algebra - Formulae
- Four problems that require us to substitute before solving equations.
Deadline: 23 March 2017 (Thursday) - to be submitted in the Maths Tray on the Teachers' Table

2. 2013 S1 Maths Common Test Question Paper
- Attempt the paper for discussion on next Monday (next lesson), except last question

3. Bring along SASMO paper (equations) on Monday for discussion.

## Tuesday, 21 March 2017

### Homework 21 March 2017

Mathematics Textbook 1 (7th edition)
Chapter 5: Linear Equations and Simple Inequalities

Exercise 5A (p119)
Attempt the questions circled on writing papers.
Copy the question (i.e. the equation given) and solve systematically.

Deadline: To be submitted on 22 March 2017 (Wednesday)
Estimated duration: 40 minutes

## Monday, 20 March 2017

### [Menu] 20 March 2017 Monday

Scope of today's lesson:

1. In the course of solving the equation,   3(1 + 2x) - (5 + x) = 10 + x

we recapped:
• Expansion, Distributive Law
• Vocabulary: Like Terms, Constant, Coefficient
• Concept: Balancing equation

2. With a quadratic equation, we will move all the terms to the LHS of the equation to see if it is possible to factorise the terms.
E.g. Solve x^2 = 81
By moving the terms to the LHS of the equation and factorising them,
we get (x + 9)(x - 9) = 0
By reasoning, the equation is valid when (x + 9) or (x - 9) is zero.
Hence, rewrite as
x + 9 = 0 and x - 9 = 0
From there, we solve to get x = -9 or x = 9.

3. Study Notes for Equations is given.
• Discussion of Example 1 (p4) - selected questions
• Discussion of Class Work 2 (p5) - selected questions

4. Homework
• Class Work 2 (p5) - Remaining questions - to be completed as Homework (Review), as instructed in the Google Classroom [estimated duration: 10 min]
[Flipped Learning]
• Class Work 4 (p9) has been assigned as a Homework (Diagnostic) - attempt as instructed.
• Watch the following video clips (It's a playlist with 5 examples) [estimated duration: 30 min]

[New!] Factorial

1! = 1
2! = 1 x 2
8! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8

Hence, if we have 9! / 9!, we will get 1
If we have 9! / 8!, we will get 9
If we have 9! / 10!, we will get 1/100 or 0.01

Using the above, attempt the following without the use of calculator

### MA-Quizzzzz... (1) Factorial

Your first encounter with "Factorial" is the SASMO worksheet on Factorisation, HCF and LCM. Here's another one.

### Algebra: Challenging Questions 3 & 4

Note: The Questions were given on 8 March 2017 (Term 1)
The post has been shifted up to 20 March 2017 for discussion.

## Friday, 17 March 2017

### Mathematics in Handicraft: Corner Bookmarks

Do you notice that the link between basic Geometrical Shapes and Origami?
Can you tell what are the angle properties that are commonly used in origami?

Going deeper: Linking Mathematics and Physics... through Origami

## Tuesday, 14 March 2017

### Let's celebrate 3.14!

It's PI π Day 3.14

(extracted from http://www.piday.org/)
Pi Day is celebrated on March 14th (3/14) around the world. Pi (Greek letter “π”) is the symbol used in mathematics to represent a constant — the ratio of the circumference of a circle to its diameter — which is approximately 3.14159.

Pi has been calculated to over one trillion digits beyond its decimal point. As an irrational and transcendental number, it will continue infinitely without repetition or pattern. While only a handful of digits are needed for typical calculations, Pi’s infinite nature makes it a fun challenge to memorize, and to computationally calculate more and more digits.

(source: https://time.is/pi_day)

## Monday, 13 March 2017

### Linking logical reasoning with Algebra!

Did you notice that ..... many puzzles that you seem to be able to solve using 'common sense' or by logical reasoning could be solved by applying basic principles in Algebra?
You have learnt how to solve simple equations and will be introduced to "simultaneous" equations soon...
Let's start exploring...

Note: You may want to register with brilliant.org to get your regular doses to puzzles

## Saturday, 11 March 2017

### Mathematics in Handicraft: DIY boxes

Watch the video clip carefully.
To create the box, we need two sheets of papers.

The one of the dimensions of the first sheet was given in the diagram.

However, the dimension of the 2nd sheet was not given.

How would you describe the dimensions in the 2nd sheet (yellow) so that one can follow to draw the lines and construct the box easily?
Hint: You may introduce a variable x for one of the missing info in the 1st sheet (pink).

## Friday, 10 March 2017

### It's Game time! Having Fun with Equations

Remember to Post the screenshot of the score to the Group Padlet.
You can put up the best score - Try this during the school holidays!

Preparation for the GAME:
• Writing Papers, Pencil/ Pen
• Calculator
Do a Screenshot of your final score and post it to the Padlet that belongs to your group.
This is going to contribute to your Group Score.