Graphing softwares (please follow up)

Hi 109ers,

Happy 45th National Day.

To update you on the happenings in SST Maths scene next 2 weeks.

Week 7

next week we will be having our e-learning lesson from Wednesday to Friday. Do check out the Maths activities on Geometry.

week 8

Ensure that you have NetLogo, TINspire and Geogebra working effectively in your learning device as we will be using them in week 8 for graphing purposes. Should you encounter any problems do inform the SST Apple Centre.

Video post (Solve the equation) by Hardy Shein Nyein Chan

This is a video production from Lee Si Yuan & Preston Ngoui on how to solve Equation (e)

ICT linear Equation

posted by Mr Johari

This activity is an introduction on function, algebraic equation involving x and y and graphical representation of linear equation.
Approach: Individual or pair work using ICT graphical tools (Grapher or Geogebra)
Resource: ICT Linear Equation worksheet.

Task 1

Complete the given worksheet
section 1, 2, 3 and 4 and answer the corresponding questions given.

In a nutshell:
A. section 1: general for y=a

observation: horizontal straight lines and parallel to each other. No slope and all lines pass through the y-axis according to given equation. eg. line of equation y=2 passes y-axis at 2. The lines do not meet (intercept).

B. section 2: general for x=b

observation: vertical straight lines and parallel to each other. since the lines are all vertical the slope cannot be defined (no value can be given). The lines pass through the x-axis according to the given equation. eg. line of equation x= 4 passes x-axis at 4.

C. section 3: general for y=mx + c, c=0

observation: diagonal straight lines (or lines at an angle) that all converge or meet at the origin (the point where the x-axis meets the y-axis). Henc

e c refers to the point where the lines meet the y-axis (in this case c=0). When m is negative the lines slope downwards (bottom left to top right) and when m is positive the lines slope upwards (top left to bottom right). m is also known as the slope or gradient (refer to geographical concept of slope / gradient of rise and run)

D. section 4: general for y=mx + c

observation: diagonal lines as in section3 but m remains the same (m=2) but the lines meet the y-axis at different values. all lines are parallel (because m=2) but intersect (meet) the y-axis according to the value of c. i.e. if y=2x+4 the slope is positive and the y-intercept (where it meets the y-axis) is at 2.

E. section 5: general for y=mx + cobservation: diagonal lines as in section3 but c remains the same (c=1). The lines have the same intersection point (i.e. meet the y-axis at y=3) but have different slope or gradient.

Conclusion

Task 2
Refer to the link on Graph (by GCSE Bitesize) to learn by graphical representation and plotting.

activity 1: learn about coordinate system

Leading questions for you to answer (post in your comment):

reference: Cartesian Plane and Descartes or intro to Cartesian Plane

1. what is a Cartesian Plane?
2. what is ordinate? abscissa? what is the significance of (x,y)
   
3. give an example of a practical use of coordinate system (provide links to examples)
4. a student was posed with the following problem 'A man Jim has twice the amount of money than his friend Lemin - present the above information as an equation in x and y and show a graphical representation of this equation'. show graphically how much will Lemin has if Jim has $4000.

Task 3

In the following task, you are required to use Geogebra.

You are provided with the graph of y against x.
A linear graph has been plotted with the equation unknown.
Please comment on the following:
(1) the shape of the graph
(2) the possible equation of this linear graph (other than y=2x)

Chapter 6: Algebra - Viva Voce

Chap 6 Algebra: Individual or Pair work Viva Voce
Posted by Nur Johari

Task 1: Algebraic Expansion - Self Revision (10 mins)
source: GCSE Bite-Maths and Maths notes
Individually do a quick

revision on algebraic expansion / simplification. The focus is on the step-by-step process in arriving at the eventual answer.
Note: You may refer to the link GCSE Bitesize:rearranging symbols or GCSE Bitesize: solving equations or the Maths notes.

Task 2: Peer Evaluation (10 mins)source: courtesy of S1-01

The following links show the work done by your friends on the topic algebraic expansion. They have created and posted a short videoclip to explain clearly how the following expression could be expanded.

(A1) 4m(7 + 3n)
(A2) 10 (6m² + 0.5m + 4)
(A3) (m + 2)(m + 5)
(A4) (3m + 2n)²

Individually select any ONE of the presentation, watch it and provide constructive criticism (to be uploaded as your personal comment). The constructive criticism could include the following:

.1 state how the explanation could be improved (eg. better video or audio presentation)

.2 state clarity of Mathematical concept (eg. the expansion is clearly shown)

.3 suggestions for improvement (eg. mathematical models could be used instead)

.4 include your name and class (this is about responsible citizenship)

Please choose any of the following students' work for your task: (click on their names for the link to their work)

• Zhi Qi & Joshua Ma
• Cheng Ngee & Su Lun
• Guang Jun & Bryan
• Su En & Shamemi
• Carisa and Pei Shan
• Zhi Chao & Soh Fan

Sample comments

Task 3: Individual / Pair Work (Algebraic Equation) (25 mins)

Individual or pair work. Create a short videoclip to explain clearly how you would solve ONE of the following equations.

Instructions
• Each clip should not be longer than 1 minute.
• Make sure your voice is clearly and distinctly captured.
• You may use PhotoBooth or QuickTime to complete the task - keeping in mind that the file size of the video clip should be as small as possible.
• Email your clip to Mr Johari at nurjohari@gmail.com and he will then review and upload your clip in the Maths blog. [you should complete the mathematical problem with step-by-step working and script during the given time]
• Remember to state the question as well as your name as your title of the post.

Reference (optional)
Sample video:

Linear Equation

Using GRAPHER, find out what kind of GRAPH will represent each of these EQUATIONS. Note, in this instance, you’ll only need to enter the LHS of each of these EQUATIONS to plot it’s graph.

What kind(s) of graphs are portrayed through these equations?

Expression and Equation

This is a continuation about algebra. We have covered definitions of the various terms used in algebra such as variables, like terms etc. We discussed about fundamental concepts and differences between expressions and equations.

Task 1:

In this task review the view clip again on how ' x finds out his value'.

Go through the site Study Guides and Strategies and attempt the following questions.

1. What is the difference between an equation and an expression?
2. What are the characteristics of a linear expression?
3. What does it mean to solve an equation?
4. Can an equation have multiple solutions?

Task 3:

Solve the following equations for the value/s of x.

1. 8x - 46 = 2
2. 8x + 46 = 2
3. -8x +46 = 2
4. 8x + 46 = 46
5. 8x + 46 = 8x

1. What is the significance of the solutions of the above equations?
2. Can an equation have multiple solutions or no solution? If so, what is the implication.