2
3
(13)(8) =
(11)(9) =
2
(12)
=
35 +(23)=
-18 – (-5)=
Want to know someone’s age without asking for a hint about it? Have them
answer the following to know it!
This age trick is made
x
Think of their age
possible by using a place
c
2. Add 5 to it
holder for the number that
(x + 5)
3. Double the sum
you are looking for.
[(x + 5) * 2]
4. Add 10 to the product
{[( x + 5) * 2] + 10}
5. Multiply the resulting number by 5
({[(x + 5) * 2] + 10} * 5)
6. Subtract 100 from the result
[({[(x + 5) * 2] + 10} * 5) – 100]
7. Divide the difference by 10
[({[(x + 5) * 2] + 10} * 5) – 100] ÷ 10
The quotient they will tell you is their age!
1.
At the end of the discussion, the student should be able to:



Solve simple equations represented by bar models to find
unknowns.
Distinguish a variable from a constant in an algebraic
expression.
Translate verbal phrases into algebraic expressions.
Determine the missing number based on the bar models below:
32
?
8
8
8
8
75
15
?
15
?
15
?
15
?
15
?
150
100
?
50
Determine the missing number based on the bar models below:
121
?
43
78
67
48
?
19
1
?
¼
¼
¼
¼
Determine what is being asked based on the bar models below:
1
¼
¼
¼
¼
¾
?
18
?
6
?
6
?
6
?
30
6
?
6
?
𝟐 𝟑
A bar model that we could use to represent + = ?
𝟕 𝟕
𝟓
𝟕
?
𝟏
𝟕
𝟏
𝟕
𝟐
𝟕
𝟏
𝟕
𝟏
𝟕
𝟑
𝟕
𝟏
𝟕
𝟏
𝟕
𝟏
𝟕
NOW TRY THIS!
A kilo of rice costs the same as 4 packets of noodles plus one egg.
If the price of a kilo of rice is Php 57, and one egg Php 9, how much
does one packet of noodles cost?
NOW TRY THIS!
A kilo of rice costs the same as 4 packets of noodles plus one egg.
If the price of a kilo of rice is Php 57, and one egg Php 9, how much
does one packet of noodles cost?
rice
noodles noodles noodles noodles
egg
NOW TRY THIS!
A kilo of rice costs the same as 4 packets of noodles plus one egg.
If the price of a kilo of rice is Php 57, and one egg Php 9, how much
does one packet of noodles cost?
Php
rice57
noodles
Php ? noodles
Php ? noodles
Php ? noodles
Php ?
egg9
Php
NOW TRY THIS!
A kilo of rice costs the same as 4 packets of noodles plus one egg.
If the price of a kilo of rice is Php 57, and one egg Php 9, how much
does one packet of noodles cost?
Php 57
Php 12
Php 12
Php 12
Php 12
Php
? Php
? Php
? Php
? Php 9
? 12
Php
At the end of the discussion, the student should be able to:



Solve simple equations represented by bar models to find
unknowns.
Distinguish a variable from a constant in an algebraic
expression.
Translate verbal phrases into algebraic expressions.
Algebra – is the branch of Mathematics that deals with the
study of symbols, the rules in manipulating these symbols, and
the modeling of real-life situations using symbols.
Numerals or Constants
Letters or Variables
(represents unknown values)
Symbols or
Signs
The Language
of
Algebra
Algebraic expression can be a number, a single variable
or a combination of letters, numbers and operational
symbols.
Terms in algebraic expression are
separated by plus (+) or minus (-)
signs.
When the operations between variables or variable
and number is multiplication or division, it is
considered as one term only.
Example: 4xyz is a single term algebraic expression so
𝟐𝟒𝒙
is
since the operations involved are
𝒂𝒃
multiplication and division.
Algebraic expressions are named according to number
of terms.
A. Monomial is an algebraic expression with one term
Examples: 25 , -4a , 9ab
B. Binomial is an algebraic expression with two terms
Examples: 4x – 3 , 11x𝟐y – 3xy , -15a + 4b
C. Trinomial is an algebraic expression with 3 terms
Examples: -4a2 + 2a + 3 , 11x4 – 4x2 – 5x , 3x2 + 2x – 1
the highest exponent of an expression with one
variable or the highest sum of the exponents of the
variables in a term of the expressions.
The degree of a monomial is the
total number of times its
variable occur as factors
Example:
𝑎2𝑏 + 𝑎2𝑏2 − 𝑎𝑏
Example:
−5𝑎𝑏2𝑐3
The degree of a polymial is the
greatest of the degrees of its terms
The degree is 4.
The degree is 6.
1 + 1=2
2+1=3
1 + 2 + 3= 6
2+2=4
a number with fixed value or a
term with no variable
Example:
Identify the constant and variable of:
5x - 2
4x2- 8xy + 3
Constant: -2
Constant: 3
Variables: x and y
Variable: x
a symbol or letter that
represents any number.
Example:
4x 2 - 8xy
It is a constant or a variable or
The term is 2 separated by a minus sign
constants and variables multiplied 𝟒𝒙𝟐 is the first term while 8xy is the
together.
second term
The term’s number part is called
the numerical coefficient while
the variable(s) is/are called the
literal coefficient(s).
Terms in algebraic
Example: 8yz
numerical coefficient:8
literal coefficients:y , z
expression are
separated by plus (+) or
minus (-) signs.
Identify what is asked from the given algebraic expression.
5
Given: 5a + 2a - 3
1. Number of terms
2. Constant
3. Degree
4. Variable/s
5. Type of Algebraic Expression
Identify whether the following is a
monomial, binomial, or trinomial.
6. 2b – 5
7. 4c2+3x – 2
8. abc
Give the degree of the following algebraic
expression:
9. 3x 2 yz + x 3 yz 2
10. 5x4 - 3x + 12
Identify what is asked from the given algebraic expression.
5
Given: 5a + 2a - 3
1. Number of terms
2. Constant
3. Degree
4. Variable/s
3
-3
5
a
5. Type of Algebraic Expression
trinomial
Identify whether the following is a
monomial, binomial, or trinomial.
6. 2b – 5
binomial
7. 4c2+3x – 2 trinomial
8. abc
monomial
Give the degree of the following algebraic
expression:
9. 3x 2 yz + x 3 yz 2 6
10. 5x4 - 3x + 12 4
Keep up the good
work everyone!
See you again
tomorrow!
At the end of the discussion, the student should be able to:



Solve simple equations represented by bar models to find
unknowns.
Distinguish a variable from a constant in an algebraic
expression.
Translate verbal phrases into algebraic expressions.
Algebra – is the branch of Mathematics that deals with the
study of symbols, the rules in manipulating these symbols, and
the modeling of real-life situations using symbols.
Numerals or Constants
Letters or Variables
(represents unknown values)
Symbols or
Signs
The Language
of
Algebra
Symbols used for operations are called
operational symbols while symbols used to
determine relation between quantities are
called relational symbols
In grammar, a phrase is a group of words that
does not express complete thoughts
Mathematical phrase does not express a
complete thought also unless it becomes an
equation.
Let’s
Try!
Mathematical
Term
Mathematical
Symbols /
Operations
Mathematical
Term
Mathematical
Symbols /
Operations
sum
increased
by
difference
plus (+)
multiply
plus (+)
product
quotient
minus (-)
times
multiply
divide
Let’s Remember!
To translate verbal
phrases to mathematical
symbols, it is important
to determine the key
word(s) that will
indicate the correct
fundamental operation to
be used.
Example
Translate the following to mathematical symbols:
1. Thrice the sum of 4 and a number
it could be any letter
Solution:
let n be the number
thrice means 3 times
sum of 4 and a number ( 4 + n)
The mathematical phrase is 3(4 + n)
Example
Translate the following to mathematical symbols:
2. Subtract two-thirds of the number
from thirty
it could be any letter
Solution: let x be the number
two thirds of the number - the
word “of” means multiply
𝟐
x
𝟑
The mathematical phrase is
𝟐
30 - x
𝟑
TRY IT!
Translate the following to mathematical symbols:
1. Five subtracted from thrice a number x
Answer: 3x - 5
thrice a number x: 3x
subtracted from: -
2. A number x increased by 1
increased by 1: +1
a number x: x
3. The product of 5 and twice a number x
Answer: x + 1
Answer: 5 (2x)
twice a number x: 2x
product means: to multiply
Examples
1. Translate 3x - 5 into a verbal
phrase
Key Word: decreased by
Possible verbal phrase :
Thrice a number x decreased by
five
Example
2. Translate 3 + 2x into a verbal
phrase
Key Word: sum of
Possible verbal phrase : The sum of
three and twice a number x
Example
3. Translate 5 ÷ n into a verbal
phrase.
Key Word: divided by
Possible verbal phrase : Five
divided by a number n
TRY IT!
1. Translate c + 10 into a verbal phrase .
Key Word: added to
Possible verbal phrase :
Ten added to a number c
2. Translate m – 5 into a verbal phrase
Key Word: difference
Possible verbal phrase :
The difference between a number m and 5
Homework # 2
Translate each into a mathematical
sentence. Use any letter to represent the
unknown unless otherwise specified.
1) Nine less than a certain number.
2) The sum of 7 and a number.
3) Fives times the product of d and e
4) Four increased by ten
5) The difference of 10 and 4
6) The quotient of 16 and 8
7) A number less than 22
B. Translate each expression in verbal phrase.
8) 14 - n
9) 3(5-m)
10) 6y
Homework # 2
1) Nine less than a certain number.
2) The sum of 7 and a number.
3) Fives times the product of d and e
4) Four increased by ten
5) The difference of 10 and 4
6) The quotient of 16 and 8
7) A number less than 22
B. Translate each expression in verbal phrase.
8) 14 – n
9) 3(5-m)
10) 6y