Tuesday, October 4, 2011

Error Analysis - Linear Equation


3  students, student A, student B and student C submitted the following solution during a recent class quiz. Your task is to evaluate their solution and identify the nature of the error(s) committed.

Task:
Go to Linoit and wait for Tr's Instruction

Reference:
Possible types of errors, among others, are:
  • Miscopy question
  • Conceptual error due to
  • Wrong understanding of algebraic fraction
  • Transfer error in an equation (negative instead of positive)
  • Multiplication/division of signs error
  • Careless error eg. Arithmetic error in addition, subtraction etc
  • others 
Student A
 Student B
  Student C




Monday, October 3, 2011

Problem Solving Heuristic

Problem Solving Heuristics

Heuristics: experience-based techniques for problem solving, learning, and discovery
Pólya worked in probability, analysis, number theory, geometry, combinatorics and mathematical physics.


source:
Maths worksheet on Number Patterns
http://www.learner.org
-------------------------------------------------------------------------------------------------------------------
Here is a math problem you may have seen.

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?
How would you solve this problem? George Pólya, a mathematician famous for problem solving, said that when you have a tough problem you should make the numbers simpler.

Click here to view/review the various strategies.

_____________________________________________________________________________

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?












Wednesday, September 28, 2011

Question 1 by Kevin Tay and Chris Kwek

The lengths of a triangle are 1/2 (X+2) cm, (3X+2) cm, 7/4(7X - 4/7) cm. If the perimeter of the triangle is 47 cm, find the lengths of each side of the triangle.

Ans: 2 3/7 OR 17/7cm, 10 4/7 OR 74/7 cm, and 34.


Workings: 1/2 of (x+2)= (X/2 + 1) cm
7/4 (7X - 4/7) = 49X/4 - 1

(X/2 +1) +3X + 2+ 49X/4 -1 = 47
63X/4 = 47-2
63X/4 = 45
63X = 45 x 4
63X = 180
X = 2 6/7

(X/2 +1) cm = 2 3/7 OR 17/7cm

(3X+2) cm = 10 4/7 OR 74/7 cm

7/4(7X - 4/7) cm = 34 cm


Enjoy!

Challenge Yourself Question 5 by Shawn Liew Hong Wei and Ryan Chew




(n x $1.60) + $0.80 = [(n+10)$0.70] + $0.10

= (n x $1.60) + $0.80 - $0.10 = [(n+10)$0.70] + $0.10 - $0.10

= (n x $1.60 + $0.70 = [(n+10)$0.70]

(n x $1.60) + $0.70 - $0.70 = [(n+10-1)$0.70]

= n x $1.60 = (n+9)$0.70

= $(1.60n) = $(0.7n+6.3)

$(1.60n - 0.7n) = $(0.7n + 6.3 - 0.7n)

= $(0.9n) = $6.30

10/9 * $0.9n = 10/9 * $6.30

= $n = $7

n = 7

i) Mrs Tan bought 7 mangoes

ii) 7($1.60) + $0.80 = $12

Mrs Tan had $12 to buy fruits

Tuesday, September 27, 2011

Challenge yourself Question 3 (Isaac gan)
















Lets D be the distance travelled by Chad when meeting Wei Liang and x be the time Chad and Wei Liang met
================================================
X-700*6km/h

730-700=0.5h <=============How much earlier did Chad begin before Wei Liang

1/2*6km/h=3km <====Distance travelled b chad before WL begun.

3km/h+6km/h=9km/h <======Total Speed travelled by WL and C

12-3=9km<=====Distance travelled by Wei Liang and Chad together

9km/9km/h<========Time taken for WL to meet Chad

x=1h+0.5h=1.5h

Geometry Solution

worksheet 1 worksheet 2 solution Graded Assignment

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? 
In order to study geometry in a logical way, it will be important to understand key mathematical properties and to know how to apply useful postulates and theorems.

Task 1:
Define the following (& # 4, 6 & 8 post as a comment)
  1. Postulate 
  2. Theorem
  3. Transversal
  4. 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:
  1. Properties of angles eg. acute, reflect etc
  2. Properties of angles and straight lines
  3. Properties of angles between parallel lines
  4. 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