Hanging Airplanes
Zack wants to hang his 10 model airplanes at different lengths
from the ceiling of his room with wire. The 1st model airplane
needs 4 inches of wire. The 2nd model airplane needs 6 inches
of wire. The 3rd model airplane needs 8 inches of wire and the
4th model airplane needs 10 inches of wire. If this pattern
continues, how many inches of wire will Zack need to hang the
10th model airplane?
Wire sells for 97 cents a yard at the hardware store. Zack only
wants to spend $4.00 for the wire. Will Zack be able to hang all
his airplanes?
Hanging Airplanes
Copyright 2008, Exemplars, Inc. All rights reserved.
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Hanging Airplanes
Suggested Grade Span
3–5
Grade(s) in Which Task Was Piloted
4 and 5
Task
Zack wants to hang his 10 model airplanes at different lengths from the ceiling of his room with
wire. The 1st model airplane needs 4 inches of wire. The 2nd model airplane needs 6 inches of
wire. The 3rd model airplane needs 8 inches of wire and the 4th model airplane needs 10
inches of wire. If this pattern continues, how many inches of wire will Zack need to hang the
10th model airplane?
Wire sells for 97 cents a yard at the hardware store. Zack only wants to spend $4.00 for the
wire. Will Zack be able to hang all his airplanes?
Alternative Versions of Task
More Accessible Version:
Zack wants to hang his 8 model airplanes at different lengths from the ceiling of his room with
wire. The 1st model airplane needs 4 inches of wire. The 2nd model airplane needs 6 inches of
wire. The 3rd model airplane needs 8 inches of wire and the 4th model airplane needs 10
inches of wire. If this pattern continues, how many inches of wire will Zack need to hang the
10th model airplane? How many inches of wire will Zack need to hang all 10 of his model
airplanes?
More Challenging Version:
Zack wants to hang his 10 model airplanes at different lengths from the ceiling of his room with
wire. The 1st model airplane needs 4 inches of wire. The 2nd model airplane needs 6 inches of
wire. The 3rd model airplane needs 9 inches of wire and the 4th model airplane needs 11
inches of wire. If this pattern continues, how many inches of wire will Zack need to hang the
10th model airplane?
Wire sells for 97 cents a yard at the hardware store. Zack pays for the wire with a 5 dollar bill.
What are the possible ways he can get change back from his 5 dollars? Find all the ways.
Hanging Airplanes
Copyright 2008, Exemplars, Inc. All rights reserved.
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NCTM Content Standards and Evidence
Algebra Standard for Grades 3–5: Instructional programs from pre-kindergarten through grade
12 should enable students to ...
Understand patterns, relations and functions.
• NCTM Evidence: Describe, extend and make generalizations about geometric and
numeric patterns.
• Exemplars Task-Specific Evidence: This task requires students to continue a pattern to
the 10th level.
Number and Operations Standard for Grades 3–5: Instructional programs from prekindergarten through grade 12 should enable students to ...
Compute fluently and make reasonable estimates.
• NCTM Evidence: Develop fluency in adding, subtracting, multiplying and dividing whole
numbers.
• Exemplars Task-Specific Evidence: This task requires students to find the total length of
wire needed in inches and find how much that wire will cost if sold by the yard.
Time/Context/Qualifiers/Tip(s) From Piloting Teacher
This is a medium-length task.
Links
This task can be used in conjunction with a unit on space travel, a science unit on how planes
fly or a discussion on hobbies.
Common Strategies Used to Solve This Task
Most students will begin making a chart to keep track of the 10 lengths of wire. They will add
the lengths and then divide that total length by 36 (or make groups of three 12 inches).
Possible Solutions
The lengths of wire are:
4”+ 6”+ 8”+ 10”+ 12”+ 14”+ 16”+ 8”+ 20”+ 22” = 130 inches
The 10th length of wire is 22 inches.
Hanging Airplanes
Copyright 2008, Exemplars, Inc. All rights reserved.
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Zack will need 130 inches/36 = 3 feet and 22 inches
He will need four yards of wire.
4 yards x $.97 = $3.88
Yes, Zack has enough to buy the wire.
More Accessible Version Solution:
The lengths of wire are:
4”+ 6”+ 8”+ 10”+ 12”+ 14”+ 16”+ 18”+ 20”+ 22” = 130 inches total
The 10th model airplane needs 22 inches of wire.
More Challenging Version Solution:
The 10th length of wire is 26 inches.
The lengths of wire are:
4”+ 6”+ 9”+ 11”+ 14”+ 16”+ 19” + 21” + 24” + 26” = 150 inches
150 inches/36 = 4 yards 6 inches
He will need five yards x $.97 = $4.85
Nickels Dimes Pennies
0
0
15
1
0
10
2
0
5
0
1
5
3
0
0
1
1
0
Task-Specific Assessment Notes
General Notes
Students will need previous experiences with situations where items are sold by a unit and they
need to buy more than is needed like in the problem where Zack will need to buy 4 yards of
wire and have 14 inches left over.
Hanging Airplanes
Copyright 2008, Exemplars, Inc. All rights reserved.
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Novice
The Novice will misunderstand the problem and will not be able to find the 10th length of wire,
the total length of all the wire or the cost of the wire. There will be no representation or the
representation will be inappropriate for finding a solution to the problem.
Apprentice
The Apprentice will use a strategy that is partially useful, leading someway toward a solution,
but not to a full solution. For example, the student may find the length of the 10th wire but not
be able to decide if $4.00 is enough to purchase the wire. There is some use, or mostly
inappropriate use, of mathematical terminology and notation. There is some use of appropriate
mathematical representation.
Practitioner
The Practitioner will find the length of the 10th wire and the cost of the wire correctly. Correct
mathematical reasoning is present along with use of mathematical terminology and notation
appropriate to the problem. There is affective use of mathematical representation that clarifies
the strategy and solution. Mathematical connections or observations are recognized.
Expert
The Expert will have a correct solution to all parts of the problem using precise and appropriate
mathematical reasoning, terminology and notation. Mathematical generalizations, connections
or observations are used to extend the solution. A sense of audience and purpose is
communicated.
Hanging Airplanes
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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Expert
Hanging Airplanes
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Expert
Hanging Airplanes
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