# 2011 S1-06 Maths Blog

## Friday, October 21, 2011

the part i did not understand about the project was that it said to ask another person to help record u but majority of my classmates screen recorded which puzzled me. But this math project was reasonable as usually when we do the math work on paper it is easier as we already understand what we are doing and we are used to do it easily. But to explain to another person is tough as he/she does not understand what you are thinking so that is the main problem in this project.

## Tuesday, October 11, 2011

## Friday, September 30, 2011

### Mathematical Patterns

Are there other types of mathematical patterns ?

Do a brief research and post your findings.

Do a brief research and post your findings.

Tessellations

## Thursday, September 29, 2011

### Number Pattern

**Activity 1**

Observe the following and complete the activity that follows:

*example 1*

*example 2*

*example 3*

*example 4*

*example 5*

click here for animation

*example 6*

**Activity 2**

What did you observe about the above examples? Do they have something in common and related to mathematics?

**Question:**

Are there other types of mathematical patterns ?

Do a brief research and post your findings.

Use the

**Linoit**to identify other types of numbers or patterns in the world

**Activity 3**

**Activity 1 Problem solving heuristics**

Here is a simple
Mathematical problem.

There are 28 students in
your classroom.

On Valentine's Day, every student gives a valentine to each of
the other students.

How many valentines are
exchanged?

**Question:**

What are the Mathematical Heuristics that you think will be suitable to solve the above problem?

## Tuesday, September 27, 2011

### Maths Ws 9 Q4 (Challenging Questions)

104 chickens and goats in a farm have 246 legs altogether. How many chickens and goats are there in the farm?

Assuming the number of chickens is 'x'

Assuming the number of goats is 'y'

x + y = 104

2x + 4y = 246 ( The number of legs time the number of animals)

(2x + 4y) - 2(x + y) = 2y

246 - 2(104) = 246 -208 = 38 (38 is 2y) <-- ( Substituting algebraic terms for numbers)

38/2 = 19

y = 19

104 - 19 = 85

x = 85

So, the number of chickens is

Done by Tobias Tang (22) 27/9/11

Assuming the number of chickens is 'x'

Assuming the number of goats is 'y'

x + y = 104

2x + 4y = 246 ( The number of legs time the number of animals)

(2x + 4y) - 2(x + y) = 2y

246 - 2(104) = 246 -208 = 38 (38 is 2y) <-- ( Substituting algebraic terms for numbers)

38/2 = 19

y = 19

104 - 19 = 85

x = 85

So, the number of chickens is

__85__and the number of goats is__19__.Done by Tobias Tang (22) 27/9/11

### Geometry Part 1

**What is Geometry?**

**Geometry**is a subject in mathematics that focuses on the study of shapes, sizes, relative configurations, and spatial properties. Derived from the Greek word meaning “

*earth measurement*”, geometry is one of the oldest sciences. It was first formally organized by the Greek mathematician

**Euclid**around 300 BC when he arranged 465 geometric propositions into 13 books, titled ‘Elements’.

**What are Angle Properties, Postulates, and Theorems?**

**Task 1:**

- Postulate
- Theorem
- Transversal
- Converse

*Nb: suggest you do a personal note or concept map to summarise the various types of geometrical properties.*

*The syllabus requires you to know the following:*

*Properties of angles eg. acute, reflect etc**Properties of angles and straight lines**Properties of angles between parallel lines**Properties of Triangle*

*courtesy of Lincoln Chu S1-02 2010*

*courtesy of Goh Jia Sheng S1-02 2010*

**Lets look at some of these Postulates****A. Corresponding Angles Postulate**

If a

__transversal__intersects two

**parallel**lines, the pairs of corresponding angles are congruent.

__Converse also true__: If a transversal intersects two lines and the corresponding angles are congruent, then the lines are parallel.*The figure above yields four pairs of corresponding angles.*

### B. Parallel Postulate

Given a line and a point__not__on that line, there exists a unique line through the point parallel to the given line. The parallel postulate is what sets Euclidean geometry apart from non-Euclidean geometry.

*There are an infinite number of lines that pass through point*

**E**, but only the red line runs parallel to line**CD**. Any other line through**E**will eventually intersect line**CD**.## Angle Theorems

### C. Alternate Exterior Angles Theorem

If a transversal intersects two**parallel**lines, then the alternate exterior angles are congruent.

__Converse also true__: If a transversal intersects two lines and the alternate exterior angles are congruent, then the lines are parallel.*The alternate exterior angles have the same degree measures because the lines are parallel to each other.*

### D. Alternate Interior Angles Theorem

If a transversal intersects two**parallel**lines, then the alternate interior angles are congruent.

__Converse also true__: If a transversal intersects two lines and the alternate interior angles are congruent, then the lines are parallel.*The alternate interior angles have the same degree measures because the lines are parallel to each other.*

**E. Same-Side Interior Angles Theorem**

If a transversal intersects two

**parallel**lines, then the interior angles on the same side of the transversal are supplementary.

*The sum of the degree measures of the same-side interior angles is 180°.*

### F. Vertical Angles Theorem

If two angles are vertical angles, then they have equal measures.*The vertical angles have equal degree measures. There are two pairs of vertical angles.*

**sources:**

**http://www.wyzant.com**

**http://www.mathsteacher.com.au/year9/ch13_geometry/05_deductive/geometry.htm**

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