Mass, volume and density: what floats, and why

By the end of the lesson, students can calculate density as mass divided by volume, measure mass and volume for a solid sample, and explain why two objects of different size can float or sink differently using the density they calculated.

Before this lesson: Students can read a triple-beam or digital balance in grams, read a graduated cylinder in milliliters, and subtract to find a volume by displacement.

• A shared balance, a graduated cylinder, water, a small stone that fits the cylinder, and a tray
• A ruler and a dry rectangular wood block; avoid splinters
• One piece of wax for observing flotation; use the supplied volume for its calculation
• Printed recording sheet or a notebook; if equipment is unavailable, use the explicitly labeled practice measurements below

55 minutes · printed activities

Student investigation record Copy these headings into a notebook: sample; prediction (float/sink); mass (g); starting water (mL); final water (mL); sample volume (mL or cm³); density; observed float/sink; explanation. Use actual measured values when equipment is available. Supplied practice measurements — illustrative values, not actual observations Stone: mass 48 g; water before 30 mL; water after 48 mL. Wax: mass 22.5 g; supplied volume 25 mL. The wax floats, so a floating water-level reading does not measure its full volume. Rectangular wood: length 4 cm, width 3 cm, height 2 cm; mass 19.2 g. If using the paper alternative, calculate and predict from these supplied values. Label the observation column “not observed” unless the teacher actually demonstrates the sample.

Show a small stone and a larger dry wood block. Ask students to predict which has more mass, then weigh both if a balance is available; do not assume which is heavier. Explain: mass describes how much matter a sample contains, while density describes mass per unit volume. Write density = mass ÷ volume, with units g/cm³ or g/mL; 1 cm³ = 1 mL. Demonstrate water displacement with the stone only: read the bottom of the meniscus at eye level, lower the stone gently, read again, and subtract the initial volume. The stone must fit the cylinder, be fully submerged, and not dissolve or absorb water during the measurement. Measure the dry rectangular wood with a ruler and use length × width × height instead; wood floats and may absorb water, so an ordinary floating water-level reading is unsuitable. Use the supplied volume for the wax rather than pushing it under with a pencil. For these compact samples, compare average density with water, about 1 g/mL at classroom temperature: less than water predicts flotation; greater predicts sinking. Equal density alone does not predict a stable position in a real demonstration. Note that hollow shapes and trapped air change an object’s average density. Use only one shared demonstration station if equipment is limited, and have groups calculate from the supplied measurements.

1. 1A stone has a mass of 48 g. Water in the cylinder reads 30 mL. After the stone is added it reads 48 mL. Volume = 48 - 30 = 18 mL. Density = 48 g ÷ 18 mL ≈ 2.7 g/mL. Since 2.7 is greater than 1, the stone sinks. Write the comparison and the sink observation on the board together.
2. 2A piece of candle wax has a mass of 22.5 g and a volume of 25 mL. Density = 22.5 ÷ 25 = 0.9 g/mL. Since 0.9 is less than 1, the wax floats. Ask why the wax does not need to be light in grams, only light for its size.
3. 3A block measures 4 cm by 3 cm by 2 cm, so its volume is 24 cm3. Its mass is 19.2 g. Density = 19.2 ÷ 24 = 0.8 g/cm3. Predict first: will it float? Then test it. This is the first prediction the class makes with a number in hand.
4. 4Careful reading: a student writes 'density = 48 ÷ 30 = 1.6'. Ask the class what went wrong: the volume used was the water alone, not the volume the sample displaced.

1. 1As a class, compute the density of a sample with mass 90 g and displacement from 50 mL to 65 mL, then state whether it floats.
2. 2Ask three students to read the same cylinder image drawn on the board, and settle the correct reading together at the bottom of the meniscus.
3. 3Together, order three materials by density before measuring them, using what students already know about each one, and record the predictions to check later.

1. 1A metal sample has a mass of 78 g and a volume of 10 mL. Compute its density and state whether it floats.
2. 2A solid plastic block has a mass of 2.4 g and a volume of 3 cm³. Compute its average density and predict whether it floats in water.
3. 3Water has a density of 1.0 g/mL. Cooking oil is 0.92 g/mL. If you pour both into one glass, which stays on top? Explain using the numbers.
4. 4A student says a big piece of wood must sink because it is heavy. Write a two-sentence reply using the word density.
5. 5A sample's mass is missing. You know its density is 2.5 g/cm3 and its volume is 8 cm3. Find the mass.

• On an exit slip: compute the density of a sample with mass 45 g and volume 50 mL, and say what it will do in water.
• Ask a student to explain the difference between 'heavy' and 'dense' in their own words; nothing written.
• Show two cylinders with different water levels and the same sample; ask which subtraction is correct and why.

• Heavier objects always sink, and lighter objects always float.

  What to do: Compare the stone and wood using the actual class measurements or the explicitly labeled supplied data. Ask students to point to the density column, then compare each density with water. Do not claim a classroom observation that was not made.

• Using the total water level as the volume of the sample.

  What to do: Have the student re-do the subtraction in front of you, pointing at both readings. Ask what part of the cylinder the 30 mL belongs to and what part the sample occupies.

• Thinking a sample that partly floats has a different density from the same material fully submerged.

  What to do: A floating sample displaces only enough water to balance its weight, so the displaced volume is smaller than its full volume. Compare two compact pieces of the same material: their density should be similar within measurement error, and approximately the same fraction of each volume is submerged. Use dimensions, a known volume, or a properly corrected sinker method to obtain full volume.