This document contains a lesson on sequences and equations. It includes examples of sequences with rules for generating the next term. Students are asked to identify rules for sequences, find missing terms, and determine if statements are true or false. The document also covers what an equation is, using variables and constants, and solving simple one-step equations using addition, subtraction, multiplication and division. Students are given practice solving and comparing equations.

2. QUARTER 3 WEEK 6
DAY 1

3. Directions: Identify the nets of the given solid
figure.
1.
2.
3.
R E V I E W

4. What do you observe in
the picture?

5. Formulating the rule in finding
the next term in a sequence
(M5AL - IIIf – 6)

6. A sequence is an ordered list of numbers.
Each number in the sequence is called a
term. The three dots (…) mean to continue
forward in the pattern. To fill in the missing
numbers or symbols in each sequence,
we need to find out the rule or pattern
for generating the next term.
SEQUENCE

7. A sequence is a list of numbers or objects
in a defined or logical order. Patterns and
repetitive sequences can be found in
nature, shapes, events, sets of numbers
and anywhere.
SEQUENCE

8. Studying sequences is not that difficult.
You simply need to analyze the given terms
and identify the rule for generating the next
term in the sequence.
SEQUENCE

9. Study the table below:
Sequence Rule Next Three Terms
a) 3, 6, 9,
12,…
Every term after the first
is obtained by adding 3
to the number preceding
it. 0 + 3= 3; 3 + 3= 6; 6 +
3= 9, …
15, 18, 21
SEQUENCE

10. Study the table below:
Sequence Rule Next Three Terms
b) 1,4,9, 16,… Multiply the counting
numbers by
itself, that is, square the
counting numbers.
1 x 1=1; 2 x 2= 4; 3 x 3=
9, …
25, 36, 49
SEQUENCE

11. Study the table below:
Sequence Rule Next Three Terms
c) 1, 2, 4, 7,… After 1 and 2, add the
previous two
numbers, then plus 1
1+2+1= 4; 2+4+1= 7
12, 20, 33
SEQUENCE

12. Study the table below:
Sequence Rule Next Three Terms
d) 1, 2, 4, 8,
16,…
Multiply the previous
term by 2.
1 x 2=2; 2 x 2=4; 4 x
2=8; 8 x 2=16, …
32, 64, 128
SEQUENCE

13. Directions: Find the next three terms in
each sequence. Then, write the rule in
finding the next term.
A C T I V I T Y 1
Sequence Next Three Terms Rule
1) 3,6,12,24, …
2) 2, 9, 16, 23,
…
3) 53, 46, 39,
32, …

14. Directions: Find the next three terms in
each sequence. Then, write the rule in
finding the next term.
A C T I V I T Y 1
Sequence Next Three Terms Rule
4) 5, 12, 26, 54,
…
5) 5, 20,
50,110, …

15. Directions: Given the first term and the
rule, make a sequence consisting of
four (4) terms.
A S S E S S M E N T
First
Term
Rule First 4 terms of
the Sequence
1) 2 Add 4 and minus
3
2) 3 Multiply by 2 and
subtract 1

16. A S S E S S M E N T
First
Term
Rule First 4 terms of
the Sequence
3) 4 Add 3 and minus
2
4) 5 Subtract 2 and
plus 5
5) 1 Add 1 times 2

17. QUARTER 3 WEEK 6
DAY 2

18. Column A (Sequence) Column B (Rules)
3) 7, 15, 31, 63, … C. Multiply by 2 and add
1
4) 56, 49., 42, 35, … D. Multiply by 2
5) 14, 41, 122, 365, … E. Add 3
R E V I E W

19. Column A (Sequence) Column B (Rules)
1) 8, 11, 14, 17, … A. Multiply by 3 and
subtract 1
2) 12, 24, 48, 96, … B. Subtract by 7
Directions: Match the sequence in Column A to the rule
that generates the terms of the sequence in Column B.
R E V I E W

20. What do you observe in
the picture?

21. Formulating the rule in finding
the next term in a sequence
(M5AL - IIIf – 6)

22. A sequence is an ordered list of numbers.
Each number in the sequence is called a
term. The three dots (…) mean to continue
forward in the pattern. To fill in the missing
numbers or symbols in each sequence,
we need to find out the rule or pattern
for generating the next term.
SEQUENCE

23. A sequence is a list of numbers or objects
in a defined or logical order. Patterns and
repetitive sequences can be found in
nature, shapes, events, sets of numbers
and anywhere.
SEQUENCE

24. Studying sequences is not that difficult.
You simply need to analyze the given terms
and identify the rule for generating the next
term in the sequence.
SEQUENCE

25. Study the table below:
Sequence Rule Next Three Terms
a) 3, 6, 9,
12,…
Every term after the first
is obtained by adding 3
to the number preceding
it. 0 + 3= 3; 3 + 3= 6; 6 +
3= 9, …
15, 18, 21
SEQUENCE

26. Study the table below:
Sequence Rule Next Three Terms
b) 1,4,9, 16,… Multiply the counting
numbers by
itself, that is, square the
counting numbers.
1 x 1=1; 2 x 2= 4; 3 x 3=
9, …
25, 36, 49
SEQUENCE

27. Study the table below:
Sequence Rule Next Three Terms
c) 1, 2, 4, 7,… After 1 and 2, add the
previous two
numbers, then plus 1
1+2+1= 4; 2+4+1= 7
12, 20, 33
SEQUENCE

28. Study the table below:
Sequence Rule Next Three Terms
d) 1, 2, 4, 8,
16,…
Multiply the previous
term by 2.
1 x 2=2; 2 x 2=4; 4 x
2=8; 8 x 2=16, …
32, 64, 128
SEQUENCE

29. Directions: Read each statement
carefully. Write TRUE if the
statement is correct. If the
statement is incorrect, write
FALSE and change the underlined
word, number, or symbol to make
it correct.
A C T I V I T Y 2

30. 1) In the sequence 3, 7, 15 and
31, you have to multiply by 2 and add 1
to get the next term which is 63.
2) The first term in a sequence is
4. If the rule is “add 5 and subtract by
2”, the first 5 terms of this sequence are
4, 7, 10, 13, and 15”.
A C T I V I T Y 2

31. 3) A pattern is a list of numbers or
objects in a defined or logical order.
4) 4, 8, 12, 16 and 20 form a
sequence. 8 is called the second term.
5) The rule of the sequence 4, 9,
19, 40, 79… is “multiply by 2 and add 1”.
A C T I V I T Y 2

32. Directions: Find the missing term and
give the pattern rule of the following
sequences.
1.
2.
A S S E S S M E N T
14 17 20 23
Rule:
24 30 36 42
Rule:

33. 3.
4.
5.
A S S E S S M E N T
5 10 20 40
Rule:
4 19 94 469
Rule:
132 121 110 99
Rule:

34. QUARTER 3 WEEK 6
DAY 3

35. R E V I E W
Directions: Give the pattern or rule for
generating each sequence.
1) 1, 4, 7, 10, 13,…
Rule:
2) 3, 8, 18, 38, 78,…
Rule:

36. 3) 60, 56, 52, 48, 44,…
Rule:
4) 2, 8, 32, 128, 512,…
Rule:
5) 2, 9, 44, 219, 1094,…
Rule:
R E V I E W

37. Consider the following:
2x 2b + 2d 2c+ 5 = 25
a + 3 = 8 4b – 6 = 10
Which are equations?

38. Simple Equations Involving
One or More Operations
(M5AL - IIIf -14)

39. An equation is a statement that two
mathematical expressions are equal.
Many equations contain variables.
EQUATION

40. Below are some examples of equations:
2 + 3 = 7 – 2 2 + 4 = 6 10 = 1+2+3+4
k + 3 = 3k – 5 2x – 5 = 7 2(2) = 8 ÷ 2
EQUATION

41. A variable or unknown is represented by a
symbol, usually a letter, that may take on
different values.
VARIABLE

42. A constant is a fixed value and does not
change.
CONSTANT

43. Example:
2a
VARIABLE AND CONSTANT
variable
constant

44. If an equation involves a variable, then a
solution to the equation is a number that when
substituted to the variable will make the
equation true. The collection of all the
solutions to an equation is called its solution
set. The process of finding a solution is called
solving an equation.
EQUATION

45. In solving an equation, you can try the
following:
1. Write the equation
2. Group similar terms on one side.
3. Perform the indicated operations.
4. Simplify the answer.
5. Check.
EQUATION

46. Example: Find the missing term in
3x ___ + 1 = 10
Working backward is also one way of solving
problems. It is all about starting with the final
solution and work back one step at a time to
get to the beginning.
EQUATION

47. When you use work backward strategy, you
use the opposite of the given operations.
(+ to -, - to +, x to ÷, or ÷ to x )
3x ___ + 1 = 10 ( from 10 subtract 1, and from
the answer divide 3 )
EQUATION

48. 10 – 1 ÷ 3 = ____
9 ÷ 3 = 3
3 is the missing term.
To see if your answer is correct, go back to
the original equation:
3 x 3 + 1 = 10 3 x 3 = 9
9 + 1 = 10 9 + 1 = 10
EQUATION

49. Directions: Solve each equation.
1. x+2 = 5
2. 4x – 5 = 11
A C T I V I T Y 3

50. 3. 3x = -9
4. 2 + 4x = 14
5. 20 – 5x = 30
A C T I V I T Y 3

51. A S S E S S M E N T
Directions: Inside the box are possible
answers for the given equations. Match the
letter of the correct solution to each
equation.
___1. 5x – 1 = 14 ___4. -4x – 3 = 13
___2. 2x =10 ___5. 3x + 3 = 15
___3. 2x – 9 = 11
A. -4 B. 4 C. 10 D. 5 E. 3

52. QUARTER 3 WEEK 6
DAY 4

53. R E V I E W
Directions: Identify what is being described
by the statement.
1. It is a sentence in mathematics that
contains an equal sign.
2. It is a symbol or letter that may
take different values.

54. R E V I E W
3. It is a fixed value that does not
change.
4. It is a number that makes an
equation true.
5. It is a process of finding the
solution of an equation.

55. Consider the following:
2x 2b + 2d 2c+ 5 = 25
a + 3 = 8 4b – 6 = 10
Which are equations?

56. Simple Equations Involving
One or More Operations
(M5AL - IIIf -14)

57. An equation is a statement that two
mathematical expressions are equal.
Many equations contain variables.
EQUATION

58. Below are some examples of equations:
2 + 3 = 7 – 2 2 + 4 = 6 10 = 1+2+3+4
k + 3 = 3k – 5 2x – 5 = 7 2(2) = 8 ÷ 2
EQUATION

59. A variable or unknown is represented by a
symbol, usually a letter, that may take on
different values.
VARIABLE

60. A constant is a fixed value and does not
change.
CONSTANT

61. Example:
2a
VARIABLE AND CONSTANT
variable
constant

62. If an equation involves a variable, then a
solution to the equation is a number that when
substituted to the variable will make the
equation true. The collection of all the
solutions to an equation is called its solution
set. The process of finding a solution is called
solving an equation.
EQUATION

63. In solving an equation, you can try the
following:
1. Write the equation
2. Group similar terms on one side.
3. Perform the indicated operations.
4. Simplify the answer.
5. Check.
EQUATION

64. Example: Find the missing term in
3x ___ + 1 = 10
Working backward is also one way of solving
problems. It is all about starting with the final
solution and work back one step at a time to
get to the beginning.
EQUATION

65. When you use work backward strategy, you
use the opposite of the given operations.
(+ to -, - to +, x to ÷, or ÷ to x )
3x ___ + 1 = 10 ( from 10 subtract 1, and from
the answer divide 3 )
EQUATION

66. 10 – 1 ÷ 3 = ____
9 ÷ 3 = 3
3 is the missing term.
To see if your answer is correct, go back to
the original equation:
3 x 3 + 1 = 10 3 x 3 = 9
9 + 1 = 10 9 + 1 = 10
EQUATION

67. Directions: Compare the solutions of
equations in each number. Use >,Use >,
<, or = in the circle.
1. 2x + 5 = 3 (x -2) 3x – 1 = 2(x+5)
2. 3x + 4 = 6x -2 4x+ 3 = 2X + 6
A C T I V I T Y 4

68. 3. 2 + 3x = x – 6 3 + 2x = x – 3
4. 2 (3x – 1) = 5x 4x = 4 + 2(x+3)
5. 2x + 1 = 3(x+1) 4x + 1 = 3(x+1)
A C T I V I T Y 4

69. A S S E S S M E N T
Directions: Find the value of the
variable that will make each equation
true. Match each letter with the correct
answer in the code below to answer the
question “What is your idea about Math
in your life”?

70. A S S E S S M E N T
1. 3x + 2 = x - 4, H 6. -4 + 3x = -2x + 6, I
2. y + 4 = 5y – 8, E 7. 9a + 1 = 8a - 4, T
3. 2b – 1 = b + 4, F 8. 2(x – 4) = 3(x – 3), L
4. 2 + 7a = 4a - 4, M 9. 2x + 4 = 3(x – 1), S
5. 5y = 3y – 8, A
CODE: __ __ __ __ __ __ __ __ __ __
-2 -4 -5 -3 2 7 1 2 5 3