Thursday, 19 October 2017

Closure... My Maths Classroom

Direct LINK to the survey

[Updated: 21 October 2017]
Click HERE to learn what your classmates shared about their learning experiences in the class :)

Responses to selected questions will be shared via the Google Classroom after today.
You will receive an email alert when it is 'delivered' :)

Saturday, 7 October 2017

Revision: SST 2016 Maths S1 Paper 2 Q4b

There are 2 ways to find xy :

Method 1: (as shown in the suggested solution document, in GoogleSite)
It uses the special products (or algebraic identities) to solve.
Note that we did not need to find x or y value in this method.

Method 2:

In this method, we attempt to solve 2 simple simultaneous equations to find out the values of x and y.
With this, we find xy.

Some of you actually use "Guess and Check" method, where you try to list down possible pairs of integers that can be add together to give 7, followed by check using the other equation. 
Do NOT use this method as it opens up many possibilities which would not worth the time to check one by one.

Revision: SST 2016 Maths S1 Paper 2 Q6

One strategy to solve this problem is to write down and organise the information available.
From there, try to pull the information together to form an equation to solve for the unknowns.

Revision: SST 2016 Maths S1 Paper 2 Q7

Given the speed of the following:

  • Adam     160 m/min
  • Bernard     120 m/min

Strategy: Put all information in a diagram and draw 'relationships' (with reference to the speed-time-distance formula) to form equations

Since we do not know the distance for the race, let it be d metres.
Since we are not given the time taken by Adam to complete the race, let the time taken be t minutes.
The 2nd diagram shows the position of Adam, Bernard and Charlie at t minutes.
Hence, what's common for all three boys is the duration, t minutes.

Using the formula, Distance = Speed x Time

With this, we know that distance covered by Charlie (at t min) = 800 m - 250 m = 550

Substitute d = 550 into first equation (i.e. time taken by Adam), we have
Time taken, t = 800 ÷ 150 = 5 minutes

Hence, Charlie's speed
= Distance covered/ Time taken
= 550 m ÷ 5 min 
= 110 m/min     (Ans)

Note: There are other 'shortcuts' to solve the problem. However, the above will give you an idea how to solve the unknown(s) systematically using the known relationships for speed-time-distance.

Revision: SST 2016 Maths S1 Paper 2 Q8

Watch the video clip (no sound) to understand the diagram

(i) Since the length of the paper is 30 cm, from the diagram, we note that
Height of letter in terms of x = 30 - x - x     cm, which is same as 30 - 2x    cm

(ii) Given the ratio Height : Width = 8 : 5
Since we can express the height of the letter in terms of x, we shall try to express the width of the letter in terms of x, too.

Refer to the line (in orange), width = 3 + x     cm

Now, with these information, we use the ratio to form the equation and use it to find x:

(iii) To find the perimeter of the letter, we need to find the (marked out in the diagram)

Saturday, 30 September 2017

6 AM Quiz #13: A & A

Click HERE To attempt the Quiz.
  • Click HERE to view responses
Answer scoreBonus score
Q3(ii) optional21

Quick reference to the Questions

Suggested Solution (updated: 3 October 2017)

It's Mensuration! It's Geometry! It's Amazing!

Friday, 29 September 2017

T4W3 Revision (29 Sep) - Algebra

This week, we made reference to the questions in the past year exam papers (of other schools) for our revision practices.

On Friday, we started revision on Algebra and discussed questions that are not found in these papers.
Below is the complete solution that we had discussed during our lesson on 29 Sep (Friday). Do take note of the presentation of the working.

As mentioned in class, this was a higher order thinking question because I had removed the 'scaffolds' (i.e. smaller parts leading to the final answer).

However, to tackle such question, always link to what you are already familiar with, then apply them - along the way, you will find yourself working on something similar to the required form.

While this is pitched as a S2 question, you can apply knowledge and skills in Mensuration (area of circle and square) and Algebra (forming equation, factorisation, re-organising the terms), and basic reasoning to solve the problem.

These questions merely help us to recall the basics of algebra.

1st question:
We need to be cautious of the substitution

2nd question: 
Manage the 3 terms like you are managing numerical fractions!
Find the common denominator, and do not forget the brackets when 'combining' the terms.

3rd question: Remember that ratio can be expressed as a fraction.
Note that it's always good to find x/y term before finding what is required.

Mentioned in class, there's more than one way to do (i).
I've presented 3 ways below how to show LHS of equation = RHS of equation.
We also spoke about NOT using any numbers to do the "shown" question.
Remember  that "hence" means make use of what is given in (i) to do (ii)

Last, but not least, we discussed this question that requires us to solve the unknowns by comparing terms

Saturday, 23 September 2017

6 AM Quiz #12: Long time no see, Algebra!

Click at the LINK to submit your answers.

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

Question 1

Question 2

Question 3

Click HERE to view responses.

Solution submitted by some of you....

Question 1 (by Zuhairi)
- by expressing ratios as fractions, hence reorganising the terms in an equation.

Question 1 (by Hafiz) 
- by solving simultaneous equations

Question 2 (by Christabel)
Simplify the RHS, that resulted both sides of equation having the same base "9'.
Then solve for k by comparing the "powers" (i.e. the index) of "9".

Question 3 (by Hao Min)
- by expanding the two factors (did you notice the 'skipped' step from line 2 to line 3?
Finally, since the base for both LHS and RHS of the equation is "2", we can solve by comparing the 'powers' to solve for x

Question 3 (by Zun Kye)
- notice that he spotted that the terms in the 2nd factor could be simplified first?

Thursday, 21 September 2017

21 Sep 2017: What we did today...

Focus of Revision on POLYONS
  • Key ideas
    • Naming polygons (up to 10 sides)
    • Revisited the formula and how to derive them, as well as the relationship: 
      • Sum of interior angles of a polygon = (n - 2) x 180º (using a pentagon to help us visualise)
      • Sum of exterior angles of a polygon is always 360º (using an equilateral triangle and square to help us visualise)
      • Interior angle + Exterior angle = 180º 
        • When one increases, the other decreases
    • How to deal with polygons of unusual shapes
  • Discussion (1) with the following papers:
    • HIHS 2017 S2 Mid-Year Exam Paper 2 Q9
    • CGS 2015 S2 Mid-Year Exam Section B Q3
    • FMS 2015 S1 EOY Exam Paper 1 Q11
    • NYGHS 2015 S1 EOY Exam Paper 2 Q5
  • Discussion (2) with handout WJEC CBAC GCSE papers 
Solution presented by Corwin

  • Note that, when the context is defined here, that we know that n must be an integer (since it represents the number of sides of a polygon), we may leave out defining n is an integer. However, when without context, we should define n when constructing the inequality. (with inputs with Ethan)

Next week (T4W3), we will move into the following topics:
  • Mensuration (Perimeter, Area, Volume), which involves simple algebra
  • Linear Graphs, Sketching
  • Algebra
  • Construction will be kept to the last week of the revision

Do attempt the other schools' exam papers to prepare for the upcoming topics.

Monday, 18 September 2017

Direct Proportion (1) Check-in (2) 3-min Quiz

Click HERE for direct link

Click HERE to view responses

3-min Quiz
Click HERE for direct link

Click HERE to view responses

Thursday, 7 September 2017

The 'magic' can be explained with...

Source: Facebook page: 5 Unknown Facts

There seems to be some 'magical' links between the digits... however, if you apply algebra (i.e. factorisation), you would be able to figure out why or how the magic works :)

Tuesday, 29 August 2017

Something more, something extra: Heron's Formula

This morning, we briefly talked about how to find area of a triangle in the absence of height, but when all three sides are given.

We can apply Heron's formula to find the area.
You would probably find the following sites interesting:

Monday, 28 August 2017

Mensuration: Transformation - from 2d to 3D

Question to be solved

What we learnt on 29 Aug 2017

Mensuration: Volume of Cone and Pyramid

The volume of a cone fills up one-third of the volume of cylinder, i.e. we need three cones to fill up a cylinder.



Saturday, 26 August 2017

6 AM Quiz: It's an Equation? It's a Line? It's Algebra!!!

Click HERE for direct link

Click HERE to view responses
Group score:

  • Group 1: 3 points
  • Group 2: 5 points
  • Group 3: -
  • Group 4: 17 points

Updated on 27 August 2017 (Sunday), 0830h

Thursday, 24 August 2017

Polygons: Who am I?

Click HERE for the direct link

Click HERE to view responses

Warming up: Area & Perimeter of Square-Rectangle

Click HERE for the direct link.

Click HERE to view responses.

Area of Parallelogram & Trapezium

Watch the following examples. Each comes with a question and the explanation on how to solve the problem.
1. Pause the question. Read the diagram carefully and think what formula would help you to solve for the unknown.
2. Think how you would solve the problem - you may need to write down an equation in order to solve for the unknown.
3. Next, continue to watch the clip and listen to the explanation. Is this similar to what you have thought of? Look out for the presentation of the working.

Area of Circle - explained through area of rectangle


Basic Geometry: How to present our working clearly? (II)

2015 S1 Maths Level Test 2 Question 5

Below illustrates different ways to present the working.

Wednesday, 23 August 2017

Basic Geometry: How to present our working clearly?

Suggested Presentation: 
  • Step-by-step working
  • At any one time, only one angle property to be cited
  • Lines may be extended or additional lines may be added, if necessary
  • Other angles (that are not labelled) can be labelled you need to make reference to them along the way (as part of the working).

You may label the angles and indicate the angle properties in the diagram. However, this must be clearly written.

However, you must not combine steps when presenting your working!
(although some of you process the steps very quickly)

When presenting your working in writing:
You must not cite more than one angle property for a single step.
You need to break down the steps, write the working clearly with any relevant angle property, if applicable.

Tuesday, 22 August 2017

Recap: Names of different types of Angles

Basic Geometry: Talking about Dimensions!

Click HERE to view

[Discussion] Which Property Applies?

Let's refer to Assignments 1 & 2, and study the working provided.
Are you able to identify the relevant angle properties to explain the working?

[Homework] 21 Aug: Basic Geometry

Part (I) Attempt the following via the GoogleForm by TODAY (22 August 2017)

Click HERE to access (2017 S1-01) Warming Up Question: Geometry (1)
<click HERE to view responses>

Click HERE to access (2017 S1-01) Warming Up Question: Geometry (2)
<click HERE to view responses>

Part (II) Submit the following assignments on THURSDAY (24 August 2017)
  • Assignment 1 - hardcopy (as discussed during lesson on 22 Aug)
  • Assignment 2 - hardcopy (as discussed during lesson on 22 Aug)

Optional: Challenging Questions

You may email a photo of your answers to me by the end of today (22 August 2017).

Remember to include clearly the Group Number.
Your responses will contribute to your group points.

Saturday, 5 August 2017

6 AM Quiz: What do they say?

Direct LINK
Click HERE to see the responses.

Direct LINK
Click HERE to see the responses.

Thursday, 3 August 2017

[Follow-up] Today's Lesson

Today, the lesson focused on deepening our understanding of median and mode through finding unknown values (of x). This is followed by a short discussion on Dot Diagram.

In the next lesson, we will move into stem-and-leaf diagram.

1. Self-Practice: Algebra - Factorisation Worksheet 1, 2 and 3
As promised, suggested answers have been uploaded to the GoogleSite

2. Practise Construction & Graphs (on your own) - you may refer to your textbook and workbook for questions

3. 6 AM Quiz is making a come-back this Saturday (starting from August).

4. Assignment 10.3
Deadline: 7 August 2017 (Monday)

5. Attempt the task in the next Blog Post (last date for submission: 12 August)
6. Google Classroom - 3 Questions
Attempt the questions if you have not done so (deadline: 3 August 2017, Thursday)

7. Stem-and-Leaf Diagram

  • Diagnostic Quiz on Stem-and-Leaf Diagram 
  • This is another opportunity to earn as much points for your group as possible through practice and making connection to real world :)
  • Complete before Monday arrives.

For those who owe homework, you need to clear the items as soon as possible as the accumulated tasks/ assignments are snowballing in an alarming rate.

How much do you know? .... Stem-and-Leaf Diagram

Click HERE to access the QUIZ to find out how much you now for Stem-and-Leaf Diagram.
Points will be contributed to the Group point.

Click HERE to view responses.

Wednesday, 2 August 2017

Data Handling: How are data communicated in Real World?

Statistical representations are widely used to 'simplify' or 'summarise' data when presented along with reports.

An example is the a recent report on the "Alarming rise in losses on consumer prepayments" (Straits Times, 1 August 2017). Look at the bar chart presented. Did you notice how huge amounts is presented on the vertical axis?

In these two weeks (3 to 12 August), you shall look out for examples of charts used in reports any of the following and share with the class how charts are used in our daily life.

It would be even better if you could spot charts do not present the data appropriately or are misleading; and tell us why it's not appropriate or misleading.
Any duplicated charts, regards who posted it first will not be counted in group points.

How points are awarded:
  • Chart: Appropriate OR Misleading [1 pt]; 
  • Description of what chart attempts to communicate [1 pt];
  • If it is a misleading chart - elaborate why it is misleading [1 pt]
  • Acknowledge source (URL of source) [1 pt]
Click HERE for direct link to padlet

Made with Padlet

Monday, 31 July 2017

Revisiting what we learnt...

Make a guess! 
 Enter your answer in "Comments"


Thursday, 27 July 2017

[Follow-up] Today's Lesson

Refer to the following posts for lessons conducted this week (Key Focus: Data Handling)

Things to complete - Compulsory

1. 2015 Level Test 2 Revision (Deadline: 31 July 2017)

2. Maths Blog activities (Deadline: 28 July 2017)
3. Google Classroom
  • Task 1: Data Handling (Deadline: 28 July)

  • Task 2: Linear Graphs (Deadline: 27 July)

[Homework 1] Quizzes: Bar Graph vs Histogram..... Dot Diagram

Complete the following by Saturday (29 July 2017, 12 noon)

(A) Click HERE to access Quiz 1: Histogram, Frequency Table, Mean-Median-Mode
  • Click HERE to view responses

(B) Click HERE to access Quiz 2: Dot Diagram
  • Click HERE to view responses

[Homework 2] Reporting Data in an Appropriate & Objective Manner

We looked at a few examples that illustrate how data, when not presented partially or appropriately might lead to strong reactions from the reader.

Discussion 1: Is the difference of the rate really that 'great'?
Source: The Straits Times (26 July 2017)

Discussion 2: 
1. What was the message the charge trying to convey?
2. What was misleading about the chart?
3. What could be done to make the information presented more objectively and appropriate?

Study Notes (p24) Misleading Information in Statistics

Note: You should have recorded your responses to the three questions in your study notes.

Task 1 (to be completed by Friday, 25 July)
Study Notes (p24)

Click HERE to open the padlet

Made with Padlet

Task 2 (to be completed by Friday, 25 July)
Study Notes (p25)

Click HERE to open the padlet

Made with Padlet