Imagine a balance scale with 3 apples on one side and 2 apples + a 100g weight on the other side. It balances perfectly.
🍎🍎🍎 = 🍎🍎 + 100g
🤔 How much does one apple weigh? Can you write this as an equation?
Think about: If both sides balance, they're equal. Let a = weight of one apple. Then 3a = 2a + 100. Subtract 2a from both sides: a = 100g. That's algebra!
Observation 2: Age Puzzle
"I am twice as old as my sister. In 5 years, I will be 1.5 times her age."
🤔 How old are we now? Can you find the ages?
Think about: Let sister's age = x, my age = 2x. In 5 years: (2x + 5) = 1.5(x + 5). Solve: 2x + 5 = 1.5x + 7.5 → 0.5x = 2.5 → x = 5. So sister is 5, I'm 10.
Observation 3: Shopping Bill
You buy 3 pens and 2 notebooks for $11. Your friend buys 1 pen and 3 notebooks for $13. All pens cost the same, all notebooks cost the same.
🤔 How much does one pen cost? One notebook?
Think about: Let p = pen price, n = notebook price.
3p + 2n = 11
1p + 3n = 13
This is a system of equations. Solve to find p = $1, n = $4.
Observation 4: Number Patterns
Look at this sequence: 2, 5, 8, 11, 14, ...
🤔 What's the pattern? What will be the 10th number? Can you find a formula?
Think about: Each number adds 3. This is an arithmetic sequence. Formula: a_n = 2 + (n-1)×3. For n=10: 2 + 9×3 = 29.
Observation 5: Rectangular Garden
A rectangular garden has length 5 meters more than its width. Its area is 84 square meters.
🤔 What are the length and width? Can you set up an equation?
Think about: Let width = w, length = w + 5. Area = w(w + 5) = 84. That's w² + 5w - 84 = 0. Solve quadratic: (w + 12)(w - 7) = 0, so w = 7m (can't be negative). Length = 12m.
Made your observations? Now let's understand the rules of algebra.