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Exploring Density

Students investigate the densities of different and and understand how density may help identify a substance.

Approximate Time: 1 hour

Relevant National Content Standards:

Next Generation Science Standards Science and Engineering Practices: Developing and using Models Modeling in 6–8 builds on K–5 experiences and progresses to developing, using, and revising models to describe, test, and predict more abstract phenomena and design systems. • Develop and use a model to describe phenomena. Science and Engineering Practices: Analyzing and Interpreting Data Analyzing data in 6-8 builds on K-5 and progresses to extending quantitative analysis to investigations, distinguishing between correlation and causation, and basic statistical techniques of data and error analysis. • Analyze and interpret data to determine similarities and differences in findings.

Disciplinary Core Ideas: PS1.A Structure and Properties of Each pure substance has characteristic physical and chemical properties (for any bulk under given conditions) that can be used to identify it.

Common Core State Standard: 7NS 2. Apply and extend previous understanding of multiplication and division and of fractions to multiply and divide rational numbers. 3. Solve real-world and mathematical problems involving the four operations with rational numbers.

Common Core State Standard: 7EE Solve real-life and mathematical problems using numerical and algebraic expressions and equations. 4. Use variables to represent in a real-world or mathematical problems, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

Common Core State Standard for Mathematical Practice 4. Model with mathematics.

Lesson Content Objectives: • Construct a density column to compare the densities of various liquids and solids • Draw conclusions about how density may help identify a substance

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Materials Needed: • One clear 2 liter bottle for the instructor’s demonstration • samples of rubbing , dish soap, , vegetable oil, and corn syrup • One or two small objects including plastic, and organic material for each group (corn kernels, grapes, , , paperclip, etc.) • One or clear plastic 100 mL graduated cylinder per small group • One overflow cup and regular cup per small group (optional) • One triple beam balance or digital scale accessible to all of the groups. • Water • Activity sheets for each student (included)

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Summary of Lesson Sequence • Introduce the lesson through a demonstration of a density column in front of the whole class. • Engage students in a whole class discussion about the density of different materials and how to compare the density of different materials. • Show students how to calculate the density of a material mathematically. • Check for students’ understanding by asking the key questions provided while they are measuring and calculating density. • To close the lesson, have students share their findings in a whole class discussion. Have students estimate the densities of the liquids in the density column based on where each groups’ objects settle in the column.

Assumed Prior Knowledge

Prior to this lesson students should be able to use the four operations on rational numbers.

Classroom Set Up

After the density column demonstration, allow students to work in small groups of three to five.

Lesson Description

Introduction

Demonstrate how to make a density column for the whole class. Discuss how the column is useful for comparing densities of materials.

To make a density column: Measure 250 ml (a bit more than 8 ) of corn syrup, dish soap, water, vegetable oil, and rubbing alcohol into separate cups. The water, and alcohol can be colored with food coloring so that they can be distinguished more easily. Dish soap is often already colored, and vegetable oil is not easily colored with food coloring, but already has a light yellow color. Corn syrup may be left clear or brown (depending on the type of syrup purchased.)

Pour each of the liquids, one at a time, very slowly into the 2- liter bottle. Be sure to pour them in the following order: corn syrup, dish soap, water, vegetable oil, then rubbing alcohol.

As the liquids settle, they will separate into individual layers.

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As students observe the demonstration, ask questions to guide their discussion such as:

“Why are the liquids separating in layers?” “What can this experiment tell us about each of the liquids we used?” “We used 250 ml of each of the liquids. Does this mean that each of the liquids have the same ?” “What physical property is this experiment useful for investigating?” “What other liquids could we have tried?” “What might have happened if we poured the liquids into the container faster?” “What might have happened if we poured the liquids into the container in a different order?”

Students should now be ready to discuss density, learn how to calculate it, and work on calculating the density of materials on their own.

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Input and Model

Explain how the density column works and introduce the concept of density.

We were able to create a density column from these different liquids because each of them has a different density. The density of an object is its mass divided by its . We used the same volume for each liquid, 250 ml, but they each had a different mass for that 250 ml of liquid. For the same volume of liquid, some were heavy and some were light. Those that are heavier - for a given volume – are more dense and ended up at the bottom. Those that are lighter – for the same volume – were less dense and ended up on top. -

Provide the activity sheet and model one density calculation for an example object, such as a cork.

mass The density of an object is found by comparing the object’s mass and volume, Density = , volume so we need to measure the mass of this object (cork, etc.) as well as its volume to calculate the density.

We will use a digital scale (or triple beam balance) to measure the mass of the object and record our results along with the units of measurement.

We can find the volume of an irregularly shaped object using an overflow cup. We fill the overflow cup up to the overflow spout and place another cup under the spout. When we immerse the object in the overflow cup, the amount of water that spills out of the spout will be measured using a graduated cylinder. We will record this volume along with the units of measurement.

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This is the volume of the object. (If overflow cups are not available, they can be made using a straw and glue gun as shown below. Alternatively, the volume of an object can be measured using only a graduated cylinder if the object fits in the cylinder. Simply measure the volume of water before and after immersing the object and the amount of displaced water is the volume of the object.)

For objects that float…. You must carefully submerge the object in the water to get an accurate volume reading. Using a toothpick or the point of a pencil can work well. Fingers are large and will displace a great deal of water themselves giving you an inaccurate reading.

Using an overflow cup.

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Making an overflow cup with a straw using a glue gun.

We can calculate the density of the object by dividing the mass by the volume. Record the density along with the units. Notice that the units for density are a rate.

Students should be ready to measure the mass and volume of materials on their own and calculate their densities.

Guide Students Through Their Practice

Allow students time to measure and calculate the density of one or two objects assigned to them. Each group should then drop their object in the density column and, based on where the settles, the group can estimate the density of the liquid where the object settled.

Check for Understanding

While students are conducting their investigation, ask the following guiding questions:

“Can you make predictions about which objects are more dense and which are less dense before making measurements?” “Do the of objects matter when comparing densities?” “Would the density of an object change if you changed the mass or the volume of the object (by breaking it or cutting it)?” “Why might it be useful to know the density of an object?” “Who might use this information?”

Closure Allow each of the groups to share the density of their assigned objects so the whole class can estimate the densities of the liquids in the density column based on where the objects settled in the density column. Include some of the following questions in a whole group discussion:

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“Which object was the most dense? Least dense?” “How could you predict the density of an object without measuring the mass and the volume and how would you test your prediction?” “Why might it be useful to know the density of an object?”

Suggestions for Differentiation and Extension An interactive simulation of density is available at the PhET website. In order to extend or differentiate this lesson, students can play with the simulation to better understand density.

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Name ______Exploring Density

Teacher’s demonstration for measuring mass and volume Record the mass and volume of the object and calculate the density of the object using the density formula. mass Density = volume

Object Mass (include units) Volume (include units) Density (include units)

Investigate the densities of different objects by measuring their and , and calculating their densities. Record your data on the table below. Then place your object in the density column so you can estimate the density of the liquid where your object settles.

Object Mass (include units) Volume (include units) Density (include units)

Step 1 Write what objects you have been assigned in your table. Answer the following questions as you complete Step 1: 1. Which of your samples do you predict has the greater density? Lesser density?

2. How did you make this prediction?

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Step 2 Measure and record the mass of each of the objects you have. Be sure to include the units of your measurements.

Step 3 Measure and record the volume of each of the objects you have. Be sure to include the units of your measurements. As you complete Step 3, answer the following questions: 3. Would comparing the sizes of your objects help you predict which has a greatest density? Why or why not?

4. Would comparing the of your objects help you predict which has a greatest density? Why or why not?

Step 4 Use the formula for density to calculate and record the density for each of your objects. Be sure to include the units for your calculations. As you complete Step 4, answer the following questions: 5. Would the density of an object change if you changed the mass or the volume of the object (by breaking it or cutting it)? Why or why not?

6. Why might it be useful to measure the density of an unknown object? Who might use this information?

Step 5 Carefully place your object in the density column to see which liquid it settles in. Make a prediction about the density of the liquid that it settles in.

Liquid: ______Possible density: ______(use units)

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Step 6 When each group is ready, record the objects and densities that the other groups had in a whole class discussion. Use this information to estimate the densities of the liquids in the density column.

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