Group 2: both questions submitted (25 points)

Group 3: both questions submitted (30 points)

Group 4: only Q4 submitted (10 points)

- Home
- Mathematical Framework
- Habits of Mind
- Strategies
- To do well...
- Scheme of Work
- Assessment
- ICT in action
- I have a question...
- Resource: Unit 2 Real Numbers
- Resource: Unit 3 Significant Figures
- Resource: Unit 4 Algebra (1)
- Resource: Unit 4 Algebra (2)
- Resource: Unit 4 Algebra (3)
- Fun with Construction
- Looking Back... Looking Forward
- Fun Pack (2) Let's be a Geometrical Artist!

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)

(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

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.

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?

(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 :)

Today's Class Discussion:

**1. Word Problems: **

**I think of a number (n) ...**
__Skill needed__:

**Area of rectangle**

**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.

The product of 2 numbers is 154. If the difference between the two numbers is 3, find the possible values of n

> 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))

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

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

1. 2013 S1 Maths Common Test Question 6

2.

3.

In relation to the formula, Speed = Distance / Time

We spent some time to understand the difference between distance and displacement; speed and velocity.

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

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.

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

Chapter 5: Linear Equations and Simple Inequalities

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

Scope of today's lesson:

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

(with answer, x = 3)

we recapped:

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.

4. Homework

*[New!] Factorial*

We spent about 10 minutes to discuss what factorial is about...

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

1. In the course of

(with answer, x = 3)

we recapped:

- Expansion, Distributive Law
- Vocabulary: Like Terms, Constant, Coefficient
- Concept: Balancing equation

2. With a

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]

We spent about 10 minutes to discuss what factorial is about...

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

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

Click HERE to see responses

**Suggested answer**

Click HERE to see responses

Note: The Questions were given on 8 March 2017 (Term 1)

The post has been shifted up to 20 March 2017 for discussion.

The post has been shifted up to 20 March 2017 for discussion.

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*

Can you tell what are the angle properties that are commonly used in origami?

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)

Read on:

*Note: Do you notice something "un-usual" about this post?*

(extracted from http://www.piday.org/)

(source: https://time.is/pi_day)

Read on:

- Can you solve it? Pi Day puzzles that will leave you pie-eyed
- March 14 is Pi Day: 14 things to know about the irrational number

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...

Click HERE to access the puzzles!

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

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).

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

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!

**Writing Papers, Pencil/ Pen****Calculator**

What we did...

1. Factorisation by grouping - we reviewed the method/ skill with 4 questions (including a question you did in the Google Classroom).

2. We also applied factorisation to evaluate arithmetic expressions.

Watch the clips in the playlist:

3. (Incidental learning) We explored how*sine, cosine *and *tangent functions *look like.

Study Notes: p20 Challenge Yourself Q2

Homework

1. Prepare for the next lesson by reading the posts in the blog

2. Attempt "Spot the Error" worksheet (finish up Q3 & Q4) for discussion in next lesson

3. Optional: Attempt Algebra Challenging Questions 3 & 4

1. Factorisation by grouping - we reviewed the method/ skill with 4 questions (including a question you did in the Google Classroom).

2. We also applied factorisation to evaluate arithmetic expressions.

Watch the clips in the playlist:

3. (Incidental learning) We explored how

Study Notes: p20 Challenge Yourself Q2

Homework

1. Prepare for the next lesson by reading the posts in the blog

2. Attempt "Spot the Error" worksheet (finish up Q3 & Q4) for discussion in next lesson

3. Optional: Attempt Algebra Challenging Questions 3 & 4

For most of us, we look at the diagram and would be able to tell the answer.

However, how often have we thought how our brain processes this?

Source: brilliant.org

However, how often have we thought how our brain processes this?

Source: brilliant.org

The topic, Equation, is built on Algebra.

**Key Ideas **

Formulae are meaningful equations.

Equations/ formulae describes relationship between variables (which we will look in greater depth).

We will learn techniques to solve equations (i.e. to find out the unknown variables, usually denoted by*x*). That is where we carry out the **balancing act **(i.e. to balance the equation through addition/ subtraction/ multiplication/ division).

**Let's access the Health Promotion Board website to use the ****BMI Calculator**

*Source: Health Promotion Board, Singapore website (http://www.hpb.gov.sg/)*

Formulae are meaningful equations.

Equations/ formulae describes relationship between variables (which we will look in greater depth).

We will learn techniques to solve equations (i.e. to find out the unknown variables, usually denoted by

Do take some time to watch the video clips to see if the notion of balancing equation (concept) is clear to you.

You will be hearing words like "balancing", "add/ subtract to both sides", "multiply/ divide both sides by".

From now, we shall refrain from using words like layman operations like "moving", "cancelling", "changing the sign"

Basic concepts of Balancing Equations

E.g. 1: Solve*x* + 35 = - 20

E.g. 2: Solve**5 ***x* = 935

E.g. 3: Solve**9***x* - 8 = 73

You will be hearing words like "balancing", "add/ subtract to both sides", "multiply/ divide both sides by".

From now, we shall refrain from using words like layman operations like "moving", "cancelling", "changing the sign"

Basic concepts of Balancing Equations

E.g. 1: Solve

E.g. 2: Solve

E.g. 3: Solve

This morning, we received our Level Test 1 papers. How well did the class do?

Well... how "well" is "well"? It's vague.

To add clarity, we use 3 measures to help us interpret data - Mode, Median and Mean

(a topic that we'll do into greater details in Term 2/3).

Using this example (before we look into the class data), we learnt how to interpret the table**(**known as the **frequency table) **and draw out what is the mode, median from the table. Mean is what we referred to as "average" in primary school.

Simply put across:

With the above knowledge, given the TOTAL Grade Score,

Well... how "well" is "well"? It's vague.

To add clarity, we use 3 measures to help us interpret data - Mode, Median and Mean

(a topic that we'll do into greater details in Term 2/3).

Using this example (before we look into the class data), we learnt how to interpret the table

Simply put across:

**Mode**: The most frequently occurred item**Median**: The value of the middle item- The items have to be arranged in ascending/ descending order (of the values it carries)
- If there are odd number of items, e.g. 13, then the middle item is at the 7th position (6 before and 6 after this item). The value of the 7th position item is the median.
- If there are even number of items, e.g. 20, then the items would be divided into 2 equal halves. So, we find the average of the value in the 10th and 11th position.
**Mean**: Same as the "average" we learnt in primary school- Find the sum of all the values of the items, then divide by the number of items.

With the above knowledge, given the TOTAL Grade Score,

- we can find out the mean subject grade of the class
- we are able to find the maximum (i.e. the largest possible) number of students who can score Grade 1
- we can find, if everybody scored either A1 or A2, what is the number of students who scored A1 or A2

How many ways can our mind think when trying to answer this question:

Let's hear what Jo Boaler, professor of mathematics education at Stanford, says...

Pay attention from 3:23 onwards

Some of us might be amazed when Jo Boaler said our mind grows when we make mistakes!

Well, keep in mind that our mind grows when we realised that we make mistakes and struggle to figure out what has gone wrong and explore how to reconnect and make sense of our prior knowledge and experiences when we seek to understand find the solution.

Let's hear what Jo Boaler, professor of mathematics education at Stanford, says...

Pay attention from 3:23 onwards

Some of us might be amazed when Jo Boaler said our mind grows when we make mistakes!

Well, keep in mind that our mind grows when we realised that we make mistakes and struggle to figure out what has gone wrong and explore how to reconnect and make sense of our prior knowledge and experiences when we seek to understand find the solution.

What we did today:

- Went through 2-to-3 Activity for Factorisation (Special Product & Cross Method)
- Introduction to
**Factorisation by Grouping**

Look out for review questions & diagnostic questions coming from the Google Classroom

There will be 6 AM Quiz tomorrow morning (4 March 2017)

Remember to refer to the resources at: Maths Blog Tab: Resource: Unit 4 Algebra (3)

Homework Set A

To be submitted on next Tuesday (7 March 2017)

2-to-3 Activity on S1 Mathematics: Algebra - Factorisation (by Special Product)

- we discussed some of the questions and clarify the doubts during lesson today.

You may find the suggested solution in the GoogleSite - to check your working.

Homework Set B

To be submitted on next Tuesday (7 March 2017)

Attempt the following questions in WRITING Papers (foolscap)

Copy question. Remember to show your working neatly. Write clearly.

Do**NOT** divide the page into 2.

On top of the page, write down:

Mathematics Textbook 2

Chapter 3 (p94) Review Questions

Topic: Factorisation using Cross Method

Q3 (a)(b)(c)(d) Q4 (a)(b)(c)(d)

Mathematics Workbook 2

Chapter 4 (p28) Review Questions

Topic: Factorisation using Special Product

Q33 (b)(d)(h)(p)

You may try the remaining questions on your own.

To be submitted on next Tuesday (7 March 2017)

2-to-3 Activity on S1 Mathematics: Algebra - Factorisation (by Special Product)

- we discussed some of the questions and clarify the doubts during lesson today.

You may find the suggested solution in the GoogleSite - to check your working.

Homework Set B

To be submitted on next Tuesday (7 March 2017)

Attempt the following questions in WRITING Papers (foolscap)

Copy question. Remember to show your working neatly. Write clearly.

Do

On top of the page, write down:

Mathematics Textbook 2

Chapter 3 (p94) Review Questions

Topic: Factorisation using Cross Method

Q3 (a)(b)(c)(d) Q4 (a)(b)(c)(d)

Mathematics Workbook 2

Chapter 4 (p28) Review Questions

Topic: Factorisation using Special Product

Q33 (b)(d)(h)(p)

You may try the remaining questions on your own.

What we did in class:

- Revision:
- Discussion of selected questions of Mock Test 2 question paper (Y2016 S1 Maths Level Test 1) - on the presentation of working (being clear and systematic) and to clarify doubts
- Went through briefly Homework (Workbook) for Unit 02
- Answered enquiries
- All suggested solution are available in the GoogleSite

**(Continue with) Factorisation by Cross Method**- A systematic approach - recognising the pairs of factors required to be placed in the 'cross frame' to test out the numbers
- How to check if the factors are correct
- Method 1: Using the "middle" terms (multiplying the terms in the column)
- Method 2: By expansion
- [Homework] A 2-to-3 Activity was issued out - You should be able to answer all the Type A questions. You should also be able to answer most of the remaining questions.
__Note__: Typoerror in Collection 5, Type B question. Replace the variable "a" by "x". There should be only 1 variable in this quadratic expression.- We will discuss this worksheet on Friday's lesson

As mentioned, taking into account you spending time to prepare for this week's level test:

- Deadline for the submission of the SDL topic, Percentages have been postponed to next Monday (6 March 2017)
- No Google Classroom activities will be assigned these 2 days

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