Algebraic Expression
Quarter 4 Week 2 Day1
Lord Jesus, I ask for Your help as I begin this new school year. Allow me to experience Your presence in the many blessings You put before me. Open my eyes to the new challenges and exciting opportunities that this new school year brings. Open my heart and mind to new friends and new teachers. Give me a generous spirit to be enthusiastic with my studies and courage to accept new opportunities. Help me to be attentive to my teachers and let me experience Your presence in my new friends. Jesus, inspire me to do my best this year! Amen.
PRAYER
ATTENDANCE
Provide students with a list of verbal phrases and ask them to translate each into an algebraic expression. Example phrases: "Four more than twice a number"
"The difference between a number and three"
"Five times the sum of a number and two"
"The product of a number and nine, decreased by six" "The ratio of a number and four, minus seven"
Feedback (Optional)
Like how your facial expression can convey your emotions, a mathematical expression illustrates the value of the variables provided.
DAY 1 Short Review
Hook: Start with a real-life problem that can be modeled by an algebraic expression. For example, "If you earn Php10 per hour and work h hours, how much do you earn in total?" Introduce the expression 10h.
Lesson Purpose
Match the non-math definition to the words related to the lesson
1. Refers to replacing one player on the court with another from the team's bench.
2. Means carefully looking at something, thinking about it, and deciding its value or importance.
Unlocking Content Vocabulary
3. The act of including or combining something with another to make it larger or more complete.
4. In a painting, artists sometimes scrape off paint or cover parts of the canvas to create negative space or draw attention to specific elements.
5. Reproducing or creating additional instances or versions of something to increase availability, distribution, or impact. Choices: Addition, Multiplication Subtraction, Substitution, Evaluate
SUB-TOPIC 1: Evaluating Algebraic Expressions and its Applications.
Explicitation
Meaning of Algebraic Expressions
An algebraic expression is a mathematical phrase that includes numbers, variables, and operations (addition, subtraction, multiplication, division, exponents). Unlike equations, algebraic expressions do not have an equal sign (=).
1. 3x+5
2. 2a−7b
3. 4m2+6m−3
In these expressions:
• Variables (e.g., x,a,b,mx, a, b, m) represent unknown values.
• Constants (e.g., 5, -7, -3) are fixed numbers.
• Coefficients (e.g., 3 in 3x3x3x, 2 in 2a) are numbers multiplying a variable.
Examples of Algebraic Expressions:
To evaluate an algebraic expression, substitute given values for the variables and perform the operations following the order of operations (PEMDAS):
• Parentheses
• Exponents
• MD Multiplication and Division (from left to right)
• AS Addition and Subtraction (from left to right)
Evaluating Algebraic Expressions
Example 1: Evaluate 4x−2 when x=3.
Solution:
4(3)−2=12−2=10
Example 2: Evaluate 5a+2b when a=2, b=4.
Solution:
5(2)+2(4)=10+8=18
To evaluate algebraic expressions, replace the given values for the variables and then simplify the resulting numerical expressions.
1. Substitute the given values for each variable.
2. Simplify first the expression within the parenthesis.
3. Perform all indicated operations and simplify the result.
Steps to follow in evaluating algebraic expressions:
Worked Example
Example no. 1
Evaluate a+7 when:
1. a=3
2. a=12
1. To evaluate, substitute 3 for a in the expression, and then simplify. a+7
Substitute. 3+7
Add. 10
When a=3, the expressiona+7 has a value of 10.
Worked Example
2. To evaluate, substitute 12 for a in the expression, and then simplify. a+ 7
Substitute. 12+7
Add. 19
When a=12, the expression a+7 has a value of 19.
Worked Example
Example no. 2
Evaluate 9x−2, when
1. x=5
2. x=1
Solution:
Remember ab means a times b, so 9x means 9 times x.
1. To evaluate the expression when x=5, we substitute 5 for x, and then simplify. 9x-2
Substitute 9(5) - 2
Multiply. 45-2
Subtract 43
2. To evaluate the expression when x=1, we substitute 1 for x, and then simplify. 9x-2
Substitute 9(1) - 2
Multiply. 9-2
Subtract 7
Example no. 3
Evaluate x2 when x=10.
Solution: We substitute 10 for x, and then simplify the expression. x2
Substitute 10 for x 102 Use the definition of exponent. 10 x 10
Multiply. 100
When x=10, the expression x2 has a value of 100.
Example no. 4
Example no. 5
Generalization:
• An algebraic expression is a mathematical phrase containing numbers, variables, and operations.
• Evaluating an algebraic expression means substituting given values for the variables and solving using the order of operations (PEMDAS).
• What is an algebraic expression?
• How do you evaluate an algebraic expression?
• What are the steps in the order of operations (PEMDAS)?
• Solve: Evaluate 3x+2y3x + 2y3x+2y when x=4x = 4x=4 and y=5y = 5y=5.
• Give one real-life situation where algebraic expressions are used.
(Choose the correct answer)
Multiple Choice
2. Which of the following is an algebraic expression?
a) 5+3=8
b) 2x+4
c) 10>5
d) 7−2=5
3. In the algebraic expression 4x+7, what is the coefficient of x?
a) 4
b) 7
c) x
d) 11
4. If y=3y = 3y=3, what is the value of 2y+5?
a) 6
b) 8
c) 11
d) 12
5. Which real-life situation best represents an algebraic expression?
a) The total price after a discount
b) Counting the number of apples in a basket
c) Checking the time on a clock
d) Naming the days of the week
THANK YOU