We made an attempt to link the Pascal Triangle with the expansion of (a + 1)^n
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.
The use of diagrams to organise information to aid visualisation
(B) After lesson (SASMO Preparation)...
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.
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
> 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
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
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.
1. In the course of solving the equation, 3(1 + 2x) - (5 + x) = 10 + x
(with answer, x = 3)
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
Class Work 2 (p5) - Remaining questions - to be completed as Homework (Review), as instructed in the Google Classroom [estimated duration: 10 min]
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
(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.
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).
3. (Incidental learning) We explored how sine, cosine and tangent functions look like.
Study Notes: p20 Challenge Yourself Q2
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
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
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
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:
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.
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)