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Variables and Algebraic Expressions

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Variables and Algebraic Expressions

Algebraic expressions illustration

📚 Part 1: Understanding Variables

1. What is a variable in algebra?

A number that never changes

A symbol that represents an unknown quantity

A mathematical operation like + or -

The answer to an equation

2. Which of these are correct ways to write "3 times b" in algebraic notation? (Tick all that apply)

3b

3 × b

3xb

b3

3. Look at this pattern: 5, 8, 11, 14, 17, ...

What is the constant increase? _______

What variable could you use to represent the position in the pattern? _______

✏️ Part 2: Writing Algebraic Expressions

4. A cinema ticket costs $12. Write an algebraic expression for the total cost of n tickets.
5. Complete the table for the pattern that starts at 3 and increases by 4 each time:

Position (n): 1, 2, 3, 4, 5

Value: 3, 7, 11, _____, _____

Algebraic rule: ________________

6. Sarah has $50 and spends $8 each week. Write an expression for how much money she has left after w weeks.
7. Translate these word expressions into algebraic expressions:

a) A number x increased by 7: __________

b) Five times a number y: __________

c) A number m decreased by 12: __________

d) Half of a number p: __________

🎯 Part 3: Problem Solving

8. A rectangular garden has a length that is 5 metres more than its width. If the width is w metres, write expressions for:

a) The length: __________

b) The perimeter: __________

9. Look at this growing pattern of squares:

Pattern 1: 4 squares

Pattern 2: 7 squares

Pattern 3: 10 squares

Pattern 4: 13 squares

a) How many squares would be in Pattern 10? __________

b) Write an algebraic rule for Pattern n: __________

10. Explain in your own words how you found the rule in question 9:

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