Algebraic Word Problems: Using Algebra to Solve Equations

WEEK 10: USING ALGEBRA FOR SOLVING WORD PROBLEMS

Subject: Mathematics

Class: JSS 1

Term: Second Term

Week: 10

Age: 10 – 12 years

Topic: Using Algebra for Solving Word Problems

Sub-topic: Understanding and Applying Algebra to Solve Word Problems

Duration: 40 minutes

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Behavioural Objectives

By the end of the lesson, students should be able to:

1. Identify unknown values in word problems and represent them using algebraic symbols.
2. Form simple algebraic equations based on given word problems.
3. Solve basic algebraic equations using addition, subtraction, multiplication, and division.
4. Apply algebraic problem-solving techniques in real-life situations.

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Keywords

• Algebra
• Equation
• Variable
• Unknown number
• Word problems

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Set Induction

The teacher will begin by asking the students simple numerical puzzles such as:

• “I am thinking of a number. If I add 5 to it, the result is 12. What is the number?”
• “If a number is multiplied by 3, the result is 21. What is the number?”

Students will attempt to solve these problems mentally before being introduced to algebraic expressions.

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Entry Behaviour

Students are already familiar with basic operations such as addition, subtraction, multiplication, and division.

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Learning Resources and Materials

• Number cards
• Algebraic equation charts
• Whiteboard and marker
• Flashcards with algebraic word problems

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Building Background/Connection to Prior Knowledge

The teacher will remind students about their previous lessons on algebraic symbols and how they represent numbers in expressions.

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Embedded Core Skills

• Critical Thinking
• Problem-Solving
• Numeracy
• Logical Reasoning

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Learning Materials

• Lagos State Scheme of Work
• Mathematics Textbook for JSS 1
• Teacher’s Lesson Notes

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Instructional Materials

• Chart showing algebraic expressions and their meanings
• Word problem flashcards
• Number line

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Content

Definition and Explanation of Algebraic Word Problems

1. Algebra is the branch of mathematics that deals with numbers and symbols (letters) to represent unknown values.
2. In algebra, we use letters like $x$, $y$, or $n$ to represent unknown numbers.
3. A word problem describes a mathematical situation that we need to translate into an equation and solve.

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Steps for Solving Word Problems in Algebra

1. Identify the unknown number and represent it with a letter (e.g., $x$).
2. Translate the word problem into an algebraic equation.
3. Solve the equation using basic operations.
4. Check the solution by substituting the value back into the original problem.

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Examples

Example 1:

What number when added to 8 gives 20?

Solution:
Let the unknown number be x
Equation:
$x+8=20$
Subtract 8 from both sides:
x=20−8
$=12$
The number is 12.

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Example 2:

Think of a number. Subtract 5 from it and the result is 15. What is the number?

Solution:
Let the unknown number be x
Equation:
$x-5=15$
Add 5 to both sides:
$x=15+5$
$=20$
The number is 20.

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Example 3:

When a number is multiplied by 5, the result is 20. What is the number?

Solution:
Let the unknown number be x
Equation:
5x=20
Divide both sides by 5:
x=20÷5
$=4$
The number is 4.

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More Examples

4. A number divided by 4 gives 3. What is the number?
5. A certain number added to 10 results in 25. What is the number?
6. If 3 times a number equals 18, find the number.
7. A number decreased by 7 equals 12. Find the number.
8. Twice a number is equal to 30. What is the number?
9. When a number is divided by 5, the result is 6. Find the number.
10. The sum of a number and 14 equals 40. Find the number.

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Evaluation (Fill-in-the-Blank Questions with Options)

Choose the correct answer for each question.

1. If $x+5=15$, then x is ___.
   a) 5
   b) 10
   c) 15
   d) 20

2. A number multiplied by 6 gives 42. The number is ___.
   a) 5
   b) 6
   c) 7
   d) 8

3. If $=10$, then x is ___.
   a) 6
   b) 12
   c) 14
   d) 16

4. When a number is divided by 3, the result is 9. The number is ___.

5. The sum of a number and 20 is 50. The number is ___.

6. A number doubled equals 36. Find the number.

7. If $x+7=21$, then x is ___.

8. A number divided by 2 gives 8. What is the number?

9. If 5 times a number equals 45, find the number.

10. A number decreased by 9 results in 15. What is the number?

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Class Activity Discussion (FAQs with Answers)

1. What is algebra?
   Algebra is the use of symbols and letters to represent numbers in equations.

2. Why do we use letters in algebra?
   Letters help us represent unknown values in a problem.

3. What are algebraic equations?
   They are mathematical statements that show relationships between numbers and symbols.

4. How do I solve an algebraic word problem?
   Identify the unknown, form an equation, and solve for the unknown.

5. What is a variable in algebra?
   A variable is a letter that represents an unknown number.

6. Can algebra be used in real life?
   Yes, algebra helps in budgeting, calculations, and problem-solving.

7. What operation should I use to solve “A number plus 7 equals 20”?
   Use subtraction: $x+7=20$ so $x=20-7$.

8. How do I check my answer?
   Substitute your answer into the original equation.

9. What does “solve for x” mean?
   It means finding the value of x that makes the equation true.

10. Why is algebra important?
    Algebra is a foundation for advanced mathematics and real-life applications.

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Teacher’s Activities

• Explain algebraic word problems with real-life examples.
• Guide students in forming and solving equations.
• Use number lines and charts to demonstrate solutions.

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Learners’ Activities

• Answer algebraic word problems.
• Form equations from given statements.
• Solve equations using different methods.

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Evaluation Questions (Short Answers)

1. Solve for x: x+4=12
2. If 3x=27, find x.
3. A number subtracted by 6 equals 10. Find the number.
4. Solve for x: 2x=18 
5. When a number is divided by 7, the result is 5. Find the number.

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Conclusion

The teacher marks and provides feedback on students’ work.

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Algebra: Using Symbols and Shapes to Solve Equations