THIS WEEK'S LESSON ACTIVITIES
INSTRUCTOR__________________________
LEVEL___Math E_______
DATE____________ CLASS
Topic: Megabucks – Beating the Odds
Guiding Question: You won Nevada’s Megabucks, do you choose cash or annuity?
The Nevada Megabucks Slot Machine gives winners the choice between a one-time cash
payout or a 30-year annuity. In this task, students will evaluate the two prize options by
making reasonable assumptions to help them decide on an option.
Lesson Objectives:
The students will be able to:
1) Identify and assign values to assumptions
2) Use accountable talk stems to question and explain reasoning
3) Substitute values (assumptions) to solve equations
CCR Math Content Standards Aligned to this Lesson:
A.CED.1 Create equations that describe numbers or relationships
A.REI.1 Understand solving equations as a process of reasoning and explain the
reasoning.
CCR Math Practice Standards Aligned to this Lesson:
1. Make sense of problems and persevere in solving them.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
Reading: (see the multi-day plan for details)
Text-dependent Questions:
Why do you think John Waggoner wrote
this article?
Perhaps a lot of people were choosing the
tempting lump sum payout without looking
at the long-term cost of the decision.
Why does the author write, in line 13-14,
The lump sum of $360.2 million vs. $550
that one reason is “purely mathematical”?
million in 30 payments. Annuity is the
lump sum plus interest.
Why should one opt for the lump sum?
Line 27 – 29. Interest rates are so low.
You an earn a better return than the 2.8%
treasury note.
Create a scenario, based on the evidence, If interest rates for the treasure notes
that would support choosing the annuity
were higher than interest you would
option.
receive when investing on your own.
What is the take-home monetary amount of Line 40. Find 25% of $550 million.
a $550 million prize after the lottery
Subtract that amount from $550 million.
withholds federal tax?
How much would you have to set aside for Find an additional 10% of your take-home
your own federal taxes?
amount.
Why should you make charitable
contributions in the current year?
Why does Schatsky say, “Protect yourself”
in line 54?
Why would taking the lump sum require
discipline? Line 48.
What would $550 million yield over 30
years with a 2.8% rate?
Why is ‘taking a deep breath’ the first thing
a Powerball winner should do?
Line 44. You can deduct charitable
contributions on your income tax. This
may be reduced by 80% the following
year.
A winner may be taken advantage of or
not very financially savvy.
One possible answer: It may be tempting
for some to blow the entire sum on boats,
houses, travel etc. and not invest.
You may want to direct students to an
online annuity calculator.
One possible answer: the winner will be
so excited that they should take a deep
breath to think clearly about which version
of the prize they should choose.
How I will scaffold my lessons to reach all of my students' levels:
Ask guiding questions to help students determine assumptions and values for those
assumptions. Some students may use an annuity calculator; others may work the
problem on their own and add in tax rates etc. Depending on the assumptions, the
problem can be as simple or complex as needed. Accountable talk stems provide
discussion scaffolding. The article adds authenticity to the task and will reinforce the
concept through reading and writing. Graphic organizers.
How I will assess my students' mastery of the lessons:
Monitor student progress by listening to small group discussions and accountable talk.
Evaluate the activity sheet. Students write a 60-second summary to exit class.
Assign and evaluate homework assignment (see Take-home Activity Sheet following this
lesson).
My reflections of the lessons (what worked, what didn't, what I might change for
next time):
Resources:
Shakelford, Michael. “Megabucks.” Wizard of Odds, July 15, 2013.
http://wizardofodds.com/games/slots/megabucks/’
Slowbe, Jason. “Cash or Gas?” National Council of Teachers of Mathematics (NCTM)
Waggoner, John. “Advice for the lucky Powerball jackpot winners.” USA Today,
November 29, 2012.
http://www.usatoday.com/story/money/personalfinance/2012/11/28/powerball-winneradvice/1732757/
Multi-day Plan:
Day 1: Present students with the task: You have just won the $150 million Mebabucks
Jackpot at a local casino and are given the option of taking the one-time cash prize or
collecting the prize over a 30-year annuity. Which prize is best for you? (see activity
sheet). Distribute Activity Sheet. Students work in groups on question 1 ad 2. Facilitate
a discussion based on the reasons a person may choose the cash or annuity option. In
pairs or small groups, students complete question 3. Guide students as they determine
their assumptions. What do you need to know to answer this question? Where can you
locate this information? Students assign numbers to their assumptions and can utilize
outside resources to locate interest rates, tax rates etc. (for example: an annuity payout
calculator http://www.calculator.net/annuity-payout-calculator.html). In lieu of outside
resources, what is a reasonable guess for the amount the state withholds for one lump
some payout (40%), the state income tax on said annual income (about 30%), interest
rates, etc. Encourage students to challenge one another’s answers to these questions
and to request evidence that supports their responses. As necessary, focus the
discussion on mathematical justifications, not on personal preferences. Option: write
Accountable Talk stems on the board to help students with the discussion:
I don’t understand _________ about your solution.
Can you explain __________.
I see your point, but _____________.
What happens when you ______________.
Have you considered trying _____________.
How did you reach that conclusion?
What if you had started with ________ rather than ________?
I want to add to what __(name)___ said about ________.
Additional Accountable Language Stems:
http://curriculum.dpsk12.org/lang_literacy_cultural/literacy/elem_lit/curric_instruc_assess/i
nterdisc_units/AccountableTalkFeaturesandLanguageStems.pdf
Discuss results using Accountable Stems.
The instructor then reads the article aloud to students. Students then read the article
independently and answer text-dependent questions (see table above) in small groups.
Assign homework (Take-home Activity Sheet)
Day 2: Review Take-home Activity Sheet. Select a few students to present their financial
summaries and discuss. Remind students to use Accountable Talk stems when
responding or providing feedback. Distribute the Wizard of Odds article found at:
http://wizardofodds.com/games/slots/megabucks/ Discuss the article and calculations.
Determine how the author arrived at the algebra:
1 = 0.7844 + j × (1/368)3/3 j × (1/368)3/3 = 1 - 0.7844
j = 3 × (1 - 0.7844) / (1/368)3
j = $32,238,319
Day 3: Read “Pennies Ready to Pop”. Design your own slot machine. Include the
theme, probability, break-even point, minimum prize amount, price per pull, etc. Include a
two-paragraph write-up as to why we should play your machine. Present your slot
machine to the class.
CA$H OR ANNUITY?
Congratulations! You have just won the $150 million
Megabucks Jackpot and now you must choose to collect your winnings now or opt for the 30year annuity.
1. Complete the chart (and add a few ideas of your own) for the lifestyle of each person who
would choose each prize:
CASH
ANNUITY
Age
Occupation
Financial circumstances
2. Which prize would be best for you? Explain why.
3.a. Before you calculate which prize would be the best choice for you, please list your
assumptions:
b. Solve and discuss your reasoning. Show your calculations.
4. Change one or more assumptions in question 3.b. Could this change the prize you
selected? Discuss and support your answer with calculations.
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CA$H OR ANNUITY?
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Advice for the lucky Powerball jackpot winners by John Waggoner
USA Today, November 29, 2012
The first thing a Powerball winner should do: Take a deep breath.
Then find a private place -- where neighbors won't hear you -- and scream your lucky head
off.
Once you've gotten that out of the way, you've got some big decisions to make. The first:
Lump sum or annuity?
Take the lump sum, says Mark Bass, a financial planner in Lubbock, Texas. One reason is
purely mathematical.
The current estimated pre-tax jackpot is $550 million, doled out in 30 payments. If you
want a lump sum, you'll get $360.2 million. (If you die before all the payments are made,
your heirs get the remaining payments).
Why the difference in the lump sum and the 30-year payments? The $550 million is an
estimated annuity payment, which is based on the actual lottery pot plus interest earned
from U.S. government securities.
A lottery official said late Wednesday that the jackpot increased to $579.9 million by the
time of the drawing, making the cash option $379.8 million.
Interest rates are so low now that you should opt for the lump sum, Bass says. The 30-year
Treasury note currently yields just 2.8%. You can probably earn better returns than that in
the next three decades.
You'll owe taxes in the year you claim your prize, not the year you win it, says John Hagerty,
spokesman for the Virginia lottery. How much time you have before your ticket expires
depends on the state in which you purchase it, according to the Powerball website.
If you do decide to take the lump sum, do it this year. "There's a strong possibility that tax
rates will be higher in 2013 than 2012," says Melissa Labant, director of tax advocacy at the
American Institute of CPAs. Should Congress fail to act, the highest tax rate will rise to
39.6% from 35% now.
The lottery will withhold 25% federal tax, as well as any state taxes applicable. You'll be in
the top tax bracket, so you'll have to make sure you put aside another 10% for federal
taxes.
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You should also make charitable contributions this year: Should Congress fail to act by the
end of the year, your ability to deduct charitable contributions could be reduced up to 80%,
she says.
Why would you take the annuity payments? Worries that you might not be disciplined
enough to handle the lump sum. "You don't get windfalls like this in millions of lifetimes,
much less twice in one lifetime," says Gary Schatsky, a New York financial planner. "You
have to make sure that any moves you make are done after careful consideration."
Taxes are just one thing to think about when you've been handed so much money. "Plan
very carefully what your next steps are," Schatsky says. "Protect yourself from those who
have their hands out, or those who are selling products."
Contributing: Associated Press
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Take-home Activity Sheet
Complete the table for the following prizewinners. Should they choose the
lump sum or the annuity? Why?
Winner
Lump sum (why?)
Annuity (why?)
25 year-old single
mother of three
80 year-old with a large
extended family
Retired 65-year old with
no next of kin
A young undocumented
citizen
A dual-income,
financially stable couple
Your teacher
You are a financial planner. Choose one of the above winners and write a twoparagraph financial summary to persuade your client to choose either the
lump sum or annuity. Include mathematical calculations.
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