Isotopic pennies - Integrating Chemistry and Algebra II

In this lesson, student use a system of equations to determine the number of each type of “atom” in a closed container.

Learning outcomes

Students will be able to:

Set up a system of equations to determine the number of “atoms” in a closed container
Connect this activity to the way scientists are able to determine the relative abundance of isotopes in a sample
Set up and solve a system of equations from data they collect

Teacher planning

Time required

45 minutes

Materials needed

Each student or pair of students will need:

1 empty balloon
10 pre-1982 pennies
10 post-1982 pennies
1 balloon with 10 pennies, some pre-1982 and some post-1982
balance

Student handouts

Isotopic pennies: Document by the author; Open as PDF (19 KB, 2 pages; also available as Microsoft Word document)

Pre-activities

Before beginning this lesson:

Students should to be able to define the term isotope and calculate atomic mass when given the masses of isotopes and their respective percent abundances.
Students should be familiar with setting up and solving systems of equations.

Make sure you record the number of pre- and post-1982 pennies in each balloon.

Activities

Students will collect the mass data of an empty balloon, pre- and post-1982 pennies, and their assigned balloon. They will then use that information to set up their system in order to determine the number of pre- and post-1982 pennies they have in their balloons.

Distribute the lab sheets and materials for the experiment.
Begin the lab with a discussion about the historical composition of pennies. Tell students that the United States penny was first issued in 1909 and was composed of 95 percent copper and 5 percent zinc. All pennies were made with this composition until 1982 when the high cost of copper dictated a major change in composition. Since 1982, United States pennies have been produced with 97.6 percent zinc and a thin plating of copper. Since each metal has a different density, pre- and post-1982 pennies have different masses.

Have students look at the second page on their lab sheets and complete the pre-lab questions. They will be answering the following questions.

What is an isotope?
What is the difference in pre- and post-1982 pennies?
Suppose you have a paper bag containing only pencils and pens. The total number of items is 25. From the data given below, set up and solve a system of equations to determine the number of pens and pencils in the bag.

ITEM	MASS
One pencil	2 grams
One pen	5 grams
Empty bag	0.5 grams
Bag + mixture of pencils and pens	104.5 grams

What percentage of pencils and pens are in the bag?

Explain that, in this lab, a mixture of pre- and post-1982 pennies will represent the naturally occurring mixture of two isotopes of an imaginary element. With this mix of pennies, they will simulate one way scientists can determine the relative amounts of different isotopes present in a sample of an element. They have been given a sealed balloon with a total of 10 pre- and post-1982 pennies. They must determine the number of each type of penny in the container.
Have students calculate the following information and enter their data into the table on their lab sheets.

Number on balloon	Balloon #
Mass of 10 pre-82 pennies
Average mass of 1 pre-82 penny
Mass of 10 post-82 pennies
Average mass of 1 post-82 penny
Mass of empty balloon
Mass of balloon and 10 pennies

Once students have completed their tables, instruct them to use a system of equations to determine the number of pre-82 and post-82 pennies in their balloons.

Assessment

Evaluate student responses to the post-lab questions.

Critical vocabulary

isotope: one of two or more atoms with the same atomic number but with different numbers of neutrons
system of equations: a collection of two or more equations with a same set of unknowns
percent abundance: the amount of an isotope of an element that exists in nature, usually expressed as a percentage of the total amount of all isotopes of the element

Comments

This activity worked best when the Algebra II teacher has students do it after they calculate the atomic mass of an element simulation in chemistry class. However, this activity can be done in either an Algebra II or Chemistry as a standalone activity. It will be helpful to students either way.

North Carolina curriculum alignment

Mathematics (2004)

Grade 9–12 — Algebra 2

Goal 2: Algebra - The learner will use relations and functions to solve problems.
- Objective 2.10: Use systems of two or more equations or inequalities to model and solve problems; justify results. Solve using tables, graphs, matrix operations, and algebraic properties

Science (2005)

Grade 9–12 — Chemistry

Goal 1: The learner will develop abilities necessary to do and understand scientific inquiry.
- Objective 1.01: Design, conduct and analyze investigations to answer questions related to chemistry.
  - Identify questions and suggest hypotheses.
  - Identify variables.
  - Use a control when appropriate.
  - Select and use appropriate measurement tools.
  - Collect and organize data in tables, charts and graphs.
  - Analyze and interpret data.
  - Explain observations.
  - Make inferences and predictions.
  - Explain the relationship between evidence and explanation.
  - Identify how scientists share findings.
Goal 2: The learner will build an understanding of the structure and properties of matter.
- Objective 2.02: Examine the nature of atomic structure.
  - Subatomic particles: protons, neutrons, and electrons.
  - Mass number.
  - Atomic number.
  - Isotopes.