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Unit M2

Archimedes & the Case of the Missing Gold

The Basics of Density

Heating Up and Spreading Out

Is Putty or Clay More Dense?

Lab: Is Putty or Clay More Dense?

Duration: Approximately 70 minutes

In this fun and informal lab, students come up with ways to determine the density of irregularly shaped pieces of clay and putty. Students can then go on to determine whether or not sample are pure (without cutting them open) just as Archimedes did.

LEARNING OBJECTIVE

Students will determine volume using dimensions and using displacement.

Students will calculate density by using volume measurements and mass measurements.

Materials

- Scales or balances (with gram display)
- Rulers (cm)
- Graduated Cylinders (Variety of sizes)
- Paper Clips
- Small Random Portions of Silly Putty (or similar) and Modeling Clay

Teacher Tune-ups

Teaching Notes

ACTIVITY OVERVIEW

- Review two ways to determine volume (20 minutes)
- Present the question (5 minutes)
- Observe teams (20 minutes)
- Discuss findings (15 minutes)
- Relate the lab to Archimedes' Eureka! moment (10 minutes)

Review two ways to determine volume (15 minutes)

Students attempt to create “bricks” (rectangular prisms) with the dimensions 2cm x 2cm x 5cm out of Silly Putty.

Students are encouraged to measure frequently with a ruler, change the brick to have more or less material, cut/smash with the ruler edge.

When most are complete (not necessary for all to finish), ask students to calculate the volume of their bricks with a ruler (20 cubic cm).

Elicit student-constructed definition of volume… encourage “how much space a shape takes up” or “the number of cubic units”

Discuss or write down any observations or challenges that students recall from the experience.

Honor the fact that the students know the formula for volume (l x w x h), but let the in on the fact there is another very different way to determine volume. It involves water, a paper clip, and a graduated cylinder. Let them play with apparatus and their brick to come up with a few ideas.

Seize upon the thinking of students on the right track. Eventually the procedure of displacement is demonstrated by teacher or student.

Note water level prior to submerging brick.

Note water level while brick is submerged.

Determine the difference (how much water was displaced).

KEY CONCEPT:

1 mL = 1 cc

Discuss. Come up with student created definitions of mL and cc.

Students compare the volume as determined by displacement to the volume calculated from the dimensions’ measurements. It will probably not match. This is because neither is super precise. Ask students:

Think about which method you think might be more precise.

Intended answer:

Displacement is more precise, because the shape of a handmade brick won’t be very regular.

Give students time to adjust the size of their bricks if they feel that they can get closer to an accurate representation of 20 cc.

Present the question (5 minutes)

Ask students for an informal definition of density.

Then present them with the main question of the lab:

Is silly putty of the modeling clay more dense?

Students will likely quickly answer one way or the other, but the work here in this lab is providing proof.

Allow teams to develop plans.

Observe teams (20 minutes)

There are several approaches that students may go with. Encourage creative thinking. Do not try to manage students' progress. They will have ample time later in the lab to learn about the effectiveness, efficiency, and reliability of various methods.

:

- Students may attempt to create two bricks that are the same size and then measure the mass of each.
- Students may create larger samples of brick shapes, use a ruler to calculate volume, and them measure the mass. From these data, students can determine the density by using density = mass/volume. Larger samples may be more reliable and using multiple samples of varying sizes is possible if the formula is used.
- Students may use displacement instead of the dimensions to determine volume. This way the lack of regularity of the shape won't interfere with their precision. However, using the best sample size with the appropriate graduated cylinder can be an interesting challenge for them to think through.
- Students may drop sample of each substance into water in an attempt to see if their interact with water differently (perhaps one floats and one doesn't).
- Generally speaking, multiple trials and using samples of various sizes will improve validity of findings.

Discuss findings (15 minutes)

Allow students to present findings.

Take notes on chart paper. Be sure to note data that groups collected and compare findings.

Encourage students to ask each other questions.

Relate the lab to Archimedes' Eureka! moment (15 minutes)

There are several ways to relate this lab the famous story of Archimedes in the tub.

One way is to allow to secretly combine putty and clay in one sample while leaving others pure. By using displacement to determine the density of the mixed sample, it should differ from the densities of the "pure samples." For example, if the modeling clay is denser

Another way to do this is to hide a few heavy steel marbles (or similar) inside one sample of clay or putty and set it next to a sample of the same substance. Even if the samples are different sizes, the students should be able to determine which one has the marbles because the densities (average densities) should "give it away."

Students should be encouraged to think about how difficult it would be to determine the volume of an irregular mass of clay or putty without using displacement.

BETA Version - Please send comments and corrections to info@serpinstitute.org