Solving Literal Equations
Content Standards and Learning Competencies
Content Standards
The learner should understand the rearrangement of a formula to make a different variable the subject of the formula.
Performance Standards
By the end of the lesson, the learners are able to rearrange a formula to make a different variable the subject of the formula. (NA)
Learning Competencies
LC 9. Solve Problems Involving literal equations.
Objectives
1. Accurately solve problems involving literal equations.
Lesson Overview
1
Subject
MATHEMATICS
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Grade Level & Section
Grade 7
3
Quarter
4th Quarter
4
Week
Week 5 D3
5
Topic
Solving Literal Equations
Learning Resources
1
Amusing Algebra (2024)
Solving literal equations clue mystery activity. https://www.teacherspayteachers.com/Product/Solving-Literal-Equations-Clue-Mystery-Activity-6109358?st=e2ed7bee0bf6ad1824978c9f5fd01822
2
Cachet (2014)
Rate-Time-Distance problems (Powerpoint slides). https://www.slideserve.com/cachet/4-8-rate-time-distance-problems
3
Chilimath (2024)
Solving Literal Equations. Chilimath. https://www.chilimath.com/lessons/intermediate-algebra/literal-equations/
4
Glencoe & McGraw-Hill (n.d.)
Teaching Algebra with Manipulatives. Sault Area Public Schools. https://www.saultschools.org/cms/lib/mi17000143/centricity/domain/137/a2tam.pdf
Additional Learning Resources
1
Metropolitan Community College (n.d.)
Solving Literal Equations. Metropolitan Community College. https://mcckc.edu/tutoring/docs/blue-river/math/equat_inequ/Practice_Solving_Literal_Equations.pdf
2
Oronce, O.A., et al (2007)
e-math I Elementary Algebra. Rex Bookstore, Inc. Sampaloc, Manila
3
Pleacher, D. (n.d.)
Equation Analysis Test #2. Pleacher. https://www.pleacher.com/mp/puzzles/mathpuz/eqtstan3.html2
4
S2Tem Centers (2019)
Literal Equations Breakout. S2Tem Centers. https://www.s2temsc.org/uploads/1/8/8/7/18873120/solvingliteralequationsbreakout.pdf
5
Studylib (n.d.)
Equation Analysis Assessment. Studylib. https://studylib.net/doc/9713503/equation-analysis-assessment
Activating Prior Knowledge
Recall Previous Concepts
Students recall their understanding of solving equations for a variable.
Identify Inverse Operations
Review how to use inverse operations such as addition, subtraction, multiplication, or division.
Understand the Goal
Recognize that the goal is to isolate the variable (get it alone on one side of the equation).
Lesson Purpose and Intention
Clear Objective
Today, we will Solve Problems Involving Literal Equations
Formula Rearrangement
Learn to rearrange formulas to make different variables the subject
Real-World Application
Apply literal equations to solve practical problems
Reading the Key Idea: Solving Problems Involving Literal Equations
Recall Previous Activity
Remember "The Road Trip Query" from the previous lesson where you solved for t in the formula d = rt.
Continue Problem Solving
Apply the formula to solve the complete problem.
Answer Key Questions
What is the formula for finding "t" in d=rt? What are the given data? How will you solve for time? How long will they travel for the 240-kilometer trip?
George Polya's Problem-Solving Steps
1. Understand the Problem
Identify what is given and what needs to be found
1
2. Make a Plan
Determine which formula to use and how to approach the solution
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3. Carry Out the Plan
Execute the calculations and solve for the unknown variable
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4. Look Back and Reflect
Check if the answer makes sense and is reasonable
4
Worked Example: The Road Trip Problem
Problem Statement
Two friends Ben and John are having a road trip when they pass by a road sign "Speed Limit 60kph". Ben asked his friend "If we need to travel for 240 kilometers to our destination? How long are we going to travel?"
Understand the Problem
Given: Speed (r) = 60 kph, Distance (d) = 240 km; Unknown: Time (t)
Make a Plan
Use the formula d = rt and solve for t
Carry Out the Plan
t = d/r = 240 km ÷ 60 kph = 4 hours
Teaching Notes on Problem Solving
Connect to Prior Knowledge
You can ask the learners, what steps in solving problems they used in their elementary. Then connect it to George Polya's steps.
Apply Literal Equations
Let the learners apply the literal equations they solved in dealing with the word problems.
Emphasize Units
Emphasize that a unit of measure is needed in giving the final answer.
Activity 4: Let's Solve! - Problem 1
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Problem Statement
Find the diameter of a coin if the circumference is 22 centimeters. (Use π = 3.14)
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Formula Application
Use the formula for circumference: C = πd
3
Solve for Diameter
d = C/π = 22 cm ÷ 3.14 = 7 cm
Activity 4: Let's Solve! - Problem 2
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Solution
s = 11 cm
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Calculation
s = P ÷ 4 = 44 cm ÷ 4 = 11 cm
3
Formula
P = 4s for a square
4
Problem
The perimeter of a square picture frame is 44 cm. Find the length of a side of the picture frame.
Activity 4: Let's Solve! - Problem 3
Problem Statement
The perimeter of a rectangular swimming pool is 56 meters. Its length is 12 meters. Find the width of the swimming pool.
Formula and Solution
Using the perimeter formula for a rectangle: P = 2l + 2w
56 = 2(12) + 2w
56 = 24 + 2w
32 = 2w
w = 16 meters
Activity 4: Let's Solve! - Problem 4
Problem Statement
Two sides of a triangle have lengths 5dm and 8dm. The perimeter is 20dm. Find the length of the third side of the triangle.
Formula Application
Perimeter of triangle = sum of all sides
20 = 5 + 8 + third side
Solution
Third side = 20 - 5 - 8 = 7 dm
Activity 4: Let's Solve! - Problem 5
Problem Statement
The area of a rectangular lot is 63 square meters. The width of the lot measures 7 meters. Find its length.
Formula and Solution
Area of rectangle = length × width
63 = length × 7
length = 63 ÷ 7 = 9 meters
Making Generalizations and Abstractions
One-Minute Paper
Learners create a "One-Minute Paper" where they write down the most important concept they learned and a question they still have.
Pair Discussion
Students pair up to discuss their insights and clarify doubts about literal equations.
Reflection
Students consider how literal equations apply to real-world situations and problem-solving.
Evaluation: Problem 1
Problem Statement
Marie is traveling to her grandmother's house which is 360 kilometers away. If she drives at a constant speed of 90 km/h, how many hours will it take for her to reach her destination?
Formula
d = r × t
Solution
t = d ÷ r = 360 km ÷ 90 km/h = 4 hours
Evaluation: Problem 2
Problem Statement
A triangular billboard has an area of 45 square feet and a base of 15 feet. Find the height of the billboard.
Formula
A = ½ × b × h
Where A is area, b is base, and h is height
Solution
45 = ½ × 15 × h
45 = 7.5 × h
h = 45 ÷ 7.5 = 6 feet
Evaluation: Problem 3
Problem Statement
A rectangular garden has a length of 40 meters and a width of xxx meters. If the perimeter of the garden is 130 meters, find the width of the garden.
Formula
P = 2l + 2w
Solution
130 = 2(40) + 2w
130 = 80 + 2w
50 = 2w
w = 25 meters
Evaluation: Problem 4
1
Problem Statement
A bus travels 180 kilometers at a speed of 60 km/h. How many hours will it take to complete the trip?
2
Formula
d = r × t
3
Solution
t = d ÷ r = 180 km ÷ 60 km/h = 3 hours
Evaluation: Problem 5
Problem Statement
A triangular signboard has an area of 36 square inches and a height of 9 inches. Find the length of its base.
Formula
A = ½ × b × h
Where A is area, b is base, and h is height
Solution
36 = ½ × b × 9
36 = 4.5 × b
b = 36 ÷ 4.5 = 8 inches
Answer Key for Evaluation Problems
4
Problem 1
Hours for Marie to reach grandmother's house
6
Problem 2
Height of triangular billboard in feet
25
Problem 3
Width of rectangular garden in meters
3
Problem 4
Hours for bus to complete trip
8
Problem 5
Base length of triangular signboard in inches
Formula Transformations in Literal Equations
This chart illustrates the relative complexity levels of different formula types when solving literal equations. Distance-Rate-Time formulas are typically the most straightforward, while Volume formulas tend to be more complex due to having more variables and often involving exponents.
Common Formulas for Literal Equations
These common formulas are frequently used when solving literal equations in Grade 7 Mathematics. Students should become familiar with manipulating these formulas to solve for different variables.
Steps for Solving Literal Equations
Step 1: Identify the Variable
Determine which variable you need to solve for in the given formula.
Step 2: Rearrange Terms
Move all terms containing the target variable to one side of the equation.
Step 3: Factor Out the Variable
If necessary, factor out the target variable from all terms containing it.
Step 4: Isolate the Variable
Divide both sides by the coefficient of the variable to solve for it.
Real-World Applications of Literal Equations
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Transportation
Calculating travel time, distance, or speed using d = rt
Construction
Finding dimensions of structures using perimeter and area formulas
Finance
Calculating interest, principal, or time using interest formulas
Science
Determining force, mass, or acceleration using F = ma
Engineering
Calculating electrical values using Ohm's Law (V = IR)
Common Mistakes in Solving Literal Equations
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Incorrect Application of Operations
Applying addition when multiplication is needed or vice versa.
2
Forgetting to Apply Operations to All Terms
Only applying an operation to one term instead of all terms on one side of the equation.
3
Sign Errors
Making mistakes with positive and negative signs when rearranging terms.
4
Unit Conversion Errors
Forgetting to convert units or using inconsistent units in calculations.
5
Omitting Units in Final Answer
Not including the appropriate unit of measure in the final answer.
Tips for Success with Literal Equations
Regular Practice
Solve a variety of problems regularly to build confidence and skill.
Double-Check Work
Verify your solution by substituting it back into the original equation.
Mind Your Units
Always include appropriate units in your final answer.
Organize Your Work
Write each step clearly to avoid careless errors and make it easier to check your work.
Ask Questions
Don't hesitate to seek clarification when you're unsure about a concept or procedure.
Lesson Reflection and Next Steps
Key Takeaways
Literal equations are formulas with multiple variables that can be rearranged to solve for any variable.
Skills Developed
Students have practiced isolating variables, applying formulas to real-world problems, and following a systematic problem-solving approach.
Future Applications
These skills will be essential in more advanced mathematics courses and in practical situations requiring mathematical problem-solving.
Next Lesson Preview
In our next lesson, we will explore more complex applications of literal equations in various fields.