Learn to use letters and symbols to represent unknown numbers in mathematical expressions. Master variables through age problem solving activities.
Scenario: You're solving age mysteries! Sarah is 8 years old, and her mom is 25 years older than her. How old is Sarah's mom? Instead of writing "Sarah's mom's age," we can use a letter like 'm' to represent the unknown age. So we write: m = 8 + 25 = 33.
This is your introduction to algebra! Letters and symbols can represent unknown numbers, making math problems easier to solve and understand.
Variables are letters or symbols that represent unknown numbers. They're like placeholders for numbers we don't know yet.
An algebraic expression combines numbers, variables, and operations (+, -, ×, ÷) without an equals sign.
Look for words like "how many," "what number," or "unknown" in word problems. These tell you there's a number you need to find.
Example: "How old is Tom?" → Tom's age is unknown, so we can use 't' for Tom's age
Pick a letter that makes sense for the unknown. Use the first letter of what you're looking for, or common letters like x, y, n.
Example: "How many apples?" → use 'a' for apples, or 'n' for number
Translate word problems into algebraic expressions using your chosen variables and the given information.
Example: "5 more than a number" → x + 5
Choose a variable for each unknown:
Write expressions for these phrases:
1. Choose a variable for "how many cookies"
2. Choose a variable for "what's the height"
3. Choose a variable for "how many days"
4. Choose a variable for "what's the price"
5. Write an expression for "5 more than x"
6. Write an expression for "3 times y"
7. Write an expression for "n minus 4"
8. Write an expression for "a divided by 2"
9. Tom is 12. His sister is 3 years older. Write an expression for his sister's age.
10. A book costs $8. You have $20. Write an expression for how much money you'll have left.
11. You have 15 stickers. You give away some. Write an expression for how many you have left.
12. A rectangle has length 5 and width w. Write an expression for the area.
Wrong: Using 'x' for both age and weight in the same problem
Correct: Use 'a' for age and 'w' for weight
Wrong: "5 more than a number" → 5x
Correct: "5 more than a number" → x + 5
Variables represent unknown numbers in math problems
Choose meaningful letters for your variables
Algebraic expressions combine numbers, variables, and operations
Practice translating word problems into algebraic expressions