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The Density of Coins

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Summary

Students will conduct a science experiment where they will learn that the different denominations have characteristic densities that can be used to help identify the type of coin being used.

Coin Type(s)

  • Cent
  • Nickel
  • Dime

Coin Program(s)

  • Generic

Objectives

Students will learn that the different denominations have characteristic densities that can be used to help identify the type of coin being used.

Major Subject Area Connections

  • Science

Minor/supporting Subject Area Connections

  • Math

Grades

  • Sixth grade
  • Seventh grade
  • Eighth grade

Class Time

Sessions: One
Session Length: 90 minutes
Total Length: 46-90 minutes

Terms and Concepts

  • Cent
  • Density
  • Dime
  • Mass
  • Nickel
  • Penny
  • Volume

Materials

  • Pennies
  • Nickels
  • Dimes
  • Water
  • Graduated cylinders
  • Balances
  • Calculators
  • Pencils
  • Paper
  1. Divide the students into pairs. Distribute five of each coin (pennies, nickels, and dimes) to each pair.
  2. Have each pair of students create a data table where they will include columns for coin type, mass, volume and density.
  3. Have each group use a balance to measure and record the mass of each set of five coins in their data table.
  4. Have the students fill a graduated cylinder to the 20 mL point
  5. Have the students drop one coin group (pennies, nickels, or dimes) into the water and record the height that the water rises to, then subtract the initial 20 mL from the new height to find the volume for the coin group and record that volume in their data table.
  6. Have the students perform the same measurement for the remaining coin groups separately and record the results.
  7. Using a calculator, have the students divide the mass of each set by the volume of that coin group. This calculation will be representative of the density of that coin group. Have them write these densities in the data table. Have the students share their answers. Note that the mass, volume and therefore density of circulating coins may vary slightly due to wear, but these discrepancies should be minor.

Enrichments/Extensions

  • Give students data about “unknown” coins. Have them use the knowledge the students have developed to identify what type of coin the information relates to.
  • Have students find the density of coins of larger denominations (half-dollar, dollar) to demonstrate their understanding of the process of finding a coin’s density.

Use the lab notebooks to determine whether the students have met the lesson objectives.

Discipline: Math
Domain: 6.SP Statistics and Probability
Grade(s): Grade 6
Cluster: Summarize and describe distributions
Standards:

  • 6.SP.4. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
  • 6.SP.5. Summarize numerical data sets in relation to their context, such as by:
    • Reporting the number of observations.
    • Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
    • Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
    • Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

Discipline: Mathematics
Domain: 6-8 Number and Operations
Cluster: Compute fluently and make reasonable estimates.
Grade(s): Grades 6–8
Standards:

In grades 6–8 all students should

  • select appropriate methods and tools for computing with fractions and decimals from among mental computation, estimation, calculators or computers, and paper and pencil, depending on the situation, and apply the selected methods;
  • develop and analyze algorithms for computing with fractions, decimals, and integers and develop fluency in their use;
  • develop and use strategies to estimate the results of rational-number computations and judge the reasonableness of the results; and
  • develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Discipline: Mathematics
Domain: 6-8 Number and Operations
Cluster: Understand meanings of operations and how they relate to one another.
Grade(s): Grades 6–8
Standards:

In grades 6–8 all students should

  • understand the meaning and effects of arithmetic operations with fractions, decimals, and integers;
  • use the associative and commutative properties of addition and multiplication and the distributive property of multiplication over addition to simplify computations with integers, fractions, and decimals; and
  • understand and use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems.

Discipline: Mathematics
Domain: 6-8 Number and Operations
Cluster: Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
Grade(s): Grades 6–8
Standards:

In grades 6–8 all students should

  • work flexibly with fractions, decimals, and percents to solve problems;
  • compare and order fractions, decimals, and percents efficiently and find their approximate locations on a number line;
  • develop meaning for percents greater than 100 and less than 1;
  • understand and use ratios and proportions to represent quantitative relationships;
  • develop an understanding of large numbers and recognize and appropriately use exponential, scientific, and calculator notation;
  • use factors, multiples, prime factorization, and relatively prime numbers to solve problems; and
  • develop meaning for integers and represent and compare quantities with them.

Discipline: Mathematics
Domain: 6-8 Measurement
Cluster: Apply appropriate techniques, tools, and formulas to determine measurements.
Grade(s): Grades 6–8
Standards:

In grades 6–8 all students should

  • use common benchmarks to select appropriate methods for estimating measurements;
  • select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision;
  • develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes;
  • develop strategies to determine the surface area and volume of selected prisms, pyramids, and cylinders;
  • solve problems involving scale factors, using ratio and proportion; and
  • solve simple problems involving rates and derived measurements for such attributes as velocity and density.

Discipline: Mathematics
Domain: 6-8 Measurement
Cluster: Understand measurable attributes of objects and the units, systems, and processes of measurement.
Grade(s): Grades 6–8
Standards:

In grades 6–8 all students should

  • understand both metric and customary systems of measurement;
  • understand relationships among units and convert from one unit to another within the same system; and
  • understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume.

Discipline: Science
Domain: 5-8 Content Standards
Cluster: Physical Science
Grade(s): Grades 6–8
Standards:

  • Properties and changes of properties in matter
  • Motions and forces
  • Transfer of energy

Discipline: Science
Domain: 5-8 Content Standards
Cluster: Science as Inquiry
Grade(s): Grades 6–8
Standards:

  • Ability necessary to do scientific inquiry
  • Understand scientific inquiry