Algebraic Perimeter Problems

Name:

Date:

Geometric shapes with algebraic expressions

🎯 WALT (We Are Learning To)

We are learning to:

Write algebraic expressions to represent the perimeter of shapes
Simplify expressions using algebraic properties
Solve real-world problems involving algebraic perimeters
Explain our mathematical reasoning clearly

✅ Success Criteria

I can:

Identify algebraic expressions for unknown side lengths
Write and simplify perimeter expressions correctly
Solve practical perimeter problems with variables
Explain my methods and reasoning

📐 Part 1: Writing Perimeter Expressions

1. A rectangle has length (x + 3) and width (x - 1). Write the algebraic expression for its perimeter.

2. A triangle has sides of length 2x, (x + 5), and (3x - 2). Write and simplify the perimeter expression.

3. A square has side length (2x + 1). What is the perimeter expression in its simplest form?

4. An equilateral triangle has each side measuring (3x - 4) centimetres. Write the simplified perimeter expression.

💡 Hint for struggling learners: Remember that perimeter = sum of all sides. For a rectangle: P = length + width + length + width = 2(length + width)

🔧 Part 2: Real-World Problem Solving

5. A rectangular garden has length (x + 7) metres and width x metres. If x = 4, what is the actual perimeter of the garden?

Step 1: Write the perimeter expression: ________________

Step 2: Substitute x = 4: ________________

Step 3: Calculate the final answer: ________________ metres

6. A triangular park has sides measuring (2x + 3), (x + 8), and (3x - 1) metres. If the total perimeter is 46 metres, find the value of x.

Explain your reasoning:

7. Create Your Own Problem: Design a real-world perimeter problem involving a shape with algebraic side lengths. Include the context, the shape, and show the solution.

Your Problem:

Your Solution:

8. Problem Exchange: Swap your problem from Question 7 with a classmate and solve their problem below.

Classmate's Problem:

Your Solution:

🌟 Extension for Advanced Learners: Create a composite shape (made of rectangles and triangles) with algebraic side lengths. Write and simplify its perimeter expression, then solve for a specific variable value.

🤔 Reflection & Communication

9. Explain in your own words: How do you simplify an algebraic perimeter expression? Give an example.

10. What strategies did you use when solving for unknown variables in perimeter problems?

📚 Key Vocabulary Reminder:

Variable: A letter (like x) representing an unknown number
Expression: A mathematical phrase with numbers, variables, and operations
Like terms: Terms with the same variable (e.g., 3x and 5x)
Simplify: Combine like terms to write in the shortest form

♿ Dyslexia-Friendly Support: Use colour coding for different terms, work step-by-step, and ask for help explaining your thinking verbally if writing is challenging.