Halloween Time

Halloween Time
My husband and I are hoping to avoid eating Halloween candy
this year.
I plan to buy our candy on the way home from school on
Halloween day so it won’t sit in our house tempting us to eat it.
I also want to buy the exact amount of candy we need so there
won’t be leftovers to tempt us. That’s where we need your help.
We plan to give out Jolly Ranchers. We usually let the trick-ortreaters choose the number of candies they want.
Last year we kept track of what children took. Unfortunately, my
husband and I got home late last Halloween and missed many
of the trick-or-treaters, so our list is limited.
When we are home on time, we usually have about 120 trick-ortreaters. If this is the case, do your best to mathematically
determine the number of Jolly Ranchers we should buy.
Remember, we want to have enough but not too many extra!
I look forward to getting your mathematical advice.
Halloween Time
Copyright 2008, Exemplars, Inc. All rights reserved.
1 of 15
Costume
Goblin
Witch
Punk Rocker
Dice
Dora the
Explorer
Dracula
Tennis
Player
Princess
Dollar Bill
Harry Potter
Bob the
Builder
Number of
Candies
Taken
2
3
11
4 and 3
3
Costume
Dragon
Ninja Turtle
Butterfly
Humpty Dumpty
Bear
Number of
Candies
Taken
5
1
6
5
3
2
1
Pumpkin
Tree
5
3
6
5
5
1
Darth Vader
Bunny
Bumble Bee
Wizard
8
3
4
2
Halloween Time
Copyright 2008, Exemplars, Inc. All rights reserved.
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Halloween Time
Suggested Grade Span
6–8
Grade(s) in Which Task Was Piloted
7 and 8
Task
My husband and I are hoping to avoid eating Halloween candy this year.
I plan to buy our candy on the way home from school on Halloween day so it won’t sit in our
house tempting us to eat it.
I also want to buy the exact amount of candy we need so there won’t be leftovers to tempt us.
That’s where we need your help.
We plan to give out Jolly Ranchers. We usually let the trick-or-treaters choose the number of
candies they want.
Last year we kept track of what children took. Unfortunately, my husband and I got home late
last Halloween and missed many of the trick-or-treaters, so our list is limited.
When we are home on time, we usually have about 120 trick-or-treaters. If this is the case, do
your best to mathematically determine the number of Jolly Ranchers we should buy.
Remember, we want to have enough but not too many extra!
I look forward to getting your mathematical advice.
Halloween Time
Copyright 2008, Exemplars, Inc. All rights reserved.
3 of 15
Costume
Number of
Candies Taken
Costume
Number of
Candies Taken
Goblin
2
Dragon
5
Witch
3
Ninja Turtle
1
Punk Rocker
11
Butterfly
6
Dice
4 and 3
Humpty Dumpty
5
Dora the Explorer
3
Bear
3
Dracula
2
Pumpkin
5
Tennis Player
1
Tree
3
Princess
6
Darth Vader
8
Dollar Bill
5
Bunny
3
Harry Potter
5
Bumble Bee
4
Bob the Builder
1
Wizard
2
Alternative Versions of Task
More Accessible Version:
(Use the same chart that appears in the original version of the task.)
My husband and I are hoping to avoid eating Halloween candy this year.
I plan to buy our candy on the way home from school on Halloween day so it won’t sit in our
house tempting us to eat it.
I also want to buy the exact amount of candy we need so there won’t be leftovers to tempt us.
That’s where we need your help.
We plan to give out Jolly Ranchers. We usually let the trick-or-treaters choose the number of
candies they want.
Last year we kept track of what children took. Unfortunately, my husband and I got home late
last Halloween and missed many of the trick-or-treaters, so our list is limited.
Determine the typical number of Jolly Ranchers each child took last year.
Teacher Note:
See page 9 of the PDF to print a complete worksheet with the chart.
Halloween Time
Copyright 2008, Exemplars, Inc. All rights reserved.
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More Challenging Version:
Refer to the original version of the task, and ...
I can buy my candy from several stores. Determine which gives the better deal.
• Candy’s Candy Shop: 1 bag (containing 250 candies) for $3.99.
• Sweet Tooth’s: 2 bags (containing 100 candies each) for $ 3.49.
• Sugar Store: Individual Jolly Ranchers are 18 cents each.
Teacher Note:
See page 10 of the PDF to print a complete worksheet with the chart.
NCTM Content Standards and Evidence
Data Analysis and Probability Standard for Grades 6–8: Instructional programs from prekindergarten through grade 12 should enable all students to ...
Select and use appropriate statistical methods to analyze data.
• NCTM Evidence: Find, use and interpret measures of center and spread, including mean
and interquartile range.
• Exemplars Task-Specific Evidence: This task requires students to find measures of
Central Tendency – mean, median, mode and range.
Understand and apply basic concepts of probability.
• NCTM Evidence: Use proportionality and a basic understanding of probability to make and
test conjectures about the results of experiments and simulations.
• Exemplars Task-Specific Evidence: This task requires students to use measures of
center and proportionality to make conjectures about the results of a simulation.
Time/Context/Qualifiers/Tip(s) From Piloting Teacher
This is a medium-length task. It took students only one class period to complete.
Students in my class had just studied a unit on statistics. This task provides the opportunity to
combine statistics and probability concepts with concepts of proportionality.
To print a copy of the more accessible version of the task with the chart, refer to page 9. To
print a copy of the more challenging version of the task with the chart, refer to page 10.
Halloween Time
Copyright 2008, Exemplars, Inc. All rights reserved.
5 of 15
Links
This task would obviously be given during the Halloween season.
Common Strategies Used to Solve This Task
Most students find a measure of center and multiply that measure of center by 120 to get the
total amount of candy needed.
Possible Solutions
Tennis Player
1
Bob the Builder
1
Ninja Turtle
1
Goblin
2
Dracula
2
Wizard
2
Witch
3
Die
3
Dora the Explorer
3
Bear
3
Tree
3
Bunny
3
Die
4
Bumble Bee
4
Dollar Bill
5
Harry Potter
5
Dragon
5
Humpty Dumpty
5
Pumpkin
5
Princess
6
Butterfly
6
Darth Vader
8
Punk Rocker
11
Min
LQ
Median
UQ
Max
Mean: 3.95652174 x 120 children = 474.782609 candies
Mode: 3 x 120 = 360 candies
Median: 3 x 120 = 360 candies
Halloween Time
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So, 360 to 475 would be an acceptable range of answers to give.
Is 11 an outlier?
5–2=3
3 x 1.5 = 4.5
4.5 + 5 = 9.5
So yes, 11 is an outlier.
More Accessible Version Solution:
Refer to the solution for the original version of the task.
More Challenging Version Solution:
Refer to the solution for the original version of the task, and …
Candy’s Candy Shop: 0.01596 cents each
Sweet Tooth’s: 0.01745 cents each
Sugar Store: 18 cents each
So, Candy’s Candy shop is the least expensive per candy. However, since the candies must be
bought at bulk pricing, another shop might be less expensive for a particular number of candies
needed. For example, if the student thought that 360 candies were needed, then Sweet Tooth's
($6.98 for 400) would be cheaper than Candy's shop ($7.98 for 500).
Task-Specific Assessment Notes
General Notes
Students will need to look at the data through several lenses to make a mathematically
supported conclusion.
Novice
The Novice will draw a conclusion without mathematical support, or no conclusions will be
drawn. Representations will be confusing and will not support a solution. The Novice will use no
math language, or it will be used incorrectly.
Apprentice
The Apprentice will have an approach that would work but it will have many calculation errors
that lead to incorrect solutions. Arguments will be made with some mathematical basis, but the
student's reasoning will be flawed. Some awareness of audience will be present through
narrated work, and an attempt will be made to relate the task to personal experiences. The
Apprentice will attempt math representations to record and communicate problem solving, but
they will have errors.
Halloween Time
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Practitioner
The Practitioner will choose and execute a correct strategy showing evidence of applying prior
knowledge. Arguments will be constructed with an adequate mathematical basis, and a sense
of audience will be communicated. The Practitioner will use formal math language throughout to
communicate ideas. Math connections will be recognized, and math representations will be
accurate and used to solve problems and portray solutions.
Expert
The Expert will reach a correct solution. There will be evidence of analyzing the situation in
mathematical terms and extending prior knowledge. The Expert will make deductive arguments
to justify decisions and will use precise math language to communicate ideas. Math
connections will be used to extend the solution, and math representations will be constructed to
analyze relationships.
Halloween Time
Copyright 2008, Exemplars, Inc. All rights reserved.
8 of 15
More Accessible Version Worksheet
My husband and I are hoping to avoid eating Halloween candy this year.
I plan to buy our candy on the way home from school on Halloween day so it won’t sit in our
house tempting us to eat it.
I also want to buy the exact amount of candy we need so there won’t be leftovers to tempt us.
That’s where we need your help.
We plan to give out Jolly Ranchers. We usually let the trick-or-treaters choose the number of
candies they want.
Last year we kept track of what children took. Unfortunately, my husband and I got home late
last Halloween and missed many of the trick-or-treaters, so our list is limited.
Determine the typical number of Jolly Ranchers each child took last year.
Costume
Number of
Candies Taken
Costume
Number of
Candies Taken
Goblin
2
Dragon
5
Witch
3
Ninja Turtle
1
Punk Rocker
11
Butterfly
6
Dice
4 and 3
Humpty Dumpty
5
Dora the Explorer
3
Bear
3
Dracula
2
Pumpkin
5
Tennis Player
1
Tree
3
Princess
6
Darth Vader
8
Dollar Bill
5
Bunny
3
Harry Potter
5
Bumble Bee
4
Bob the Builder
1
Wizard
2
Halloween Time
Copyright 2008, Exemplars, Inc. All rights reserved.
9 of 15
More Challenging Version Worksheet
My husband and I are hoping to avoid eating Halloween candy this year.
I plan to buy our candy on the way home from school on Halloween day so it won’t sit in our
house tempting us to eat it.
I also want to buy the exact amount of candy we need so there won’t be leftovers to tempt us.
That’s where we need your help.
We plan to give out Jolly Ranchers. We usually let the trick-or-treaters choose the number of
candies they want.
Last year we kept track of what children took. Unfortunately, my husband and I got home late
last Halloween and missed many of the trick-or-treaters, so our list is limited.
When we are home on time, we usually have about 120 trick-or-treaters. If this is the case, do
your best to mathematically determine the number of Jolly Ranchers we should buy.
Remember, we want to have enough but not too many extra! I look forward to getting your
mathematical advice.
I can buy my candy from several stores. Determine which gives the better deal.
• Candy’s Candy Shop: 1 bag (containing 250 candies) for $3.99.
• Sweet Tooth’s: 2 bags (containing 100 candies each) for $ 3.49.
• Sugar Store: Individual Jolly Ranchers are 18 cents each.
Costume
Number of
Candies Taken
Costume
Number of
Candies Taken
Goblin
2
Dragon
5
Witch
3
Ninja Turtle
1
Punk Rocker
11
Butterfly
6
Dice
4 and 3
Humpty Dumpty
5
Dora the Explorer
3
Bear
3
Dracula
2
Pumpkin
5
Tennis Player
1
Tree
3
Princess
6
Darth Vader
8
Dollar Bill
5
Bunny
3
Harry Potter
5
Bumble Bee
4
Bob the Builder
1
Wizard
2
Halloween Time
Copyright 2008, Exemplars, Inc. All rights reserved.
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Novice
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Apprentice
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Practitioner
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Practitioner
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Expert
Halloween Time
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