1. THE NATURE OF MATHEMATICS
TABII MATEMATIK
THE NATURE OF MATHEMATICS

2. FITRAH MATEMATIK Penyelesaian masalah Logik / mantik
Perkiraan (Calculation)
Sistem nombor
Sukatan
Algebra

3. PROBLEM SOLVING NCTM’s thinking mathematics standards Problem solving
Communication
Reasoning
Making connections

4. THE HEART OF MATHEMATICS.
Through problem solving, children learn that there are many different ways to solve a problem and that more than one answer is possible. It involves the ability to explore, think through an issue, and reason logically to solve routine as well as non-routine problems. In addition to helping with mathematical thinking, this activity builds language and social skills such as working together.

5. Penyelesaian Masalah Apa itu masalah?
2+2=?
12x34=?
Apakah yang anda faham tentang masalah?
Bagaimana anda menakrifkan sesuatu masalah matematik?

6. Proses Penyelesaian Masalah
Apabila berhadapan dengan situasi bermasalah, anda perlu
berfikir untuk mencari penyelesaian
menggunakan satu model penyelesaian masalah yang berkesan
Apakah model penyelesaian masalah yang anda ketahui atau pernah gunakan?

7. Model Polya
Apakah langkah-langkah dalam Model Polya?

8. Memahami Model Polya
Sila baca “The nature of Problem Solving” halaman 7.

9. Mengaplikasi Model Polya
Lihat contoh-contoh berikut
Contoh 4
Bolehkah anda selesaikan Contoh 5 dengan cara yang lain?

10. Rumusan Penyelesaian masalah
merupakan suatu proses
perlu berfikir (memahami situasi, organise data)
kegunaan model boleh membantu
perlu menguasai pelbagai strategi
Apakah strategi-strategi penyelesaian masalah yang anda tahu?

11. Men at Work
Two men, working at the same rate, took 5 days to lay the bricks of a wall. If the rate of one man was doubled and that of the other man was halved, how long would they have taken to finish the wall?

12. A Simple Solution
Day 1
Day 5
1st workman
2nd workman

13. After Day 1

14. After Day 2

15. After Day 3

16. After Day 4

17. Refleksi Adakah anda Memahami masalah yang diberikan?
Merancang satu pelan tindakan / strategi yang baik?
Melaksanakan pelan tindakan yang disediakan?
Menyemak jawapan anda?

18. PROBLEM SOLVING Polya’s Model (How to solve it) Understand the problem
Devising a plan
Carrying out the plan
Looking back

19. MATHEMATICAL LOGIC
Reasoning is used to think through a question and come up with a useful answer. It is a major part of problem solving.

20. LOGIK Penaakulan induktif Penaakulan deduktif
Pemikiran mantik (Operators and laws of logic)
Bukti matematik

21. REASONING Inductive reasoning
First observing patterns then predicting the answers to more complicated problems
Reasoning from particular facts or cases to a general conjecture
A generalisation made based on observed occurrences
Also called the scientific method

22. REASONING Deductive reasoning
Reaching a conclusion based on a given set of assumptions or premises
A general axiom is given to the learner eg “Triangles are closed, three-sided figures”
The learner considers a given figure and if the figure contains the features of a triangle with certainty, a conclusion is then made eg “Figure ABC is a triangle”

23. NOMBOR & PERKIRAAN (NUMBERS & CALCULATION)
Sistem nombor
Mesir / Babylon
Hindu-Arab
Alat perkiraan
Nombor
Nombor asli
Nombor perdana
Nombor integer
Nombor nisbah
Nombor tak nisbah

24. NUMBERS
Number sense and numeration: Number sense is much more than merely counting, it involves the ability to think and work with numbers easily and to understand their uses and relationships. Number sense is about understanding the different uses for numbers (describe quantities and relationships, informational tools).

25. MATHEMATICAL CALCULATION
Number sense is the ability to count accurately and competently, to see relationships between numbers, and to be able to take a specific number apart and put it back together again.
It is about counting, adding, and subtracting. Counting and becoming familiar with numbers will help children understand all other aspects of math.

26. MEASUREMENT
Measurement is finding the length, height, and weight of an object using appropriate units. Time is measured using hours, seconds, and minutes.
Measurement is an important way for young children to look for relationships in the real world.

27. ALGEBRA Polinomial Pemfaktoran Persamaan Ketaksamaan
Nisbah, perkadaran

28. SUKATAN & UKURAN
Perimeter
Luas
Luas permukaan
Isipadu