Saving for the New Year
To start the new year, I have decided to start a savings account
so that I can buy myself a little something special on New
Year’s Day next year. I have decided to put one dime in a jar
on the 1st day of every month between January 1st and
December 1st. I have decided to put 2 dimes in the jar on the
2nd day of every month between January 2nd and December
2nd. I have decided to put 3 dimes in the jar on the 3rd day of
every month between January 3rd and December 3rd.
I will continue doing this every day, adding a dime every day for
each day every month. If I keep my New Year’s resolution, how
much money will I have to spend on myself on New Year’s Day
next year?
Saving for the New Year
Copyright 2008, Exemplars, Inc. All rights reserved.
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Saving for the New Year
Suggested Grade Span
6–8
Grade(s) in Which Task Was Piloted
6
Task
To start the new year, I have decided to start a savings account so that I can buy myself a little
something special on New Year’s Day next year. I have decided to put one dime in a jar on the
1st day of every month between January 1st and December 1st. I have decided to put 2 dimes
in the jar on the 2nd day of every month between January 2nd and December 2nd. I have
decided to put 3 dimes in the jar on the 3rd day of every month between January 3rd and
December 3rd.
I will continue doing this every day, adding a dime every day for each day every month. If I keep
my New Year’s resolution, how much money will I have to spend on myself on New Year’s Day
next year?
Alternative Versions of Task
More Accessible Version:
To start the new year, I have decided to start a savings account so that I can buy myself a little
something special on New Year’s Day next year. I have decided to put 1 penny in a jar on the
1st day of every month between January 1st and December 1st. I have decided to put 2
pennies in the jar on the 2nd day of every month between January 2nd and December 2nd. I
have decided to put 3 pennies in the jar on the 3rd day of every month between January 3rd
and December 3rd.
I will continue doing this every day, adding a penny every day for each day every month. If I
keep my New Year’s resolution, how much money will I have to spend on myself on New Year’s
Day next year?
More Challenging Version:
To start the new year, I have decided to start a savings account so that I can buy myself a little
something special on New Year’s Day next year. I have decided to put 1 dime in a jar on the 1st
odd day of every month between January 1st and December 1st. I have decided to put 2 dimes
Saving for the New Year
Copyright 2008, Exemplars, Inc. All rights reserved.
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in the jar on the even-numbered days of every month between January 2nd and December 2nd.
I have decided to put 3 dimes in the jar on the odd-numbered days of every month between
January 3rd and December 3rd.
I will continue doing this every day, adding a dime every day for each day every month. If I keep
my New Year’s resolution, how much money will I have to spend on myself on New Year’s Day
next year?
My friend has also decided to start a savings account so that she can buy herself a little
something special on New Year’s Day next year. She has decided to put 1 penny in a jar on the
1st day of every month between January 1st and December 1st. She has decided to put 1
nickel in the jar on the 2nd day of every month between January 2nd and December 2nd. She
will continue doing this every day, adding a penny on every odd day of the month and a nickel
on every even day of the month. If she keeps her New Year’s resolution, what will be the
difference in the amount of money each of us will save?
NCTM Content Standards and Evidence
Algebra Standard for Grades 6–8: Instructional programs from pre-kindergarten through grade
12 should enable students to ...
Understand patterns, relations and functions.
• NCTM Evidence: Represent, analyze and generalize a variety of patterns with tables,
graphs, words and, when possible, symbolic rules.
• Exemplars Task-Specific Evidence: This task requires students to use the relationship of
the number of days in each month and the amount of money saved each day of the month
to find a total amount saved.
Number and Operations Standard for Grades 6–8: Instructional programs from prekindergarten through grade 12 should enable students to ...
Understand numbers, ways of representing numbers, relationships among numbers and
number systems.
• NCTM Evidence: Work flexibly with fractions, decimals and percents to solve problems.
• Exemplars Task-Specific Evidence: This task requires students to find a total amount of
money saved.
Saving for the New Year
Copyright 2008, Exemplars, Inc. All rights reserved.
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Time/Context/Qualifiers/Tips From Piloting Teacher
This task took 45 minutes for most students. It is obviously best given after the new year, but it
could be adapted to any other date like a birthday or other holiday. You will want to have
calendars available to which students can refer while solving the task.
Links
This task could be given during New Year’s celebrations or even at the beginning of the school
year. The task could be changed so that the first dime is put in on the first day of school and the
last on the last day of school. The task could also accompany activities in an economics class.
Common Strategies Used to Solve the Task
Most students in my pilot determined the amount saved each month. Others will determine how
many one cent days there are, two cent days there are, etc. Still others will find the sum of
money saved for a month with 28 days x 12 months and then will add to that sum the money
saved on the extra days of months with more than 28 days. Some students may use a formula
for finding the sum of numbers, while others will determine the sum using lengthy calculations.
Possible Solutions
Seven months have 31 days, four months have 30 days and one month has 28 days.
You can use the summation formula [n(n + 1)]/ 2 for finding the sums:
For months with 31 days:
[31(32)]/2 x 7 months = 3,472
For months with 30 days:
[30(31)]/2 x 4 months = 1,860
For months with 28 days:
[28(29)]/2 x 1 month = 406
3,472 + 1,860 + 406 = 5,738 x $0.10 = $573.80
More Accessible Version Solution:
Seven months have 31 days, four months have 30 days, and one month has 28 days.
You can use the summation formula [n(n + 1)] / 2 for finding the sums:
Saving for the New Year
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For months with 31 days:
[31(32)] /2 x 7 months = 3,472
For months with 30 days:
[30(31)] /2 x 4 months = 1,860
For months with 28 days:
[28(29)] /2 x 1 month = 406
3,472 + 1,860 + 406 = 5,738 x $0.01 = $57.38
More Challenging Version Solution:
Total Days
Number
Even Days (1¢)
Number
Odd Days
( x .05)
January
31
15
16
.80
February
28
14
14
.70
March
31
15
16
.80
April
30
15
15
.75
May
31
15
16
.80
June
30
15
15
.75
July
31
15
16
.80
August
31
15
16
.80
September
30
15
15
.75
October
31
15
16
.80
November
30
15
15
.75
December
31
15
16
.80
Total from even days = $1.79
Total from odd days = $9.30
Grand total = $11.09
$573.80 – $11.09 = $562.71 that I will have saved more than she has
Task-Specific Assessment Notes
General Notes
This task does not lend itself well to using math language to communicate the solution, so the
student should not be penalized for not doing so.
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Novice
The Novice will demonstrate little or no understanding of the task. An incorrect or a correct
answer could be posted with no supporting work.
Apprentice
The Apprentice will have a partially correct solution. The Apprentice may not reach a correct
answer because of a computation error, an omission error, a reasoning error or an error in
carrying out the pattern.
Practitioner
The Practitioner will have a correct solution and show all supporting work. Representations or
math language will be used to communicate the solution.
Expert
The Expert will rely on an efficient approach or prior knowledge to solve the task.
Communication with the audience will be clear and purposeful. The Expert will extend the
solution by creating a rule for solving the task, verifying the solution, or going above and beyond
task requirements.
Saving for the New Year
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Novice
Saving for the New Year
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Apprentice
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Apprentice
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Practitioner
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Practitioner
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Expert
Saving for the New Year
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