Mineral Density: Teaching accuracy, slope, and percent error in the Earth science classroom
Summary
In this lab activity, students not only explore the meaning of density, but also use their math skills to graph mass/volume data, write an equation for a line and interpret the slope of the line. Students also find the density of two unknown mineral samples and use those values to differentiate between the two minerals. At the end of the lab, students and teacher discuss the following ideas: (1) density is a physical property that is independent of sample size, (2) why the students' measured density values are not the same as the known density values reported in the textbook , and (3) the "messy" nature of science, which requires multiple and repeatable measurements and requires careful attention to detail.
CollapseLearning Goals
The purpose of this lab activity is for students to
1. Practice measuring carefully and accurately.
2. Plot their measurements of mass and volume on an x-y graph and create a line of best fit.
3. Understand that the slope of the line is the same as that mineral's density, and relate density, mass and volume to the variables in their equation for the line of best fit.
4. Use their nascent laboratory skills to find the density of two unknown minerals.
5. Recognize that density is a physical property of minerals and may be used to differentiate between minerals.
New Vocabulary: Students will learn about the difference between mass, weight, and volume. Students develop an understanding of what density means and how it is different from weight/mass/volume. Students will know the difference between heft and density. Students will review slope. Students will determine the percent error in their measurements (known density-calculated density/known density).
1. Practice measuring carefully and accurately.
2. Plot their measurements of mass and volume on an x-y graph and create a line of best fit.
3. Understand that the slope of the line is the same as that mineral's density, and relate density, mass and volume to the variables in their equation for the line of best fit.
4. Use their nascent laboratory skills to find the density of two unknown minerals.
5. Recognize that density is a physical property of minerals and may be used to differentiate between minerals.
New Vocabulary: Students will learn about the difference between mass, weight, and volume. Students develop an understanding of what density means and how it is different from weight/mass/volume. Students will know the difference between heft and density. Students will review slope. Students will determine the percent error in their measurements (known density-calculated density/known density).
Context for Use
This lab/discussion activity is designed for an 8th grade earth science classroom, for 28 students at 7 (4-person) lab stations. However, any science class seeking to teach about density of solids could use this lesson. Estimated time needed is five 45-minute class periods. Students should already know how to record data in their science notebooks, how to measure volume by displacement, how to use a triple beam balance and how to read the meniscus in a graduated cylinder. INTERDISCIPLINARY CONNECTION: I try to do this activity shortly after their math lessons on equations of a line and slope. Density naturally fits in the earth science curriculum before a lesson on minerals.
Description and Teaching Materials
Prior to doing the lab, I use ideas from a Science Scope article (Peterson-Chin, 2004) to introduce density in a qualitative way during a class discussion. The discussion also includes examples of measuring density and the units for density. I specifically go over how to measure the volume of an irregularly shaped object by water displacement.
Each student receives a lab handout with the procedure. I then give each group five pieces of the same mineral, but of different sizes. Make sure the samples will fit in the graduated cylinders you have. I use seven different minerals so that each lab station has a unique mineral (and students can't copy). The minerals I use are: quartz, hematite, muscovite, orthoclase feldspar, plagioclase feldspar, gypsum, garnet, or pyrite. Students predict the value of their mineral's density, knowing that the density of water is 1 gram/cubic centimeter. Students make a data table in their notebook (with teacher guidance as needed) and make their mass/volume measurements.
Students first calculate the density of each mineral piece (density=mass/volume). Students then plot their volume-mass data on an x-y graph and then enter their data onto a spread sheet and make a line of best fit. I talk with the groups that their line should have a y-intercept of zero and ask them why that should be. I also discuss with groups that the data should be linear. I expect there to be a lot of scatter in data as students tend to be sloppy in their measurements.
I help the students see that the slope of the line is the relationship between mass and volume of a substance and is therefore the density of that material. Students compare the slope of the line (density) with the known density value and calculate the percent error in their measurements. The students' grade in the lab is a function of how low their percent error is, so if a group wants to redo their measurements, they can. I have not done this lab before, so at this time I don't know what a reasonable percent error is for the 13-15 year old age group. On average, I would expect older students to be able to make better measurements than younger students can.
When I am confident each group is doing measurements and calculations correctly, I have the students find the densities of two unknown minerals, which may look somewhat similar but density is a distinguishing property (apatite/beryl or topaz/corundum or halite*/calcite). Students make their mineral identifications based on density.
Materials needed: mineral samples, triple beam balances, graduated cylinders of various sizes, thread, lab notebooks, and spreadsheet program.
*halite will dissolve a little in the water; students should measure its mass first; they should also dry the halite sample off when done.
References
Peterson-Chin, L., April 2004, Looking at density from different perspectives, Science Scope, Vol 27, #7, pp 16-20.
Each student receives a lab handout with the procedure. I then give each group five pieces of the same mineral, but of different sizes. Make sure the samples will fit in the graduated cylinders you have. I use seven different minerals so that each lab station has a unique mineral (and students can't copy). The minerals I use are: quartz, hematite, muscovite, orthoclase feldspar, plagioclase feldspar, gypsum, garnet, or pyrite. Students predict the value of their mineral's density, knowing that the density of water is 1 gram/cubic centimeter. Students make a data table in their notebook (with teacher guidance as needed) and make their mass/volume measurements.
Students first calculate the density of each mineral piece (density=mass/volume). Students then plot their volume-mass data on an x-y graph and then enter their data onto a spread sheet and make a line of best fit. I talk with the groups that their line should have a y-intercept of zero and ask them why that should be. I also discuss with groups that the data should be linear. I expect there to be a lot of scatter in data as students tend to be sloppy in their measurements.
I help the students see that the slope of the line is the relationship between mass and volume of a substance and is therefore the density of that material. Students compare the slope of the line (density) with the known density value and calculate the percent error in their measurements. The students' grade in the lab is a function of how low their percent error is, so if a group wants to redo their measurements, they can. I have not done this lab before, so at this time I don't know what a reasonable percent error is for the 13-15 year old age group. On average, I would expect older students to be able to make better measurements than younger students can.
When I am confident each group is doing measurements and calculations correctly, I have the students find the densities of two unknown minerals, which may look somewhat similar but density is a distinguishing property (apatite/beryl or topaz/corundum or halite*/calcite). Students make their mineral identifications based on density.
Materials needed: mineral samples, triple beam balances, graduated cylinders of various sizes, thread, lab notebooks, and spreadsheet program.
*halite will dissolve a little in the water; students should measure its mass first; they should also dry the halite sample off when done.
References
Peterson-Chin, L., April 2004, Looking at density from different perspectives, Science Scope, Vol 27, #7, pp 16-20.
Teaching Notes and Tips
Even though the concept of density is introduced in 6th grade, 8th graders usually have little experience and understanding regarding the concept. I usually try to teach density again at 8th grade because the students NEED to review the ideas with a mind that is starting to handle abstract concepts. Because density differences drive convection in both the atmosphere and mantle, understanding density is fundamental to grasping some basic earth science processes.
I recommend using smallish mineral samples because the sample has to fit into the mouth of the graduated cylinders you have.
This lab requires that the teacher circulate among the lab groups to check on and refine the students' measurement techniques. I expect the students to measure to the nearest tenth of a gram. When the students calculate density, it is a good time to discuss significant figures because students WILL ASK how many decimal places they should have.
I have never taught density before with such a direct math connection. Usually I have the students consider a mineral's density by asking themselves if a mineral feels heavier for its size or lighter for its size. Most students have an idea of how heavy a hand-sized rock should be. After all, they are accustomed to picking up rocks with an average density of 2.65 grams/cubic centimeter and actually have a good feel for a sample being heavier than it should be. This is a perfectly fine way to estimate a mineral's heft. However, I want my students to develop a more sophisticated understanding of density that includes how density can be expressed mathematically.
I recommend using smallish mineral samples because the sample has to fit into the mouth of the graduated cylinders you have.
This lab requires that the teacher circulate among the lab groups to check on and refine the students' measurement techniques. I expect the students to measure to the nearest tenth of a gram. When the students calculate density, it is a good time to discuss significant figures because students WILL ASK how many decimal places they should have.
I have never taught density before with such a direct math connection. Usually I have the students consider a mineral's density by asking themselves if a mineral feels heavier for its size or lighter for its size. Most students have an idea of how heavy a hand-sized rock should be. After all, they are accustomed to picking up rocks with an average density of 2.65 grams/cubic centimeter and actually have a good feel for a sample being heavier than it should be. This is a perfectly fine way to estimate a mineral's heft. However, I want my students to develop a more sophisticated understanding of density that includes how density can be expressed mathematically.
Assessment
Each lab group receives a grade based on:
1. the percent error in density measurement (a reasonable %error for this age group has yet to be determined).
2. correctly identifying the two unknown minerals based on the minerals' densities.
1. the percent error in density measurement (a reasonable %error for this age group has yet to be determined).
2. correctly identifying the two unknown minerals based on the minerals' densities.
Standards
6.II.A.5. The student will distinguish between volume, mass and density.
8.I.B.3 The student will use appropriate technology and mathematics skills to access, gather, store, retrieve and organize data.
8.III.A.6 The student will classify and identify rocks and minerals using characteristics including but not limited to density, hardness and streak.
9-12.I.B.2 The student will distinguish between qualitative and quantitative data.
9-12.I.B.3 The student will apply mathematics and models to analyze data and support conclusions.
8.I.B.3 The student will use appropriate technology and mathematics skills to access, gather, store, retrieve and organize data.
8.III.A.6 The student will classify and identify rocks and minerals using characteristics including but not limited to density, hardness and streak.
9-12.I.B.2 The student will distinguish between qualitative and quantitative data.
9-12.I.B.3 The student will apply mathematics and models to analyze data and support conclusions.