similar solids

Practice makes perfect

Notes
source: http://www.glencoe.com/sec/math/prealg/prealg03/study_guide/pdfs/prealg_pssg_G095.pdf

Essential Formulae 

Activities
Click on diagrams below and attempt the questions that follows:
Activity 1:  Similar solids (click here to start)

Activity 2: Volume and Surface area of Similar solids (click here to start)

Activity 3: Perimeter, Area and Volume: Changes in scale (click here to start)

Similar solid

Trigonometry Summary

Trigonometry

Covert Footwork Competition

Are you creative? Love problem solving and intrigue by logical thinking problems. Participate in Covert Footwork Competition below. To participate complete the form attached.

Part 1: By Boon Pin, Sylvia, Esther, Yoshiki and Gavin

Part 1:

The flag pole is estimated to be of 4.8 m and the degree of accuracy is not measured. 

Activity 1: Using Ratios (Done by Adil, Yu Tao and Jonathan)

According to visual perceptions, the three of us have derived with a flag post ratio of 1:3:9. This is because the flag pole has three segments. The shortest one, being the one at the bottom, has a height of 50.5cm. Using perspective as a form of estimation, we estimated the flag poles to be split into 3 heights of 3 times the height of the segment below it. Therefore, the ratio 1:3:9 was achieved. Taking one unit and multiplying it by the total of the number of units of the segments, a total of the height 656.5. We feel that the result was quite accurate and it does make sense in our check in terms of perspective.

About Pythagoras ...

Video 1 (About the Man)

Video 2 (Proof)



Video 3

So What do you think about Pythagoras? Post comment about the Man, his contributions or the Pythagoras Theorem

Trigonometry Activity 2

Group Activity 2

Post your solution as comments

Trigonometry Activity 1

Group Activity 1

Post your solution as comments

Similarity and Congruency - Answer Key

answer key courtesy of Mr YU Yoong Kheong (MOE/ETD)

Congruency

If one shape can become another using Turns, Flips and/or Slides, then the two shapes are called Congruent:

On-Line Quiz 

Please click here.

source: http://www.mathsisfun.com/geometry

Standard Form

Multitude of sizes

following the post by Kat Yong Jie.

Secret Worlds: The Universe Within

View the Milky Way at 10 million light years from the Earth. Then move through space towards the Earth in successive orders of magnitude until you reach a tall oak tree just outside the buildings of the National High Magnetic Field Laboratory in Tallahassee, Florida. After that, begin to move from the actual size of a leaf into a microscopic world that reveals leaf cell walls, the cell nucleus, chromatin, DNA and finally, into the subatomic universe of electrons and protons.

Click here to see the transformation.

Index Notation and The Powers of 10

sources:
wikipedia
http://www.contracosta.edu
Powers of Ten™ (1977)

Powers of ten in real life

I loved this video, watched it long ago, and since we are learning Standard Form, this will be a good video.

Standard Form

What is Standard Form?

Practical Use

Scientific notation is the way that scientists easily handle very large numbers or very small numbers. For example, instead of writing 0.0000000056, we write 5.6 x 10^-9. 

Click here for fundamental concept and worked examples

------------------------------------------------------------------------Operation

Multiplication or Subtraction

Watch the following video and review the example on page 25 and 26.

Reference: Maths Notes

------------------------------------------------------------------------
Addition and Subtraction



Reference: Maths Notes

Self Reflection Term 2

Please complete the following e-Self Reflection. The key objective is to assist you in building your competency as wellas mastery of the subject. Thank you.

Pythagoras Solution

Level Test 2 Answer Key

Pythagoras Theorem

Topic: 
Pythagoras Theorem


Syllabus:

·       Identify a right-angled triangle and its hypotenuse.

·       Define the Pythagoras’ theorem and understand its symbols.

·       Find the unknown side of a right-angled triangle when the other two sides are given.

·       Solve problems involving right-angled triangles with Pythagoras’ theorem.

·       Determining whether a triangle is right-angled given the lengths of 3 sides.

Who is Pythagoras?

Pythagoras (569-500 B.C.E.) was born on the island of Samos in Greece, and did much traveling through Egypt, learning, among other things, mathematics. Not much more is known of his early years. Pythagoras gained his famous status by founding a group, the Brotherhood of Pythagoreans, which was devoted to the study of mathematics. The group was almost cult-like in that it had symbols, rituals and prayers. In addition, Pythagoras believed that "Number rules the universe,"and the Pythagoreans gave numerical values to many objects and ideas. These numerical values, in turn, were endowed with mystical and spiritual qualities.

What's Pythagoras Theorem?

Pythagoras' theorem states that in any right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

click here on proof and other facts on Pythagoras

What’s a Right Angled triangle?

A right angled triangle has a right angle of 90° as one of its interior angles. In the image here the right angle is marked with the white square.

Any triangle like this is a right angled triangle, it doesn't matter which side the right angle is on or what size the triangle is - the rule applies to all of them.

What’s the Hypotenuse?

According to some sources the word hypotenuse derives from the Greek words for hypo (under) and teinein (stretch) or tenuse (side).

The hypotenuse is the longest side of a right angled triangle. As you can see, the hypotenuse is the side marked in purple on the image above.

What are the other two sides?

Now you know which side the hypotenuse is then this is easy, it's the two other sides marked in orange on the picture above.

OK, so now we know which side is which, what use is it?

Well, understanding the rule means that you can calculate lots of things without having to know the exact exact length of each side?

For example, if you knew that side x was 3 metres and side y was 4 metres long then you would be able to work out the length of the hypotenuse quite easily?

On the image here the hypotenuse is z and the other 2 sides are x and y .

Firstly you need to work out the sum of the squares of both x and y:

X² is 3 x 3 = 9

Y² is 4 x 4 =16

Z² = X² + Y² (25)

The sum of the other 2 sides squared is 25

The length of the hypotenuse therefore is the square root of 25

√25 = 5 ( 5 x 5 = 25)

Watch the video for examples on the application of Pythagoras Theorem

source:
http://www.geom.uiuc.edu/~demo5337/Group3/hist.html
http://www.ies.co.jp/math/java/geo/pythagoras.html

Indices (Exponent) Song

Quadratic - fundamental

Quadratic Equation and Graphs.

Click here for information on

.1 What is the general form of a Quadratic Equation

.2 Types of solution. {one, two or no solution}

.3 Quadratic Graphs and nature of roots

Derivation of Quadratic FormulaQuadratic Equation SolverFactoring QuadraticsCompleting the SquareQuadratic Equation Explorer

click here for slider activity

Mensuration (reflective)

Use the following linoit collaborative platform to consolidate your learning and understanding:
Individually post at least 1 Key Learning point and 1 Question.

Elaboration on

.1 Key learning Points
- What have I learnt from the lesson?
- What are my take ways which will be useful for my learning?
- Useful Formulae taught?

.2 Questions?
- something that I would like to know more
- something that I would like to clarify

Quadratic - completing the square

Completing the square is a technique to solve Quadratic Equation.
Key questions to ask when using this technique are:

• What is Completing the Square technique?
• Why do we use Completing the Square?
• When is it used?
• How is the Completing the Square technique applied?

The following resources will be used to aid your understanding of the topic on Completing the Square.

Resource 1

Media and Video

Video 1

Video 2: Fundamental


video 3: summary and song


Resource 2

ACE Learning

The link is shown as follows:

Resource 3

Worksheet 3 for notes, worked examples and practice questions.

E-Learning 2012

Hi all,

First and foremost, I thank you all for being wonderful students. When I was away I came to realise how challenging it must have been to be a student in Singapore and my conference with my colleagues (educators and technologists from all over the world) testify that you are certainly capable of achieving great things (results, character et all). They marvel at your works and would like to have the opportunity to meet you eventually.

As we kick start to e-learning week, be clear of the objectives (refer to e-learning portal) and what it hopes to achieve. Below is just brief info to guide you.

Content

Clear rules: simple, relevant, easy to understand (from content to examples) and engaging (teacher teaching, use of ICT or Maths blog - choice is yours)

Worksheet

The worksheet style must be similar to the one I used in class. Content must contain the introduction, information, examples and some questions (with your own solutions)

for sample worksheet: Please refer to googlesite

Grouping and Task

The style of working is up to the respective team.

You may work independently and then consolidate or meet and discuss or work on-line at the designated time.

Remember that learning should take place anywhere and anytime. The key is to work smart. Note that failure to plan is planning for failure.

To support your learning you may refer to any of these sites.

• ACE Learning
• http://www.ask.com/questions-about/Mensuration-in-Maths
• http://www.cimt.plymouth.ac.uk/projects/mepres/allgcse/bkb7.pdf
• http://www.ascenteducation.com/india-mba/iim/cat/questionbank/mensuration.shtml
• http://www.youtube.com/watch?v=JhHOv3ajuN8
• http://www.excellup.com/ClassEight/matheight/mensurationexone.aspx
• http://www.transum.org/software/sw/starter_of_the_day/Similar.asp?ID_Topic=23

Source: e-learning site

Kinematics ( Review )

1. Definition

• Speed ➙ Rapidity of movement or action. The rate at which something moves.

• Distance ➙ How far something has travelled

• Displacement ➙ Distance with direction

• Total distance travelled ➙ The total distance an object has travelled over a period of time.

• Time ➙ The indefinite continued progress of existence and events in the past, present and future regarded as a whole

• Velocity ➙ The speed of something in a given direction

• Average speed ➙ The speed that is calculated from an object that travels at different speeds in different times

• Acceleration ➙ The rate at which an object increases its speed

• Deceleration ➙ The rate at which an object increases its speed

2. Formulae ( Relationship ) 

• Speed = distance/time 

➙ 

This can be rearranged to make it easier to solve it things such as

{ Distance = Speed x Time or Time = Distance / Speed }

If any one of them were to be unknown, use the known values to calculate the following. 

• Distance - Time graph

➙

• Speed - Time graph

➙ 

3. Key learning points from motion detector activity

• Graphs for:

    Distance/Time=Speed

    Speed/Distance=Acceleration

    Speed/Time=Velocity

• The direction of movement affects whether the graph slopes upwards or downwards ( velocity ).

• Speed ≠ Velocity, Speed is the rate at which an object moves, however velocity is the measurement of how fast an object is moving.

Done by : Teri, Jasmine, Ada, Yong Jie, Kang Xiong and Bryan

Kinematics (Review)

1. Definition

Speed - Is the velocity of a object which is in motion over a period of time.

Distance - Is the space between two different objects, both moving and stationary objects.

Displacement  - Is an imaginary path from one object to another, and it must be the shortest path.

Total distance travelled - Is a numerical amount of space covered by the object in motion over a certain period of time. It can only be calculated after the object is not in motion.

Time - Is to measure a sequence in numerical value, and it can be used to find speed of a particular object, given the total distance travelled.

Velocity - Is the speed of an object in motion, with the direction as well.

Average speed - Is the common constant speed calculated after an object moves a certain distance over a period of time.

Acceleration - Is the motion of speed increasing over a period of time.

Deceleration - Is the motion of speed decreasing over a period of time.

2. Formulae (Relationship)

Distance - Time Graph: This graph shows the amount of distance an object takes and the time it takes to move that distance. You can find the speed of the object by its gradient. A straight horizontal line on this graph shows that the object is stationary. A straight sloping up line shows constant speed. A concave line shows . A convex line shows acceleration. 

Speed - Time Graph: This shows the speed of an object at a certain time. A straight horizontal line shows constant speed. A straight sloping up line shows constant acceleration.  

Velocity - Time Graph: This shows the speed and direction of an object at a certain time. A straight horizontal line shows no speed in no apparent direction. A sloping up line shows acceleration forwards.

3. Key learning points from motion detector activity.

•We have learned how to use the motion detector and can pally this knowledge to future projects in which we may need to use it,we will have a good idea on how to operate the device as well as how to tabulate the results in Ti-Nspire

•We have learned how the speed over time differs from the velocity over time graph.It shows us the huge difference and the impact of the actions of the person moving and how it affects both graphs and how to be able to see two graph change with the same movements made by the person.

•We have learned that the results from the motion detector can be plotted on a graph in terms of distance from the motion detector as well as velocity.The graphs also help us grasp the concept of velocity and distance with the changes of the persons movement from a position to another.

Done by: Adil, Kenneth, Mateen, Yu Tao and Me

Kinematics (Review)

1. Definition:

• Speed - The speed is the distance covered over a period of time measured by distance over time. (km/s, m/s, km/min)

• Distance - The distance is the measurement of how far the length is through space. (10 meters, 1 kilometer, 12 millimeter)

• Displacement total distance travelled - It is the length of how far something is from the start after it has travelled.

• Time - Time is the measurement of how long/duration the object took to travel over a certain distance measured in seconds, minutes or hours.

• Velocity - It is an object moving with a direction.

• Average speed - It is the total distance over the average of the total speeds consisting of different speed.

• Acceleration - Acceleration is how much the speed increases over time. Whereas the symbol is m/s^2.

• Deceleration - Deceleration is how much the speed decreases over time.

2. Formulae (Relationship):

• Speed = Distance/time

An object takes time to cover a certain distance. As the unit of speed is m/s, the formula of speed is distance divided by time.

• Distance - time graph

Distance on the y -axis and time on the x -axis. Distance-time graphs is a way to visually show a collection of data. It allows us to understand the relationships between the data. The y -axis (distance) is the distance in relative to the origin point which is the 0 mark. This distance will change overtime if the object is moving whether the object is moving towards or away from the origin point

• Speed - time Graph

Features of the graphs is that when an object is moving with a constant velocity, the line on the graph will be horizontal. If it has a constant accelerating velocity then the line on the graph will be straight as if on the y -axis it shows a straight line where it stays at a certain point on the y-axis and move on the x- axis it will be a constant velocity as it changes in time but not on the speed axis.

3. Key learning points from the motion detector activity:

• We learnt that speed, distance and time can be represented onto graphs. Distance-time graphs show the distance travelled according to time while a velocity-time graph shows the speed the person travelling according to time.
• We learnt how to use a motion detector. With the sound measuring the distance. We also learnt tips and tricks to manipulate the motion detector without walking.
• We learnt how to incorporate technology into Math. Using TI-Nspire to do plot and learn graphs was very useful.

Done by: Joel, Abiyyu, Desiree, Claire, Daniel and Irfan. (*^▽^*)

Kinematics (Review)

1. Definition - speed, distance, displacement, total distance travelled, time velocity, average speed, acceleration, deceleration

Speed is the motion of the object and how fast it moves, calculated by distance over time.
Distance - the amount of space between two points.
A displacement of an object with respect to an initial point is define as the vector distance from the initial point to the final point; how far something is from the start until where it has travelled.
Total distance traveled, the distance traveled during the journey of an object.
Time, The duration for the whole journey, how long it does.
Velocity, the acceleration of the motion of the object. Average speed, the distance traveled/ total time traveled.
Acceleration, the increase in speed over time.
Deceleration, the decrease in speed over a period of time.

2. Formulae (relationship)
speed = distance / time


 distance-time graph



speed-time graph



3. Key learning points from motion detector
I) I have learnt that the actual accuracy could not be that accurate and straight, as we have expected
II) I have learnt that velocity has something to do with motion
III) I have learnt that the velocity changes only when there is motion.

Boon Pin, Gavin, Sylvia, Yoshiki, Esther