Subject(s) Math Grade Level 9th Duration



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Radioactive Dice Decay
Author(s)

Maisha Murry

Mathew Bye
Subject(s)

Math
Grade Level

9th
Duration

Two-Three 70 minute periods


Rationale (How this relates to engineering)

Radioactivity naturally occurs in our environment. Different radioisotopes are used for the production of electricity, sterilizing food, medical treatment, and etc. Students need to have some basic understanding of how radioactivity relates to them and their environment.


Exponential decay based on the half-life of the isotope. The half-life
Activity Summary

Students will learn that radioactive decay is unpredictable and spontaneous. They will also learn that the decay of one atom to another is irreversible. (This principle can be illustrated using popcorn) Students will learn that exponential decay is when a quantity deceases at a rate proportional to its value. Students will learn how the half-life of a radioactive isotope is subject to exponential decay. Students will learn that the half-life of a radioactive isotope is the time required for a quantity of radioactivity to decay by half. These principles will be illustrated using dice.


Objectives

Upon completion of this lesson, students will be able to…

  1. Understand the unpredictability and spontaneity of radioactive decay.

  2. Understand that the decay of one atom to another is irreversible

  3. Understand exponential decay of radioactive isotopes


Standards

Mathematics

Patterns, Functions, and Algebra Standards (Pg 170)

  • Generalize patterns using functions or relationships (linear,

quadratic and exponential), and freely translate among tabular, graphical and symbolic representations.

  • Describe problem situations (linear, quadratic and exponential) by using tabular, graphical and symbolic representations.

Physical Science

Nature of Matter (Pg 137)

  • Describe radioactive substances as unstable nuclei that undergo random spontaneous nuclear decay emitting particles and/or high energy wavelike radiation.



Background Knowledge

Students should some general knowledge of radioactivity. Students should also be able to graph points.


Materials Required

Handout (Below)

Popcorn Popper

Popcorn Kernels

Cooking oil

50 dice for each students (A total of 1250 dice are needed for a group of 25 students)

50 Ziploc Bags

25 boxes (The tops of printer paper boxes would work best)

Black Marker

Graphing Paper

Geiger Counter for Alpha

Geiger Counter for Beta

Mental Lanterns containing thorium (Alpha-α Source)

Uranium Glazed Pottery (Alpha-α, Beta-β, Gamma-γ Source)

Pencils
Activities

Teacher Information

The teacher will introduce Radiation and Radioactive decay. First probe students with questions like what is radiation to gage your students understanding of the subject.



  • Radiation is energy in the form of waves or moving subatomic particles. Explain the most commonly known sources of radiation (Note: Constantly ask your students question about each of the different area before you tell them the answer.)

    • Alpha-α particle (A Helium Atom-2 Protons & 2-Neutrons)

    • Beta particle (An Electron)

    • Photons-Gamma- γ Rays (Come from inside the nucleus), X-Rays (Come from outside the nucleus)

  • Radioactive decay is a process when an unstable atom loses energy by emitting radiation

Using a popcorn popper (or hotplate, skillet), cooking oil and popcorn demonstrate the following

  • The unpredictability and spontaneity of radioactive decay by popping popcorn.

  • That the decay of one atom to another is irreversible by showing a popcorn kernel un-popped and popped.

Using a Geiger Counter (one for alpha and beta) demonstrate the different shielding methods for alpha particles beta particles and gamma rays.

  • Alpha particle can be shielded (stopped) by a sheet of notebook paper

  • Lower energy Betas can be shielded (stopped) by aluminum foil.

  • Gamma Rays can be shielded (stopped) by lead or H2O.

Following the demonstration each student will be given 50 dice in a Ziploc bag, a box and additional Ziploc bag labeled “Decayed Dice.” Review the student handout procedure and have students complete the math lab.



Radioactive Dice Decay Student Handout
Procedure

  1. Obtain 50 dice, place them into a Ziploc bag and roll them out into the box. Please do not make too much noise, and be careful not to loose any.

  2. Every time you roll the dice, some dice will decompose (decay) and you must remove them. Place them in the Ziploc bag marked “Decayed Dice.”

  3. For the first trial, if an even number (2,4,6) is rolled, the dice has decayed and must be removed. Count the remaining dice and record this information the data table under the “# of Dice Left.”

  4. Put the remaining dice in the container and roll again. Remove the even numbered dice, and record the number of dice remaining in the data table.

  5. Continue rolling dice, removing even numbered dice and recording in the data table, until all the dice have been removed. You have completed Trial # 1.

  6. For Trial # 2 repeat steps 2-5, but this time the odd numbered (1, 3, 5) dice are radioactive and decay.

  7. For Trial # 3 repeat steps 2-5, but this time only dice numbered 1 and 6 decay.

  8. For Trial # 4 repeat steps 2-5, but this time dice numbered 1, 2, 3, 4 decay.

  9. Make a graph of the results. On the x-axis goes the number of tosses, and on the y-axis goes the number of dice remaining. All data will go onto the same graph, so everyone shall use the same scale. Turn your paper sideways (landscape) and use the following scale: 1 Toss = 1 Line (x-axis) and 2 dice = 1 line (y-axis).

  10. Answer the following post math lab questions in complete sentences.

Radioactive Dice Decay Math Lab
Name Date


Trial # 1: Even Numbers

Toss #

# Dice Left

0

50






















































































































































































































Trial # 2: Odd Numbers

Toss #

# Dice Left

0

50














































































































































































































Radioactive Dice Decay Math Lab
Name Date


Trial # 3: Dice 1 & 6

Toss #

# Dice Left

0

50





















































































































































































































Trial # 4: Dice 1,2,3,4

Toss #

# Dice Left

0

50



















































































































































































































Radioactive Dice Decay Math Lab
Answer the following post math lab questions in complete sentences.


  1. Describe any patterns that you see in the data. (Use words like increasing and decreasing, x-axis and y-axis)




  1. For the first two trials (even and odd dice), how many tosses did it take for half of the dice to decay? Compare this number to the other two trials.




  1. Based on questions number one and two, define in your own words what half –life means.



  1. Think about what would happen if you started with only 40 dice. Explain how you think the data and graph would look different.

Radioactive Dice Decay Math Lab




    1. Try using 40 dice and repeat trial # 1 only.

    2. Do you agree with your answer for # 4 above? Why or Why not?



Trial # 1: Even Dice Numbers

Toss #

# Dice Left

0

50








































































































































  1. Suppose you were to start with 100 dice and redid all 4 trials.

    1. How would the data look different?

    2. How would the data look the same?


Radioactive Dice Decay Rubric





1

2

3

4

Trials 1-4

Student completes 1 out of 4 of the Trials

Students completes 2 out of 4 of the Trials

Student completes 3 out of 4 of the Trials

Student completes all 4 Trials

Graphing

Students graphs 1 out of 4 trials neatly and correctly with the

1 Toss = 1 Line on the x-axis and 2 dice = 1 line

Students graphs 2 out of 4 trials neatly and correctly with the

1 Toss = 1 Line on the x-axis and 2 dice = 1 line

Students graphs 3 out of 4 trials neatly and correctly with the

1 Toss = 1 Line on the x-axis and 2 dice = 1 line

Students graphs all 4 trials neatly and correctly with the

1 Toss = 1 Line on the x-axis and 2 dice = 1 line on the y-axis

Behavior

Student needs improvement. Discipline is not acceptable

Student is attentive while being somewhat disruptive

Student is attentive and actively participating

Student is very attentive and actively participating without disturbing others

Questions 1-4

Student answers 1 out of the 4 questions correctly in complete sentences

Student answers 2 out of the 4 questions correctly in complete sentences

Student answers 3 out of the 4 questions correctly in complete sentences

Student answers all 4 of the questions correctly in complete sentences

Questions

5 & 6

Student answers one part of questions 5 or 6 correctly in complete sentences

Student answers part a & b of questions 5 or 6 correctly in complete sentences

Student answers all 3 out of 4 parts questions 5 & 6 correctly in complete sentences

Student answers part a & b, in questions 5 & 6 correctly in complete sentences





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