Gold Seal Lesson:
Density Determination Of An Unknown Substance

Copernicus Education Gateway

 

Subject:

 

Mathematics

Grade:

 

 

9-12

 

 

ICLE Standards:

 

 

Mathematics: Model real world phenomena with a variety of functions. Use graphs as tools to interpret relationships.

Science: Develop an understanding of the structure and property of matter.

 

 

Performance Task:

 

 

Sabrina's grandpa Jay loves to fish. For years, he has been using lead sinkers. One day while Sabrina and her grandfather were fishing, she tells him about the environmental hazards of lead. Grandpa Jay did not realize that he could purchase tin fishing weights that are more environmentally friendly. However, when Grandpa Jay went fishing a month later, his tackle box overturned, mixing his lead and his tin sinkers. Sabrina tells her grandfather that he can separate the sinkers by determining their densities, a physical property that is unique for nearly every element.

This activity will enable you to understand how Sabrina's Grandfather would be able to separate his sinkers by determining their densities.

Materials Needed:

  1. Metric balance (triple beam or electronic) and a 25 ml graduated cylinder

  2. 5 packs of different size lead fishing weights ranging from 5 grams to 100 grams labeled "Unknown A"

  3. 5 packs of different size tin fishing weights ranging from 5 grams to 100 grams marked "Unknown B"

  4. Periodic Table of Elements

  5. Graph Paper

Part I

  1. Choose another class member to be your partner for this activity. One of you will select a pack labeled "Unknown A" and the other will select a pack labeled "Unknown B". One of these is lead; the other is tin. Each pack contains 5 samples of different size lead or tin. Your task is to determine whether you have a tin pack or a lead pack.

  2. Find the mass, in grams, of each of the samples in your pack by using a metric balance.

  3. Find the volume, in cc, of each of the samples in your pack by using the displacement method; i.e., by dropping each sample into a 25 ml graduated cylinder containing a known quantity of water. The increase in the volume will be the volume of the sample. Record data in the "Mass" and "Volume" column of the Data Table below.

  4. Find the ratio of the mass to the volume for each of your 5 samples and record them in the "Mass: Volume" column of the Data Table above. What conclusion, if any, can you make about these ratios?

  5. Make a graph of your mass and volume data by plotting five points (mass, volume) corresponding to the data in your Data Table. Label the y-axis "Mass" and the x-axis "Volume." Draw a straight line through the plotted data points. Write the equation of our straight line using the "y = mx + b" form. What is the slope of your straight line? How does the slope compare to the mass to volume ratios of your five samples?

  6. Compare your data table and graph with your partner's. How are they alike? How are they different?

  7. Find the average of the five masses and the five volumes in each of your sample packs. These will be recorded on the chalkboard or the overhead projector in Part II of this activity.

Part II

  1. Select a student to be the recorder at the chalkboard or overhead projector.

  2. Record the averages for each student in the class in a chart on the chalkboard or the overhead projector. See sample chart below.

Part III

  1. Find the mass to volume ratio for the class averages computed in Part II.

  2. The Periodic Table of the Elements shows the atomic weight for each element. Examine the Periodic Table to find the elements whose atomic weights match the class mass to volume average for Unknown A and Unknown B.

  3. Identify the metal (lead or tin) of Unknown A and Unknown B.
    4. The atomic weight of an element is also called the density of the substance. Develop a formula for the density of a substance in terms of its mass and volume.
    5. Write a brief paper summarizing this activity. State what you have learned as an outcome of doing the activity.

Note to the teacher: Students will work in pairs, as a class, and individually on this activity, which allows them to see the integration of algebra/geometry with physical science. After engaging in the task, students should have an understanding that density of a substance is a constant ratio of mass to volume.

 

 

Knowledge / Skills:

 

 

Understand the characteristics of density and how it varies in materials with the change of temperature, pressure, and phase (gas, liquid, solid). (s22)

Understand the historical development of the periodic table and that the atomic number is the basis of the arrangement of the periodic table. (s78)

Perform operations with signed (positive and negative) numbers, including decimals, ratios, percents, and fractions. (m1)

Understand the best procedures for statistical data collection, organization, and display. (m5)

Understand the characteristics of measures of central tendency (i.e., mean, median, and mode). (m15)

 

 

Rubric:

 

 

3 Points = The student completes all parts of the task without coaching. He/she accurately measures and records the required data. The student plots the points and determines the equation of the line formed by the points. He/she identifies the slope of the line and properly relates it to the mass-to-volume ratio. The student sees the connection between the slope, the mass-to-volume ratio, and the Periodic Table of Elements. He/she correctly identifies the substance in his/her sample and develops a formula for density in terms of mass and volume. The student's work is thorough, accurate, and well organized. His/her written paper nicely summarizes the activity and is well written. It indicates a thorough understanding of the concepts present in the task.

 

 

2 Points = The student needs some coaching to complete all parts of the task. He/she has difficulty with one or more of the major components of the task. The student's work is for the most part accurate and thorough, but is not particularly well organized. His/her paper summarizes the major parts of the task, but is not well structured. The paper indicates only a partial understanding of the concepts present in the task.

 

 

1 Point = The student needs considerable coaching to complete all parts of the task. He/she has difficulty with most of the major components of the task. The student's work contains several errors, and he/she is not very thorough. The student demonstrates a lack of organizational skills. His/her paper indicates, at most, a minimal understanding of the concepts present in the task.

 

 

0 Points = The student does not complete the task and shows little, if any, understanding of the concepts present in the task. What little work is done is filled with errors, very sketchy, and very poorly organized. His/her paper, if attempted, is vague and meaningless.

 

 

Keywords:

 

 

ALGEBRA
COORDINATES
MATRIX / MATRICES
SLOPE GEOMETRY
LAB EXPERIMENT
DENSITY STATISTICS
CHARTS
DATA ANALYSIS
DATA COLLECTION
GRAPHS
INFERENCE
TABLES
COMPUTATION
TECHNICAL WRITING
CENTRAL TENDENCY

 

 

Grades:

 

 

Kg [] - 1 [] - 2 [] - 3 [] - 4 [] - 5 [] - 6 [] - 7 [] - 8 [] - 9 [x] - 10 [x] - 11 [x] - 12 [x]

 

 

ICLE Application:

 

 

D

 

 

 

 

 

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