This answer key provides:
- Correct answers for all exercises
- Detailed step-by-step solutions
- Common mistakes and misconceptions
- Alternative solution methods
- Teaching tips for educators
- Self-check guidelines for students
Excellent (4 points): Correct answer with complete work shown and proper units
Good (3 points): Correct answer with most work shown
Fair (2 points): Correct method but computational error
Needs Improvement (1 point): Incorrect answer with some work attempted
Incorrect (0 points): No work shown or completely wrong approach
Exercise 1: 90 mL
Exercise 2: 30 mL, 45 mL, 60 mL
Exercise 3: 2 L = 2000 mL, 750 mL = 0.75 L
Exercise 4: 425 mL total
Exercise 5: 320 mL remaining, 9/25 consumed
90 mL
Place the graduated cylinder on a flat surface at eye level
Locate the curved surface of the liquid at the bottom
Read at the bottom of the meniscus: 90 mL
Write down the measurement with units: 90 mL
- Reading at the top of the meniscus instead of the bottom
- Not positioning at eye level (parallax error)
- Forgetting to include units (mL)
- Reading between the wrong scale marks
30 mL, 45 mL, 60 mL
45 mL, 60 mL, 30 mL
30 < 45 < 60
30 mL, 45 mL, 60 mL
Check that each volume is indeed less than the next
- Ordering from greatest to least instead of least to greatest
- Confusing the digits (e.g., thinking 30 is greater than 45)
- Forgetting to include units in the answer
- Mixing up the order of the volumes
2 L = 2000 mL, 750 mL = 0.75 L
1 L = 1000 mL
2 L × 1000 mL/L = 2000 mL
750 mL ÷ 1000 mL/L = 0.75 L
2000 mL ÷ 1000 = 2 L ✓, 0.75 L × 1000 = 750 mL ✓
- Multiplying when dividing is needed (or vice versa)
- Forgetting the conversion factor (1 L = 1000 mL)
- Not moving the decimal point correctly
- Forgetting to include units in the final answer
425 mL
Container X = 250 mL, Container Y = 175 mL
250 mL + 175 mL = 425 mL
The total volume in the bowl is 425 mL
250 + 175 = 425, so the answer is correct
The total (425 mL) is more than either individual amount, which makes sense
- Adding incorrectly (250 + 175 ≠ 425)
- Forgetting to include units in the answer
- Mixing up addition and subtraction
- Not carrying over when adding larger numbers
320 mL remaining, 9/25 of original consumed
Initial volume = 500 mL, Removed volume = 180 mL
500 mL - 180 mL = 320 mL
Fraction = Removed volume / Initial volume = 180/500 = 18/50 = 9/25
The remaining water is 320 mL
320 mL + 180 mL = 500 mL ✓
- Subtracting incorrectly (500 - 180 ≠ 320)
- Forgetting to simplify the fraction
- Mixing up addition and subtraction
- Not borrowing when subtracting larger numbers
- Forgetting to include units in the answer
Volume: The amount of space a liquid takes up, measured in milliliters (mL) or liters (L)
Meniscus: The curved surface of liquid in a container that you read at the bottom
Graduated: Marked with regular intervals for precise measurement
Conversion: 1 L = 1000 mL (always!)
- Meniscus Rule: Always read at the bottom of the curve
- Eye Level: Look at the liquid level straight on
- Conversion: "Kilo" means thousand, so 1 L = 1000 mL
- Units: Always write mL or L in your answers
- Verification: Check your work by doing the opposite operation
Before submitting your work, check:
- □ Did I read the meniscus at the bottom?
- □ Am I looking at eye level?
- □ Did I include the correct units (mL or L)?
- □ Are my calculations correct?
- □ Did I show my work clearly?
- □ Does my answer make sense?
- □ Did I verify my answer?