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Introduction to Algebraic Concepts

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Introduction to Algebraic Concepts

Introduction to Algebraic Concepts

Algebraic symbols and equations illustration

🔤 Part 1: Understanding Algebraic Vocabulary

1. Match each algebraic term with its correct definition:
1. Variable
2. Constant
3. Coefficient
4. Expression
A. A number that doesn't change (like 5 or 12)
B. A letter that represents an unknown number (like x or n)
C. The number in front of a variable (like the 3 in 3x)
D. A combination of numbers, variables and operations (like 2x + 5)
2. Circle the variable in each expression:

a) 3x + 7 → Circle:

3
x
7

b) 5n - 2 → Circle:

5
n
2

c) 8 + 4y → Circle:

8
4
y

✏️ Part 2: Writing Algebraic Expressions

3. Write an algebraic expression for each situation:

a) Three pencils cost $x each. What is the total cost?

b) A number n increased by 8:

c) Five times a number y minus 3:

d) The cost of 4 books at $b each, plus a $2 delivery fee:

4. Fill in the blanks to complete these expressions:

a) "Two more than a number x" can be written as: x + _____

b) "Four times a number n" can be written as: _____ × n or _____n

c) "A number y decreased by 6" can be written as: y - _____

⚖️ Part 3: Solving Simple Equations

5. Solve these one-step equations. Show your working:

a) x + 7 = 15

b) n - 4 = 11

c) 3y = 21

d) m ÷ 5 = 8

6. Check if these solutions are correct by substituting back into the original equation:

a) If x = 9, does x + 3 = 12? Show your check:

b) If n = 6, does 2n = 12? Show your check:

🔢 Part 4: Patterns and Rules

7. Look at these number patterns and write the algebraic rule:

a) Pattern: 2, 4, 6, 8, 10, ...

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

Rule: The nth term = _____________

b) Pattern: 5, 10, 15, 20, 25, ...

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

Rule: The nth term = _____________

c) Pattern: 1, 4, 7, 10, 13, ...

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

Rule: The nth term = _____________

8. Use your rule from 7a to find:

a) The 10th term: _______

b) The 20th term: _______

c) The 100th term: _______

🧠 Part 5: Real-World Applications

9. Write and solve equations for these real-world problems:

a) Sarah has some stickers. After giving away 8 stickers, she has 15 left. How many stickers did she start with?

Equation: _________________

b) A cinema ticket costs $12. If Jake spent $48 on tickets, how many tickets did he buy?

Equation: _________________

10. Multiple choice: Which equation represents "A number decreased by 7 equals 20"?

x + 7 = 20

x - 7 = 20

7x = 20

x ÷ 7 = 20

🎯 Part 6: Reflection

11. In your own words, explain what a variable is and give an example:
12. What is one thing you found challenging about algebra today?
13. Write one question you still have about algebraic expressions or equations:

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