Slide 1

Induction Set

BAB 2: NUMBER PATTERNS AND SEQUENCESACTIVITY 1Number Patterns and SequencesNumbers can be arranged in sequences according to certain rules.Look at the following numbers: 1, 4, 7, 10, +3 +3 +3

2, 4, 8, 16, 32,. x2 x2 x2 x2Group activity 1:Objectives: Extend the number sequences using coins.Instructions:Collect 20 coins of some denomination.Arrange the coins according to the figures 2.1 below.Count the number of layers and coins to complete the following: 1 layer : 1 = 1 coin 2 layer : 1 + 2 = 3 coins 3 later : 1 + 2 + 3 = 6 coins4. Following this sequences, arrange the coins for the fourth layer.a) How many coins are needed?b) Do you recognise a pattern in this arrangement of coins?c) Write the numbers sequences for this activity.

Layer 1

Layer 2

Layer 3

Figure 2.1

Activity 2Completing missing terms and contruct the number sequences.If there any missing term in a number sequences, we can complete the sequences by following the pattern of the sequences.

1, 2, ___, ___, 5, ___, 77, ___,63, 189,___, ___, 5103

Solution 1, 2, 3, 4, 5, 6, 7 +1 +1 +1 +1 +1 +1

7, 21, 63, 189, 567, 1701, 5103 x3 x3 x3 x3 x3 x3

ExerciseWrite the pattern for each the following sequences1,5,9,13,17 b) 1,8,15,22,29 c) 29,26,23,20 d) 90,81,72, 64

2. Fill the missing numbers for each of the following sequences.4, __, 36, 108, __ b) __, 20, __, 40, __ c) 39, __, 33, __, 27, __

Answer:a) +4 b) +7 c) -3 d) -9a) 12, 324 (x3) b) 10, 30, 50 (+10) c) 36, 30, 24 (-3)

Activity 3Odd and Even numberEven numbers are non-zero whole numbers which can be divided by 2.Odd numbers are non-zero whole numbers which cannot be divided by 2.

Exercise:Decide whether the following numbers are even or odd numbers?123 b) 168 c) 193 d) 226 e)17 f) 71 g)177 h) 772

2) Listeven number between 10-30 odd number between 40-70.

Solution1 a) odd, b) even, c) odd d) even e) odd f) odd g) odd h) even2) a) 10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40 b) 41,43,45,47,49,51,53,55,57,59,61,63,65,67,69

Making statement about odd and even numbers

Objective: Find the sum of odd and even numbers.Thing needed: pencil, notebook and calculatorSteps: Make a list of odd numbers and of even numbers from 1 to 20 in your notebook.Add an odd number to an even number.Record your result in a table as shown below.

4) Discuss the results with your friends.

Conclusion : 1) The sum of an odd and even number is an odd number. 2) The product of an odd and even number is an even number. ODDEVENSUMPRODUCT123234512Activity 4Prime NumbersA prime number is a whole number that can only be divided by itself and the number 1The first ten prime numbers: 2,3,5,7,11,13,17,23,29

ExampleWhich of the following numbers ia a prime number?a) 31 b)65

Solution:a) 31/1 = 31, 31/31=1.31 can only divided by 1 and 31, 31 is prime.

b) 65/1=65, 65/65=1, 65/5=1365 is divisible by 1,5,65, 65 is not prime.Group Activity 4Objective : List all the prime numbers less than 100Instructions : Do this activity with group of four.Steps:Copy Table 1 into your piece of paper.Cross out 1, as shown in the table, as it is not a prime number.Circle 2 and cross out all the numbers that are divisible by 2.Circle 3 and cross out all the numbers that are divisible by 3.Circle 5 and cross out all the numbers that are divisible by 5.Circle 7 and cross out all the numbers that are divisible by 7.Circle all the remaining numbers. Write them out in a list.

123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100 Table 1

Answer: From the above activity, we find that all the circled numbers are prime numbers less than 100. Therefore, we can use the Sieve of Eratosthenes to list all the prime numbers less than 100.

Prime numbers less than 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 Activity 5FactorsA whole number can be expressed as aproduct of two whole numbers in different way.The number 6 can be divided exactly by 1,2,3,and 6 without any remainder. Therefore 1,2,3, and 6 are factors of 6.A factor of a given number is a number that divides the given number exactly without any remainder.

Determining whether a number is a factor of anotherExamplesCheck whether a) 9 ia a factor of 54 b) 7 ia a factor of 48

Solution:54/9 = 6 .. divided exactly, therefore 9 is a factor of 54.48/7 = 6 .. divided exactly, therefore 7 is a factor of 48.

ClosingHomeworkWrite down the missing number below a) 2, __, 16, __, 30, ___ b) 3, __, 45, __, 1125, ___ c) ___,2401, ___, 49, ___,

2) Find : a) Sum of odd number pairs between 151 and 157b) The difference between the smallest and the largest odd number from 230 to 540.

3) Fill the missing prime numbers11, 13,17, __, __,__31, __, 41,___,___,___

4) Write all the prime numbers between 100 and 150

5) X is the two digit whole number. If the factors of x are 1,2,4,8,11,22,44,88, find the value of x?

Answer:a) (+7) 9,23,37 b) (x5) 15, 225, 5625 c) (/7) 16807, 343, 7

a) 151 + 153 = 304, 151 + 155 = 306, 151+ 157 = 308 153 +155 = 308, 153 + 157 = 310, 155 + 157 = 312

b) smallest odd number = 232 largest odd number = 539 539-232 = 307

a) 19, 21,23 b) 37, 43,47,53 Primes number between 100-150 : 101, 103, 107, 109, 113, 127, 131, 137, 139, 149X = 88