Mathematics: Solving Algebraic Equations
Grade 7 - 4th Quarter - Week 4 Day 2
This lesson focuses on solving simple equations using properties of equality. Students will learn how to apply algebraic principles to solve problems in real-life scenarios.
Course Overview
Content Standards
The learners should have knowledge and understanding of the solution of simple equations.
Performance Standards
By the end of the quarter, the learners are able to solve simple equations.
Learning Competencies
The learners... 2. Solve problems involving algebraic expressions and formulas.
Content: Algebraic Equation
1
Week 4 Focus
Algebraic Equation
2
Specific Topic
2.2 Solving Equations by Applying Properties of Equality
Short Review:
Help Me!
Let us help Shaina find her easy way home. The other way she was using was closed due to the pavement of the road, so she needed to find another way to go home.
Solve Equations
To help Shaina, let us solve the following equations and find the correct route going to their home.
Lesson Activity Answer:
6x = -36
x = -6
x - 10 = -20
x = -10
x + 9 = 12
x = 3
-7 = x/7
x = -49
x - 5 = -14
x = -9
-21 = 3x
x = -7
Lesson Activity Answer
Correct Path: B
The correct solution path through our maze activity is option B, which leads Shaina safely home.
Success!
By correctly solving these equations using properties of equality, we've helped Shaina find her way home.
Essential Question
How do you justify your process for solving an equation?
Key Vocabulary
1
Equivalent Equations
Equations that have the same solutions
2
Solution
A value that makes an equation true
3
Inverse Operations
Two operations that undo each other
4
Linear Equation
Equation in form ax + b = 0
5
Equation
Statement that two expressions are equal
Unlocking Vocabulary Content
Equation
A statement that two expressions are equal
Linear equation in one variable
An equation that can be written in the form ax + b = 0, where a and b are constants and a does not equal zero
Solution
A value that makes an equation true
Inverse operations
Two operations that undo each other
Equivalent equations
Equations that have the same solutions
Introductory Video
Watch
The student will watch a short video about Justify using Properties of Equality.
Link
https://www.youtube.com/watch?v=H8wr6UOpmjc
Benefit
By watching the video, students who did not understand the lesson yesterday will be able to grasp the concepts better.
Real-Life Equation Scavenger Hunt
1
2
3
4
Group Formation
Divide the class into small groups (3-5 students per team).
Station Setup
Place task cards around the room with different real-life scenarios requiring students to set up and solve equations.
Process
Teams read the scenario, write an equation, and solve it using Properties of Equality.
Completion
After all teams finish, the class reviews the solutions together.
Scavenger Hunt Instructions
Divide into Teams
Divide the class into small groups (3-5 students per team).
Setup Stations
Place task cards around the room with different real-life scenarios requiring students to set up and solve equations. Each team starts at a different station.
Solve Equations
Teams read the scenario, write an equation, and solve it using Properties of Equality. Once they solve it, they write their answer on a sheet and move to the next station.
Review Solutions
After all teams finish, the class reviews the solutions together. The team with the most correct answers wins!
Real-Life Scenario 1
1
Real-Life Scenario
"Maria is saving money for a new phone. She already saved Php1500 and needs a total of Php2000. If she saves the same amount each week for 6 weeks, how much does she need to save per week?"
2
Write Equation
1500 + 6x = 2000
3
Apply Properties
1500 + 6x - 1500 = 2000 - 1500
4
Solve
6x = 500, x = 83.33
Real-Life Scenario 1 Solution
Set Up Equation
1500 + 6x = 2000
1
Subtract 1500
6x = 500
2
Divide by 6
x = 500 ÷ 6 = 83.33
3
Check Answer
Maria needs to save approximately Php83.33 per week
4
Real-Life Scenario 2
Problem Statement
"A jacket costs Php600 after a Php15 discount. What was the original price?"
Equation
x - 15 = 600
Solution
x - 15 + 15 = 600 + 15 x = 615
Real-Life Scenario 3
Problem
"A cake recipe calls for 3 cups of flour to make 12 servings. How much flour is needed for 20 servings?"
Equation Setup
3/12 = x/20
Solution
Cross multiply: 3 × 20 = 12 × x 60 = 12x x = 5
Real-Life Scenario 4
60
Speed (km/h)
The car's constant speed
240
Distance (km)
Total distance to travel
4
Time (hours)
Time needed for the journey
"A car travels at 60 km per hour. How long will it take to travel 240 km?"
Equation: 60t = 240�Solution: t = 240 ÷ 60 = 4 hours
Final Review & Reflection
Addition Property
Subtraction Property
Multiplication Property
Division Property
Substitution
This chart represents the relative frequency of different properties of equality used in solving algebraic equations.
Reflection Question 1
1
How did we use Properties of Equality in solving these problems?
We used Addition and Multiplication Properties to keep the equations balanced and find the unknown value.
2
Why is it important to check our solutions?
Checking ensures the solution satisfies the equation, making it valid.
3
How can we apply equations in our daily lives?
Budgeting, shopping, cooking, traveling, and other decision-making scenarios require solving for unknowns.
Addition Property of Equality
Identify
Recognize when a variable needs a value added to isolate it
Apply Same Addition
Add the same value to both sides of the equation
Simplify
Combine like terms on each side
Verify
Check that the variable is now isolated or closer to being isolated
Subtraction Property of Equality
The subtraction property of equality states that subtracting the same value from both sides of an equation maintains the equality. This is essential for isolating variables when they have terms added to them.
Example: In x + 7 = 12, we subtract 7 from both sides to get x = 5.
Multiplication Property of Equality
Eliminating Fractions
The multiplication property is especially useful when dealing with equations involving fractions, as multiplying both sides by the denominator simplifies the equation.
Solving for Coefficients
When a variable has a coefficient other than 1, we can multiply or divide both sides by the appropriate value to isolate the variable.
Division Property of Equality
Definition
The division property of equality states that dividing both sides of an equation by the same non-zero value maintains the equality.
Application
This property is essential when a variable is multiplied by a coefficient and we need to isolate the variable.
Example
In the equation 6x = -36, we can divide both sides by 6 to get x = -6.
Caution
Remember that we can never divide by zero, as division by zero is undefined.
Evaluating Learning
Answer the real-life problem solving on a ¼ sheet of paper. Please provide the equation and solution to the answer.
1
Problem
Carlos works part-time and earns Php120 per hour. Last week, he earned a total of Php1800. How many hours did he work?
2
Answer
Equation: 120x = 1800 x = 15
Step-by-Step Solution
Set Up
120x = 1800 (hourly rate × hours = total earnings)
Apply Division
120x ÷ 120 = 1800 ÷ 120
Solve
x = 15 hours
Verify
120 × 15 = 1800 ✓
Real-World Applications
Financial Planning
Calculate savings, interest, and budgets
1
Shopping
Determine discounts, taxes, and unit prices
2
Cooking
Adjust recipe ingredients for different serving sizes
3
Travel
Calculate time, distance, speed, and fuel consumption
4
Work
Determine hours, pay rates, and project timelines
5
Common Mistakes to Avoid
Applying operations to only one side
Remember to perform the same operation on both sides of the equation to maintain equality.
Sign errors
Be careful with negative numbers when adding, subtracting, multiplying, or dividing.
Forgetting to check solutions
Always verify your answer by substituting it back into the original equation.
Arithmetic errors
Double-check your calculations to avoid simple computational mistakes.
Balancing Equations: A Visual Approach
Balance Principle
Think of an equation as a balance scale. Whatever you do to one side, you must do to the other to maintain balance.
Addition/Subtraction
Adding or subtracting the same weight from both sides keeps the scale balanced.
Multiplication/Division
Multiplying or dividing both sides by the same value maintains the proportion and keeps the scale balanced.
Solving Two-Step Equations
Step 1: Isolate Variable Term
Use addition or subtraction to get the variable term alone on one side.
Step 2: Isolate the Variable
Use multiplication or division to solve for the variable.
Step 3: Check Your Answer
Substitute your answer back into the original equation to verify.
Group Practice Activity
1
Form Groups
Divide into teams of 3-4 students.
2
Assign Problems
Each group receives a set of real-world equations to solve.
3
Solve and Explain
Work together to solve each problem, documenting your steps.
4
Present Solutions
Share your solutions with the class, explaining your reasoning.
5
Reflect
Discuss as a class which properties were most useful for each problem.
Summary of Properties of Equality
Property
Description
Example
Addition
Add the same value to both sides
x - 5 = 7; x - 5 + 5 = 7 + 5; x = 12
Subtraction
Subtract the same value from both sides
x + 9 = 12; x + 9 - 9 = 12 - 9; x = 3
Multiplication
Multiply both sides by the same non-zero value
x/7 = -7; x/7 × 7 = -7 × 7; x = -49
Division
Divide both sides by the same non-zero value
6x = -36; 6x/6 = -36/6; x = -6
Homework Assignment
Instructions
Complete the following real-world problems using the properties of equality we discussed in class. Show all your work including the equation setup and solution steps.
Problem 1
A concert ticket costs x pesos after a 15% discount, making the final price 425 pesos. What was the original price?
Problem 2
Juan needs to achieve an average of 85 on four tests. If he scored 82, 88, and 79 on the first three tests, what score does he need on the fourth test?
Due Date
Submit your completed work at the beginning of our next class meeting.
Reflection and Preparation
Teacher Reflection
Prepared by: ___________________ Subject Teacher
Reviewed by: ___________________ Master Teacher/Head Teacher
Student Reflection
Take a moment to reflect on today's lesson. What concepts are you confident about? Which areas might you need additional practice with? How might you apply these equation-solving skills in your daily life?
Next Steps
In our next lesson, we'll build on these equation-solving skills to tackle more complex problems and applications. Come prepared with any questions about today's material.