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SECONDARY MATHEMATICS & SCIENCE WORKSHOP

SECONDARY MATHEMATICS & SCIENCE WORKSHOP. SINGAPORE EDUCATION SYSTEM. Kindergarden 1 : 5 years old Kindergarden 2 : 6 years old Primary 1 : 7 years old Primary 2, 3, 4, 5, 6 Secondary : Express academic and Normal academic Express academic : Secondary 1, 2, 3, 4 (‘ o’level )

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SECONDARY MATHEMATICS & SCIENCE WORKSHOP

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  1. SECONDARYMATHEMATICS & SCIENCEWORKSHOP

  2. SINGAPORE EDUCATION SYSTEM Kindergarden 1 : 5 years old Kindergarden 2 : 6 years old Primary 1 : 7 years old Primary 2, 3, 4, 5, 6 Secondary : Express academic and Normal academic Express academic : Secondary 1, 2, 3, 4 (‘o’level) Normal academic : Secondary 1, 2, 3, 4 (‘N’ level) 5 (‘O’ level)

  3. ENGLISH LANGUAGE ENGLISH LANGUAGE ENGLISH LANGUAGE LEARNERS IN THE MATHEMATICS & SCIENCE CLASSROOM

  4. ENGLISH CONNECTORS COMMON ENGLISH USAGE USUALLY INVOLVED CONNECTORS What is CONNECTORS ? EXAMPLES OF CONNECTORS ARE : • First, second, third, finally • For example, for instance, let’s take an example • But, however, on the other hand, • As a result………

  5. WHAT, WHEN, WHERE, HOW, WHAT WHAT Use : Asking about things or activities Example : What does he do during the weekends? What did you do yesterday? What is that ? What do your observe during the experiment? What is that ?

  6. WHAT What time is it? What does this sentences mean? What is the weather in bangkok? What does the word “sum” mean ? What does the word “difference” mean? What can you tell me about photosynthesis? What can you tell me about integers?

  7. WHEN Use : Asking about general or specific time Examples : When does the bus leaves for Phuket? When are you going to hand in your homework? When are you going to pass me your math book? When are you going to hand me your project?

  8. WHERE Use : Asking about places Examples : Where do you live? Where did you go during your holiday? Where did you put your book? Where did you and Khun Joy go yesterday? Where is your bag? Where is your science textbook?

  9. WHERE Where is your mathematics workbooks? Where are you going this coming Sunday? Where is John? Where is Susan? Where is MBK?

  10. HOW Use : To ask question about specific things Examples: How often do you go to the market? How often do you wash your car? How often do you play football? How often do you have science experiment? How often do you have maths test? How are you?

  11. HOW How is the science project getting on? How is your preparation for your math test getting on? How is your family getting on? How much does it cost? How long was the journey from the airport to the city?

  12. WHICH Use : Asking to specify things Examples : Which science textbook did you buy? Which math textbook did you buy? Which of the following statement is correct ? Which of the following option is true? Which boy won the race? Which girl come in first?

  13. WHICH Which answer is wrong? Which one of you did not hand up your homework? Which of the following statement do you think is correct? Which one of you get your answer wrong/right?

  14. COMMUNICATION WITH STUDENTS IN CLASS I don’t understand the question? Can you help me please? Is this answer right or wrong? Is this working correct? Is this observation correct? Is this experiment telling us that photosynthesis is important?

  15. Speak English with students in class What does “(the word)” in English? What does “(the word)” mean? How do you say “(the word)” in English? How do you spell “(the word)” ? How do you read “(the word)” ? How do you say “(the word)” in English?

  16. Asking for something Can I have a pen, please? Do you have a pen for me ? May I have a pen, please?

  17. Saying sorry Excuse me, please….. I am sorry. Sorry I am late Please accept my apology

  18. Asking to repeat Can you repeat that question, please? Can you say that again ? Could you say that again ? Pardon me?

  19. Common phrases of English Good morning Good afternoon Good evening Hello / Hi How are you Goodbye Have a nice weekend Have a nice day

  20. SAMPLE QUESTION 1 Questions to help students rely on their own understanding, ask the following : • DO YOU THINK THAT IS TRUE? WHY? • DOES THAT MAKE SENSE TO YOU? • HOW DID YOU GET YOUR ANSWER? • DO YOU AGREE WITH THE EXPLANATION?

  21. SAMPLE QUESTION : 2 To promote problem solving, ask the following : • WHAT DO YOU NEED TO FIND OUT? • WHAT INFORMATION DO YOU HAVE? • WILL A DIAGRAM OR NUMBER LINE HELP YOU? • WHAT TECHNIQUE COULD YOU USE? • WHAT DO YOU THINK THE ANSWER WILL BE

  22. SAMPLE QUESTION : 3 Questions to encourage students to speak out, ask the following • What do you think about what ……… said? • Do you agree what I have said? • Why? • Or why not? • Does anyone have the same answer but a different way to explain it? • Do you understand what …… ? • Are you confuse?

  23. SAMPLE QUESTION : 4 Question to check the students progress, ask the following: • What have you found out so far? • What do you notice about? • What other things that you need to do? • What other information you need to find out? • Have you though of another way to solve the questions?

  24. SAMPLE QUESTION : 5 Question to help students when they get stuck,ask the following • What have you done so far? • What do you need to figure out next? • How would you say the questions in your own words? • Could you try it the other way round? • Have you compared your work with anyone else?

  25. SAMPLE QUESTION : 6 Question to make connection among ideas and application, Ask the following: • What other problem does this remind you of? • Can you give me an example of ? • Can you write down the objective or aim? • Can you write down the formulae?

  26. EXAMPLE TO COMMUNICATE • CAN YOU REPEAT THAT PLEASE? • HOW DO YOU SPELL________? • WHAT DOES ____MEAN? • CAN YOU GIVE ME AN EXAMPLE? Teacher : I am reading a book about amphibians Students : Can you repeat that please? Teacher : I said : “I’m reading a book on amphibians” Students : How do you spell amphibians? Teacher : A-M-P-H-I-B-I-A-N-S Students : What does amphibians mean? Teacher : It is an animal that is born in water but can live on land Student : Can you give me an example? Teacher : A frog

  27. EXAMPLE TO COMMUNICATE Teacher: Boys and girls what do you know about photosynthesis? Students: Well we know that photosynthesis have 3 factors that limit it from going any faster. Teacher: What are the 3 factors?

  28. Students : Light intensity, carbon dioxide concentration and temperature. Teacher: That is very good class. Well done. You also speak very good English today. Keep it up.

  29. Example to Communication Teacher: Can you explain to me what is integer mean? Students: Integer mean positive and negative whole number including zero. Teacher: Excellent. That is correct. Well done and please keep it up.

  30. Example of conversation John : Ahh, excuse me do you speak English? KhunVasin : Yes John : Can you tell me when the next train going to BMK? KhunVasin : They usually depart every 5 minutes, I think one left a little while ago. John : OK, thanks and do you know how long it take to get to Siam square?

  31. Example of conversation KhunVasin : About 15 minutes from here. John : Wow, you sound like a local, do you live in Bangkok? KhunVasin: Yes, I study English in Singapore and come back to Bangkok for the holiday. John: This is my first time to Bangkok and I am abit nervous because I don’t know anybody here and I don’t speak Thailand language.

  32. KhunVasin: Don’t worry, in Thailand everybody is very friendly and you should be fine in Bangkok. John : Yes, I always find some local phrases for help. KhunVasin:Ok, your train is here. See you. Goodbye John : Goodbye and thank you very much for your help

  33. KNOW YOUR KEY WORDS • MORE THAN • LESS THAN • ALTOGETHER • AT FIRST • SUM • DIFFERENT • COMPARE • DIGITS • FIND THE LENGTH /MASS • PLACE VALUE • WHOLE NUMBER

  34. KNOW YOUR KEY WORDS • ORDINAL NUMBER • SUBTRACT • SUBTRACT 2 FROM 5 • GREATER THAN • LESS THAN • SHORT/SHORTER/SHORTEST • TALL/TALLER/TALLEST • ARRANGE THE NUMBER FROM THE GREATEST TO THE SMALLEST • ARRANGE THE STRINGS FROM THE SHORTEST TO THE LONGERST • READ THE QUESTIONS CAREFULLY

  35. KNOW YOUR KEY WORDS • FACTORS • MULTIPLES OF 2, 3 • NUMBER LINES • POSITIVE NUMBER • NEGATIVE NUMBER • INTEGERS • 3 TO THE POWER OF 2 • PRIME NUMBER • VENN DIAGRAM • INEQUALITIES • MULTIPLY

  36. KNOW YOUR KEY WORDS • DIVIDE • ADD TWO NUMBER UP TO THREE DIGITS • FACTION • MIXED NUMBER • IMPROPER FRACTION • CONVERT THE FOLLOWING FRACTION TO DECIMALS • EQUILATERAL • ISOSCELES • RIGHT ANGLE TRIANGLE • NUMBERATOR • DENOMINATOR

  37. HOW TO READ ½ : half, one over two, one divide by two ¼ : one quarter, one over four, 1/3 : one third, one over three 1/5 : one fifth = : equal to ≠ : not equal to > : greater than < : less than

  38. How to read ≈ : approximate to √ : square root ≤ : less than or equal to ≥ : greater than or equal to a≠0 : a is not equal to zero X – 3 3x = 9 3 time what number equal 9 9 – x = 3 9 minus what number gives 3 what number minus 3 gives 9

  39. FACTORS AND MULTIPLES • We can write a whole number greater than 1 as a product of two whole numbers. E.g. 18 = 1 x 18 18 = 2 x 9 18 = 3 x 6 Therefore, 1, 2, 3, 6, 9 and 18 are called factors of 18. Tip : Note that 18 is divisible by each of its factors. Factors of a number are whole numbers which multiply to give that number. The common factors of two numbers are the factors that the numbers have in common. E.g. Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 21: 1, 3, 7, 21 The common factors of 12 and 21 are 1 and 3.

  40. FACTORS AND MULTIPLES • When we multiply a number by a non-zero whole number, we get a multiple of the number. E.g. 1 x 3 = 3 1 x 5 = 5 2 x 3 = 6 2 x 5 = 10 3 x 3 = 9 Multiples 3 x 5 = 15 Multiples 4 x 3 = 12 of 3 4 x 5 = 20 of 5 5 x 3 = 15 5 x 5 = 25 Therefore, the multiples of 3 are 3, 6, 9, 12, 15, … and the multiples of 5 are 5, 10, 15, 20, 25, … The common multiple of two numbers is a number that is a multiple of both numbers. E.g. Multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, ... Multiples of 6 are 6, 12, 18, 24, 30, 36, ... The first three common multiples of 4 and 6 are 12, 24 and 36.

  41. PRIME NUMBERS,PRIME FACTORISATION • A prime number is a whole number greater than 1 that has exactly two different factors, 1 and itself. E.g. 5 = 1 x 5 Since 5 has no other whole number factors other than 1 and itself, it is a prime number. The numbers 2, 3, 5, 7, 11, 13, 17, … are prime numbers. A composite number is a whole number greater than 1 that has more than 2 different factors. E.g. 6 = 1 x 6 6 = 2 x 3 Therefore, 6 is a composite number. 4 Factors

  42. PRIME NUMBERS,PRIME FACTORISATION • The numbers 4, 6, 8, 9, 10, 12, 14, 15, 16, … are composite numbers. In other words, all whole numbers greater than 1 that are not prime numbers are composite numbers. Tip: 0 and 1 are neither prime nor composite numbers. Prime factors are factors of a number that are also prime. E.g. The factors of 18 are 1, 2, 3, 6, 9, and 18. The prime factors of 18 are 2 and 3. The process of expressing a composite number as the product of prime factors is called prime factorisation. We can use either the factor tree or repeated division to express a composite number as a product of its prime factors.

  43. PRIME NUMBERS, PRIME FACTORISATION WORKED EXAMPLE 1: Express 180 as a product of prime factors. SOLUTION: Method I (Using the Factor Tree) 180 2 x 90 2 x 2 x 45 2 x 2 x 3 x 15 2 x 2 x 3 x 3 x 5 Therefore, 180 = 2 x 2 x 3 x 3 x 5 = 22 x 32 x 5 Steps: Write the number to be factorised at the top of the tree. Express the number as a product of two numbers. Continue to factorise if any of the factors is not prime. Continue to factorise until the last row of the tree shows only prime factors. A quicker and more concise way to write the product is using index notation.

  44. PRIME NUMBERS, PRIME FACTORISATION WORKED EXAMPLE 1: Express 180 as a product of prime factors. SOLUTION: Method II (Using Repeated Division) 2 180 2 90 3 45 3 15 5 5 1 Therefore, 180 = 2 x 2 x 3 x 3 x 5 = 22 x 32 x 5 Steps: Start by dividing the number by the smallest prime number. Here, we begin with 2. Continue to divide using the same or other prime numbers until you get a quotient of 1. The product of the divisors gives the prime factorisation of 180.

  45. INDEX NOTATION If the factors appear more than once, we can use the index notation to represent the product. E.g. 3 x 3 x 3 x 3 x 3 = 35 35 is read as ‘3 to the power of 5’ 35 index base In index notation, 3 is called the base and the number at the top, 5 is called the index. E.g. 2 x 2 x 2 x 5 x 5 = 23 x 52 The answer is read as 2 to the power of 3 times 5 to the power of 2.

  46. HIGHEST COMMON FACTOR (HCF) • The largest common factor among the common factors of two or more numbers is called the highest common factor (HCF) of the given numbers. E.g. Factors of 12 are 1, 2, 3, 4, 6, and 12. Factors of 18 are 1, 2, 3, 6, 9, and 18. The common factors of 12 and 18 are 1, 2, 3 and 6. The highest common factor (HCF) of 12 and 18 is 6. Another method to find the HCF of two or more numbers is by using prime factorisation which is the more efficient way. We can also repeatedly divide the numbers by prime factors to find the HCF.

  47. SQUARES AND SQUARE ROOTS • When a number is multiplied by itself, the product is called the square of the number E.g. 5 x 5 = 25 or 52 = 25 5 is the positive square root of 25. E.g. √25 = 5 The numbers whose square roots are whole numbers are called perfect squares. E.g. 1, 4, 9, 16, 25, ... are perfect squares. Tip : 22 = 4 and √ 4 = 2 32 = 9 and √ 9 = 3 42 = 16 and √16 = 4

  48. SQUARES AND SQUARE ROOTS WORKED EXAMPLE 1: Using prime factorisation, find the square root of 5184. SOLUTION: 5184 = 26 x 34 2 5184 √5184 = √26 x 34 2 2592 = 23 x 32 2 1296 = 8 x 9 2 648 = 72 2 324 2 162 3 81 3 27 3 9 3 3 1

  49. CUBES AND CUBE ROOTS • When a number is multiplied by itself thrice, the product is called the cube of the number E.g. 5 x 5 x 5 = 125 or 53 = 125 125 is the cube of 5 and 5 is the cube root of 125. E.g. ∛125 = 5 The numbers whose cube roots are whole numbers are called perfect cubes. E.g. 1, 8, 27, 64, 125, ... are perfect cubes. Tip : 23 = 8 and ∛ 8 = 2 33 = 27 and ∛27 = 3 43 = 64 and ∛64 = 4

  50. CUBES AND CUBE ROOTS WORKED EXAMPLE 1: Using prime factorisation, find the cube root of 1728. SOLUTION: 1728 = 26 x 33 2 1728 ∛1728 = ∛26 x 33 2 864 = 22 x 3 2 432 = 4 x 3 2 216 = 12 2 108 2 54 3 27 3 9 3 3 1

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