1: Density of Metal Block

Correct Responses

• 19.2 g/cm3
  Note: Extra trailing zeroes may also be added (e.g., 19.20, 19.200)
• 19 g/cm3 [Rounds to nearest whole unit.]

Incorrect Responses

• Shows the set-up for density (mass/volume) but does not compute density or makes a computational error.
• 125 [Computes volume but not density.]
• 19.3 [No work shown; indicates density copied from table.]
• Other incorrect

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2: Procedure to Find Volume of Crown

Correct Responses

• Describes or diagrams a procedure based on displacement of water using measured water level differences:
  • i) Adding water to the beaker (sink or tray) and marking the water level.
  • ii) Placing the crown in the beaker (sink or tray) and marking the new water level.
  • iii) Measuring the volume difference before/after adding the crown using the graduated cylinder
• Describes or diagrams a procedure based on displacement of water using measured overflow:
  • i) Filling the beaker (or tray) with water.
  • ii) Placing the crown in the beaker (or tray) and collecting the overflow.
  • iii) Measuring the volume of the overflow using the graduated cylinder

Partial Response

• Describes or diagrams a partial procedure that includes displacement of water but with inadequate or no description of the steps/measurements to determine the volume.
  • Examples:
    • Put some water in the beaker and add the crown. Measure how much the level of water went up.
    • Add the crown to the beaker filled with water. See how much overflowed.

Incorrect Responses

• Mentions putting the crown in the beaker (sink or tray) of water with no explicit mention that the water level will rise/overflow and no or incorrect procedure given for measuring the volume.
  • Examples:
    • Fill the beaker to the top with water and add the crown. You can get the volume that way.
• Other incorrect

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3A: Why Scientists Repeat Measurements

Correct Responses

• Refers to accuracy, precision, reliability, experimental uncertainty, estimation of measurement error (or similar).
  • Examples:
    • It’s more reliable.
    • Each time they measure the volume it is close but not exactly the same. So, it’s better to measure it a few times to be sure.
    • They want a more exact answer.
    • To get an accurate measure of the volume.
• Refers only to computing an average or mean value (or median or range).
  • Examples:
    • To find the average volume.
    • To work out the mean.

Incorrect Responses

• Refers only to ‘mistakes’ or changes in the measurements (or similar); no explicit mention of accuracy, precision, experimental uncertainty, etc.
  • Examples:
    • In case mistakes happen.
    • To make sure it wasn’t changing.
    • To make sure the answer was right and he did not make a mistake.
    • To make sure they did it right.
    • To check if it was correct.
• Refers only to a ‘fair test’ or similar; no explicit mention of computation of average, accuracy, precision, experimental uncertainty, etc.
  • Examples:
    • To make sure it was a fair test.
    • To ensure a fair test.
• Other incorrect

3B: Obtaining Average (Median) Value

Correct Responses

• Shows (or describes) a correct method for computing the average (mean) value.
  • Examples:
    • (11.88+12.00+11.94+12.12+12.06) = 60. 60/5=12.0
    • (202+200+201+198+199)/5 = 200. 2400/200=12.0
    • They added together all of the densities and then divided by 5 to get the average.
• Shows (or describes) a correct method for determining the median value.
  • Examples:
    • 202, 201, 200, 198, 199. 200 is the median volume, so 2400/200 is the median density (12).
    • 12 is the middle value when placed in order (12.12, 12.06, 12.00, 11.94, 11.88).

Incorrect Responses

• States that it is the average, mean or median value with no or incorrect work shown.
• Shows a computation of density (mass/volume). [No determination of average or median included.]
  • Examples:
    • They did mass divided by volume.
    • 2400g/200cc = 12 g/cc
• Other incorrect

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4A: Identifying Metal in Block

Correct Response

• GOLD with an explanation based on correct density computed in previous question (19.2 g/cm3).
  • Examples:
    • Gold. The density is the same.

Incorrect Responses

• GOLD with no explanation or incorrect explanation that is NOT based on density.
  • Examples:
    • Gold. Because that is what crowns are always made of.
• SILVER (alone or mixed). [Confuses density of crown with density of the metal block.]
  • Examples:
    • It is mostly silver because the density is 12 and that’s the closest one.
• Other incorrect

4B: Reporting Composition of Crown

Correct Response

• Reports that the crown is made of a mixture (alloy) AND names specific metal(s) that might be included (reasonable composition based on density).
  • Examples:
    • The jeweler used some silver as well as gold.
    • It might have had some copper mixed in because that would lower the density and the cost.
    • The jeweler most likely used all silver except for a thin coat of gold to make it look pure gold even though it wasn’t.

Incorrect Responses

• Reports only that the crown is made of a mixture or is NOT pure gold (or similar); NO specific metals are named.
  • Examples:
    • The jeweler didn’t use the block of metal that the king gave him.
    • The jeweler used four more metals to make the crown.
• Reports SILVER (density closest to 12 g/cm3).
  • Examples:
    • The metal used is silver.
• Reports an incorrect mixture of metals based on additive densities.
  • Examples:
    • It’s silver and aluminum (10.5 + 2.7)
    • Mixture of silver and aluminum as their density adds up to 12.0 approximately.
    • Copper and aluminum.
• Other incorrect

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