Algebra: Using Symbols and Shapes to Solve Equations

Detailed Lesson Plan: Algebraic Process (Use of Symbols / Shapes)

Subject: Mathematics

Class: JSS 1

Term: Second Term

Week: 9

Age: 10 – 12 years

Topic: Algebraic Process

Sub-topic: Use of Symbols / Shapes

Duration: 40 minutes

Behavioral Objectives

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

1. Define algebra and explain its importance.
2. Use symbols, letters, or shapes to represent unknown numbers.
3. Interpret and solve simple algebraic expressions.
4. Apply algebraic representation in real-life situations.

Keywords

• Algebra
• Symbols
• Variables
• Expressions
• Letters
• Shapes

Set Induction

The teacher writes the equation “2 + □ = 5” on the board and asks students what number should replace the box. The teacher then explains that in algebra, we use symbols or letters instead of boxes to represent unknown numbers.

Entry Behavior

Students have previous knowledge of basic arithmetic operations (addition, subtraction, multiplication, and division).

Learning Resources and Materials

• Number cards
• Shapes cutouts
• Flashcards with algebraic symbols
• Chart showing algebraic expressions

Building Background / Connection to Prior Knowledge

Students are familiar with using numbers to solve problems. Now, they will learn how to use letters or shapes to replace unknown numbers in an equation.

Embedded Core Skills

• Logical thinking
• Problem-solving
• Creativity
• Critical thinking

Learning Materials

• Lagos State Scheme of Work
• Essential Mathematics for JSS 1

Instructional Materials

• Whiteboard and marker
• Algebra flashcards
• Cut-out shapes for practical demonstration

Content: Algebraic Process (Use of Symbols / Shapes)

Definition of Algebra

Algebra is the branch of mathematics where letters, symbols, or shapes are used to represent unknown numbers in equations.

Why Do We Use Symbols or Shapes in Algebra?

1. To Represent Unknown Numbers – Instead of writing a blank space, we use letters (e.g., x, y) or symbols (□, Δ) to replace missing numbers.
2. To Make Equations Simpler – Algebra allows us to express long mathematical sentences in a short form.
3. To Solve Problems Easily – Many real-life situations involve unknown values, and algebra helps us find them.

Examples of Using Symbols / Shapes in Algebra

1. Using Shapes:

   • If “Δ + 5 = 10”, then “Δ = 5”.
   • If “□ × 2 = 8”, then “□ = 4”.

2. Using Letters:

   • If “x + 3 = 7”, then “x = 4”.
   • If “y – 2 = 6”, then “y = 8”.

3. Using Symbols in a Sentence:

   • “A number increased by 4 is 9” can be written as “x + 4 = 9”.
   • “A number divided by 3 is equal to 5” can be written as “y ÷ 3 = 5”.

Real-Life Applications of Algebra

1. Shopping: If a toy and a ball cost ₦500 together, but the toy costs ₦300, how much is the ball?

   • Let “b” be the cost of the ball: b + 300 = 500.
   • Solving for “b”: b = 500 – 300 = ₦200.

2. Age Calculation: If a father is three times older than his son and the son is 8 years old, how old is the father?

   • Let “f” be the father’s age: f = 3 × 8 = 24 years.

Evaluation: Fill-in-the-Blank Questions with Options

1. Algebra is a branch of mathematics that uses ______ to represent numbers.
   a) Only numbers
   b) Letters and symbols
   c) Only letters
   d) None of the above

2. If “□ + 7 = 12”, what is the value of “□”?
   a) 5
   b) 7
   c) 12
   d) 3

3. The equation “x – 3 = 9” means that x is ______.
   a) 6
   b) 12
   c) 9
   d) 3

4. In the equation “y ÷ 2 = 4”, what is the value of “y”?
   a) 6
   b) 8
   c) 4
   d) 2

5. If a number “z” is multiplied by 5 to get 20, what is “z”?
   a) 2
   b) 4
   c) 5
   d) 10

6. If “□ – 6 = 10”, what is “□”?
   a) 4
   b) 16
   c) 6
   d) 10

7. Algebra helps us solve problems that contain ______.
   a) Only addition
   b) Only subtraction
   c) Unknown numbers
   d) Multiplication only

8. The symbol “□” in an equation represents ______.
   a) A known number
   b) An unknown number
   c) A letter
   d) A word

9. If “y × 4 = 16”, what is the value of “y”?
   a) 4
   b) 8
   c) 2
   d) 16

10. If a box contains “x” apples, and “x = 12”, how many apples are in the box?
    a) 10
    b) 12
    c) 15
    d) 20

Class Activity Discussion: FAQs with Answers

1. What is algebra?
   Algebra is a branch of mathematics that uses symbols or letters to represent numbers in equations.

2. Why do we use symbols or shapes in algebra?
   To simplify equations and represent unknown numbers.

3. What is a variable in algebra?
   A letter or symbol that represents an unknown number.

4. How do you solve “x + 5 = 10”?
   Subtract 5 from both sides: x = 10 – 5, so x = 5.

5. What is an algebraic expression?
   A mathematical phrase that includes numbers, symbols, and operations.

6. Can we use shapes instead of letters in algebra?
   Yes, shapes can represent unknown values in simple equations.

7. What does “y ÷ 2 = 6” mean?
   It means that y is 12, because 12 divided by 2 equals 6.

8. How can algebra be used in daily life?
   It is used in calculating prices, ages, and business profits.

9. Why do we use “x” or “y” in algebra?
   To replace unknown numbers so we can solve for them.

10. What is an equation?
    A mathematical statement that shows two expressions are equal, e.g., x + 3 = 5.

Evaluation Questions (Short Answer Format)

1. Define algebra in your own words.
2. Solve for x: “x + 7 = 15”.
3. Solve for y: “y – 3 = 9”.
4. Write the equation for “A number divided by 4 equals 6”.
5. Find the value of “□” in “□ × 3 = 12”.
6. What is the meaning of a variable?
7. Solve: “y ÷ 5 = 4”.
8. Give an example of how algebra is used in real life.
9. Find “x” if “x – 2 = 10”.
10. Write “A number increased by 5 equals 20” as an equation.

Conclusion

The teacher marks students’ work, provides corrections, and assigns homework for practice.

Addition and Subtraction of Directed Numbers Mathematics JSS 1