Question 1 by Chio Jia Le

Question 1: 

Read through the conversation between a mentor and a student. 

Mentor: Does anyone recall or know what we call it when 2 lines run side-by-side and never cross?

Student: Yes. Lines like that are called parallel lines.

Mentor: Great! We've already learned that quadrilaterals have how many sides? 

Student: Four.

Mentor: That's right and we call quadrilaterals with parallel sides parallelograms.

Student: But, how can all the sides be parallel if a quadrilateral is a polygon and is all closed off? 

Mentor: Great thinking! I guess what I should have said is that a parallelogram has two pairs of opposite sides that are parallel, like this:

Student: Oh, so the top is parallel to the bottom and the sides are parallel to each other. I understand now!

Mentor: Good. Now I want to tell you about a special kind of parallelogram. It's called a rhombus. A rhombus is a parallelogram, but all four sides have the same length.

Student: So a rhombus is a type of parallelogram just like a banana is a type of fruit.

Mentor: Right, we should not say that all parallelograms are rhombi, just like we don't say that all fruits are bananas.

   

Question for discussion 

Based on the above conversation discuss, with examples and justification whether the following statement is justified:

'A square is a rhombus but a rhombus is not a square'.

ANSWER: A square has all the rhombus' properties while the rhombus do not have all of the square's property. For example, a square's adjacent sides are perpendicular to each other while the rhombus' are not perpendicular. Another property is that the length of diagonals of the square are equal but the rhombus' are not the same.

Activity 3-Proving Simple Geometrical Questions

1.'A square is a rhombus but a rhombus is not a square'.
Ans: It is true.

These are both rhombuses:

  +--------+
  |        |        +--------+
  |        |       /        /
   |        |      /        /
  |        |     /        /
  +--------+    +--------+

But only this is a square:

  +--------+
  |        |
  |        |
  |        |
  |        |
  +--------+
 

2.Which of the given statements is correct? Justify your answer/s with examples.

A ) A square and a parallelogram are quadrilaterals.

B ) Opposite sides of a square and a parallelogram are parallel.

C ) A trapezoid has one pair of parallel sides.

D ) All the above

Ans: D. Quadrilaterals means four sides and a square and a parallelogram have four sides. Since their opposite angles are equal, thus the sides of a square and a parallelogram are equal. Yes, a trapezoid has one pair of parallel side as shown in the picture below.

 

4. 'All parallelograms are squares?' Do you agree with this statement?

Justify your answer with example/s.

Ans: I agree with the statement.The interior angles of a parallelogram aren't necessarily 90 degrees. All fours side are not necessarily equal in a parallelogram.

elearning 2010 : Everyday Quadrilaterals

posted by Mr Johari
Learning Objective (Activity 2)

In this learning activity, you will demonstrate your understanding of the properties quadrilateral by identifying objects around us that exhibit these shapes.

Instructions

1. Choose 2 out of the 3 special quadrilaterals - parallelogram, trapezium and kite.
2. Find objects at home that exhibit the shape of these 2 selected quadrilaterals.
3. Take a photo of each object and post them on the Wall Wisher at the class Maths blog

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)