# Density

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## Objective

Students will be able to explain the concept of density and solve density word problems by watching a demo, taking notes, doing practice problems, and performing a lab.

#### Big Idea

Substances will float or sink relative to each other depending on their density. Density can be calculated using mass and volume.

## Introduction

In this lesson students learn about the physical property of density as a way to compare different substances as well as how to perform calculations.  This lesson aligns with NGSS Middle School Physical Science Performance Expectation (MS-PS1-2): "Analyze and Interpret data on the properties of substances before and after the substances interact to determine if a chemical reaction has occurred."  Although this is a middle school expectation over half of my students are not familiar with the concept of density and very few of them have actually used the equation d=m/v.  More details concerning students' background knowledge is in the reflection section.

The lesson also is part of NGSS Science and Engineering Practice 5: "Using Mathematics and Computational Thinking," because students are required to apply algebra to chemistry problems using the equation of d = m/v.

Because I have one demonstration and two lab activities during this lesson there are several necessary resources.

1. For the Coke & Diet Coke density demonstration I use two 2-liter graduated cylinders (beakers will also work), water, two 12 oz. cans of Coke, two 12 oz. cans of Diet Coke, sugar, a packet of splenda, a balance, a weighing boat, and a stir rod or ruler.

2. For the ice cube activity each group of 4 students needs two beakers or weighing boats, two ice cubes, a container of water (which I dye blue), and a container of alcohol (which I dye red).

3. For the density of a rock lab at the end of the notes for each group of 4 students I provide one small rock, one plastic graduated cylinder (that the rock can fit into), water, and a balance.

## Engage/Explore

15 minutes

In order to engage students about density I perform a Coke/Diet Coke demonstration. This is found on the Presentation PowerPoint and beginning of the student notes.

Before the demo I set up two giant graduated cylinders (2L) in the front of the classroom filled almost all of the way to the top with water (This can also be done in a fish tank or large beakers).

I then place one can of Coke next to one and one can of Diet Coke next to the other.  I then perform the demo with having students answer questions as they go... some of which are predictions.

For the first question students predict what will happen when I place the Coke in the water.  After they answer question #1, I place the Coke into the water and it sinks (you may want to test beforehand if you are using tap water and some cans can be off so will actually float instead of sink).

After recording what happens for #2 in either words or pictures I have students predict for #3 (what will happen with Diet Coke) and then place the Diet Coke in the second graduated cylinder. The Diet Coke floats which they record for #4.

For #5 students are asked about which property accounts for the difference in Coke vs. Diet Coke.

• Some students are not sure what I am referring to, so I follow up this question with, "What is the difference between Coke and Diet Coke?"  After this, most students realize that it is the sugar that is different between the two.
• To help students see just how much sugar is in Coke I give two students the different cans (one Coke and one Diet Coke) and have them read out the amount of sugar in the Coke vs. Diet Coke.  The student with the Coke sees that there are 39grams of sugar in a can of Coke.
• I have a student weigh out 39.0g sugar on a balance in a weighing boat and I pass around so that all students can see how much sugar there is.  Many students are surprised, and we discuss why drinking soda is not very healthy because of all of the sugar.
• I then help students to realize that this extra sugar is involved with the Coke sinking and the Diet Coke floating.
• I tell students that the density of water is 1.0g/ml and then lead them to figure out that the density of the can of Coke must be >1; whereas Diet Coke must be < 1.

For number 6, I ask students how to make the Coke float and give them some time to record their answers on their own and then share with their groups.

• Many students respond that we need to take sugar out of the Coke, or we should drink some of the Coke.  When I get these answers I ask what I can do without touching the Coke can.
• Other students come to the idea that in order to make the Coke float we need to add something to the water to make the water more dense than the Coke, which I then do.
• I add salt to the water and stir and slowly the Coke rises.  This picture shows what it looks like in class.

For number 7, students want to know what I actually did to make the Coke float.  I then show students the idea of a density column by placing the graduated cylinder with the Diet Coke/Water on top of the graduated cylinder with the Coke/Salt Water.  I tell students that you can determine what is less dense or more dense based on what floats/sinks in the other.  This picture shows what this looks like at the end of the experiment.

To finish the demo I usually talk to students about how it is easier to float in the ocean vs. freshwater, and ask them if they have heard about the dead sea in Israel and tell them about my experience floating in the water there.

Here is a copy of filled in student-notes from the demo.

## Explain

20 minutes

In this section I introduce students to the idea of density in terms of how tightly packed molecules are, how less dense substances float in others, the equation of density as mass per volume, and how to find density using water water displacement.

The lesson follows the attached PowerPoint and notes graphic organizer.  This includes notes, an activity, reading, and practice questions.  The diverse nature of this lesson helps students to not only think of density as an equation, but also a physical property that can be used to understand the nature of a substance and compare it to others.

Within this section students learn about the idea of density and how less dense substances float in more dense substances.  Using this information, they show the relative densities of Coke, Diet Coke, water, and salt water.  I make sure to have them refer back to the demonstration and the density column that I showed them at the end of the demonstration.

After this students perform an experiment where they place an ice cube into alcohol where it sinks, and water where it floats.  I then have them use what they learned from the Coke/Diet Coke demonstration to come up with the relative densities of ice, water, and alcohol.

These papers (page 1 and page 2) are copies of student filled in notes regarding the information and mini experiment.

## Elaborate

30 minutes

In this section I give students a chance to practice what they have learned in the notes by performing a quick lab activity and then answering practice questions found at the end of the notes

In the lab students find the density of a rock using water displacement.  The biggest source of error is finding an accurate volume for the rock with the graduated cylinder.  The results are varied, but they all find that the density is larger than 1, and that this makes sense because the rock sinks.

After students perform the lab activity I lead them through answering four questions where they will be using the density equation, some of which they will need to preform some dimensional analysis.

I have students perform one question at a time by giving them time to start it without me, give them hints if they are stuck (underlining, circling, setting up the equation) and then going over the answer.  See Unit 1 Lesson 5 for details on how I have students problem solve using the "Plug and Chug" technique.

This is a copy of filled in notes from one of my students.

## Evaluate

30 minutes

As a final check for understanding I have students perform 5 homework questions.  The homework section is on the last page of the notes

When students come in the next day I stamp the HW and then go over the answers using my answer key

For the most part students find that these problems are not that tricky once they get used to the plug and chug technique.  Students struggle the most with problems where they are solving for the Volume given Density and Mass because volume is in the denominator in the equation.  At this point in the year I do not go too much into isolating the variable first (like I do a lot in second semester equations), but I do review how to solve for the denominator algebraically by first cross-multiplying and then dividing.  On the exam I make sure to not have any problems where they solve for volume.