BEAUTY IN NATURE : BEAUTY IN NATURE Patterns in Nature
Segments on a Circle : Segments on a Circle
SEQUENCE : SEQUENCE Target: To find the next number in the sequence.
Slide 7: According to the dictionary, happen. Sequence is the order in which events happen.
Slide 8: Certain words can be sequence clues.
Slide 9: Time-Order Words
first
next
then
finally
Slide 10: Time-Order Expression
in the morning
after that
later that day
two weeks later
What is a sequence? : What is a sequence? It can be a pattern of :
objects
music
Letters or
numbers A sequence is a pattern. Mathematically speaking…
Here is a sequence of objects : Here is a sequence of objects Correct! It would be a mouse. What animal would come next in this sequence?
Here is a sequence of sounds : Here is a sequence of sounds What sound will come next in the sequence? Correct! It will be the cow mooing.
Here is a sequence of letters. : Here is a sequence of letters. What letter will come next in the sequence? Look carefully at the letters. a a b c a a b c a a b c a Correct!
It‘s the letter a.
Here is a sequence of numbers. : Here is a sequence of numbers. What number is going to come next in this sequence? 0 2 4 6 8 10 12 14 16 Correct it is the number
18
Decide what number should come next : Decide what number should come next Look at all of the numbers in the sequence To find the next number in a
number sequence: Put your number into the sequence and check that it looks correct Find the pattern TIP!
and finish these number sequences. : and finish these number sequences. Find the Number
Look at the number sequences and see if you can work out the missing number. : Look at the number sequences and see if you can work out the missing number.
Find the number! : Find the number! 1 3 5 7 9 13 15 17 It is the number 11. 11
Find the number! : Find the number! Correct! It is the number 15. 0 5 10 ____ 20 25 30 35 40 15
Slide 21: Find the number! Correct! It is the number 11. 17 15 13 ____ 9 7 5 11
Slide 22: Find the number! Correct!
It is the number 55. 25 35 45 ___ 65 75 55
Slide 23: 34 44 54 64 ___ 84 94 Now race on to the last number sequence. Find the number! Correct!
The missing number is 74. 74
You have to find all three missing numbers! : You have to find all three missing numbers! 42 47 ___ 57 62 ___ 72 ___ 82 Solving this sequence is going to be a bit trickier. 52 67 77 The answers are: 52 67 and 77
Slide 25: Well Done!
Each number in a sequence is what we call a TERM. : Each number in a sequence is what we call a TERM. Example:
2 , 4 , 6 , 8 , 10 extremes means Name a term on the given example. Extremes are the 1st and last term Means are the terms between the 1st and last term
Example: : Example: Lets identify the means and extremes: 4 , 7 , 10 , 13 , 16 11 , 16 , 21 , 26 , 31
Sequence could be finite or infinite.. : Sequence could be finite or infinite.. 2 , 4 , 6 , 8 ,… 2 , 4 , 6 , 8 , 10 infinite finite no definite number of terms has a definite number of terms 4 , 7 , 10 , 13 , 16, . . . 4 , 7 , 10 , 13 , 16
Identify if finite or infinite. : Identify if finite or infinite. 3 , 7 , 11 , 15 , 19
22 , 25 , 28 , 31 , 34 , . . .
35 , 29 , 23 , 17 , 11
Slide 30: A sequence is a pattern. Lets try to identify their patterns. Give the next term of the sequence. 1) 1 , 4 , 9 , 16 , 25 , ___ Give the next 2 terms of the sequence. 2) 2 , 9 , 16 , 23 , 30 , ___ , ___ 36 37 44 Give the next 3 terms of the sequence. 3) 18 , 14 , 10 , 6 , 2 , ___ , ___ , __ 4) 49 , 44 , 39 , 34 , 29 , __ , __ , __ 5) 3 , 7 , 11 , 15 , __ , __ , __ 6) 3 , 6 , 9 , 12 , 15 , __ , __ , __ 7) 31 , 27 , 23 , 19 , 14 , __ , __ , __
Slide 31: A sequence is a pattern. Some set of numbers cannot be a sequence. Lets identify if the following are sequence or not. 1) 0 , 1 , 2 , 3 , 4 Sequence 2) 54 , 50 , 46 , 42 , ... Sequence 3) 13 , 20 , 27 , 42 , ... not
Slide 32: Answer on your quiz notebook Indicate whether the following is sequence or not, if sequence find the next 3 terms. 1) 5 , 10 , 15 , 20 2) 81 , 27 , 9 , 3 , 1 3) 9 , 11 , 15 , 20 4) 35 , 41 , 47 , 53 5) 43 , 36 , 29 , 22
Term is what we called a number in a sequence. : A sequence is a pattern of objects, music, letters or numbers Term is what we called a number in a sequence. Extremes are the 1st and last term Means are the terms between the 1st and last term Infinite Finite no definite number of terms has a definite number of terms
Slide 34: Assignment: Give the next three terms in the following sequence. Place in in a ¼ sheet of paper 81 , 27 , 9 , 3 , 1 , ...
10 , 15 , 20 , 25 , ...
-18 , 11 , -4 , 3 , ...