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Halloween Quilted Tablecloths
A quilter designed tablecloths to fit square tables for Halloween
parties. The tablecloths were designed using the 3 colors in the
designs shown below.
Design 1: fits a 1’ x 1’ table (with 1 ft overhanging on each side)
Design 2: fits a 2’ x 2’ table (with 1 ft overhanging on each side)
Design 3: fits a 3’ x 3’ table (with 1 ft overhanging on each side)
How many of each color quilt square will the quilter need to
make a quilt to fit a 4’ x 4’ table? A 5’ x 5’ table? How big is
each quilt? How many of each color square will she need to
make a quilt to fit any size table, and how big will any size quilt
be?
Halloween Quilted Tablecloths
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Halloween Quilted Tablecloths
Suggested Grade Span
6–8
Grade(s) in Which Task Was Piloted
7 and 8
Task
A quilter designed tablecloths to fit square tables for Halloween parties. The tablecloths were
designed using the 3 colors in the designs shown below.
Design 1: fits a 1’ x 1’ table (with 1 ft overhanging on each side)
Design 2: fits a 2’ x 2’ table (with 1 ft overhanging on each side)
Design 3: fits a 3’ x 3’ table (with 1 ft overhanging on each side)
How many of each color quilt square will the quilter need to make a quilt to fit a 4’ x 4’ table? A
5’ x 5’ table? How big is each quilt? How many of each color square will she need to make a
quilt to fit any size table, and how big will any size quilt be?
Alternative Versions of Task
More Accessible Version:
(Use the quilt designs that appear in the original version of the task.)
A quilter designed tablecloths to fit square tables for Halloween parties. The tablecloths were
designed using the 3 colors in the designs shown below.
Design 1: is made using 9 quilt squares.
Halloween Quilted Tablecloths
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Design 2: is made using 16 quilt squares.
Design 3: is made using 25 quilt squares.
How many quilt squares would be needed for designs 4, 5 and 10?
Teacher Note:
See page 8 of the PDF to print a complete worksheet with graphics.
More Challenging Version:
The original version of the task, and ...
If the quilter is putting together a display of her quilts 1 through 10, how many square yards of
fabric of each color would she need to purchase to make the quilts for this display?
Teacher Note:
See page 9 of the PDF to print a complete worksheet with graphics.
NCTM Content Standards and Evidence
Algebra Standard for Grades 6–8: Instructional programs from pre-kindergarten through grade
12 should enable all 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 analyze and
generalize the tablecloth patterns.
Time/Context/Qualifiers/Tip(s) From Piloting Teacher
This task could be adapted by changing the colors of the quilt squares to match a theme during
any time of the year. This is a short- to medium-length task in that most students could solve
the task during one class period.
To print a copy of the more accessible version of the task with the graphic image, refer to page
8. To print a copy of the more challenging version of the task with the graphic image, refer to
page 9.
Halloween Quilted Tablecloths
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Links
The way the task is written, a logical link is to Halloween, but students studying quilting will also
find this task engaging.
Common Strategies Used to Solve This Task
Most students create a chart in which to organize the data, then analyze the data and then
make generalizations about the data.
Possible Solutions
A 4’ x 4’ table would need:
4 yellow squares
4 x 4 = 16 orange squares
4 x 4 = 16 black squares
A 5' x 5' table would need:
4 yellow squares
4 x 5 = 20 orange squares
5 x 5 = 25 black squares
The quilt size will be:
(design # + 2)Ô square feet
How many of each color square will she need to make a quilt to fit any size table, and how big
will any size quilt be?
All quilts will require 4 yellow squares.
Design # x 4 will be the number of orange squares needed.
(Design #)Ô will be the number of black squares needed.
The size of any quilt will be:
d = design #
dÔ + 4d + 4 OR (d + 2)Ô square feet
Halloween Quilted Tablecloths
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More Accessible Version Solution:
Design 4 = (4 + 2)Ô = 36 quilt squares
Design 5 = (5 + 2)Ô = 49 quilt squares
Design 10 = (10 + 2)Ô = 144 quilt squares
More Challenging Version Solution:
A 4’ x 4’ table would need:
4 yellow squares
4 x 4 = 16 orange squares
4 x 4 = 16 black squares
A 5' x 5' table would need:
4 yellow squares
4 x 5 = 20 orange squares
5 x 5 = 25 black squares
The quilt size will be:
(design # + 2)Ô square feet
How many of each color square will she need to make a quilt to fit any size table, and how big
will any size quilt be?
All quilts will require 4 yellow squares.
Design # x 4 will be the number of orange squares needed.
(Design #)Ô will be the number of black squares needed.
The size of any quilt will be:
d = design #
dÔ + 4d + 4 OR (d + 2)Ô square feet
Yellow:
10 quilts x 4 yellow squares = 40 yellow squares
Each square is 1’ x 1’, so 40 square feet are needed.
1 square yard = 9 square feet.
40 ÷ 9 = about 4.44 square yards of yellow needed
Halloween Quilted Tablecloths
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Orange:
(sum of numbers 1 – 10) x 4
{[n(n + 1)]/2} x 4
[(10 x 11)/2] x 4
55 x 4 = 220 square feet
220 ã 9 = about 24.4 square yards of orange needed
Black:
1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100 = 385 square feet
385 ã 9 = about 42.8 square yards of black needed
Task-Specific Assessment Notes
General Notes
There are several parts of this task that need to be successfully addressed in order to achieve a
Practitioner level.
Novice
The Novice will make little or no progress toward a solution. No awareness of purpose or
audience will be communicated, and no connections will be made. The Novice will make no
attempt to construct mathematical representations, and little or no math language will be used.
Apprentice
The Apprentice will have a correct strategy for part of the problem, but will not be able to reach
the solution to all parts of the task. Many students, for example, will determine the number of
each color quilt square but then forget to generalize the problem or to determine the size of the
quilts. Evidence of drawing on some previous knowledge of square numbers will be present,
and correct reasoning will be present for the part of the task the student solves. The Apprentice
will show some awareness of the audience through written accounts, diagrams and the use of
mathematical symbols. Some formal math language will be used, most likely in the form of
algebraic notation. There will be some attempt made to relate the task to square numbers. The
Apprentice will attempt to construct a math representation (most likely a chart or diagram) to
record problem solving and communicate the solution.
Practitioner
The Practitioner will achieve correct solutions to all parts of the task. Work will be organized and
labeled, and evidence of solidifying prior knowledge about area and perimeter will be present.
The Practitioner will present arguments with adequate mathematical basis. Formal math
language will be used, and mathematical connections will be recognized.
Expert
The Expert will have correct solutions to all parts of the task, using deductive arguments to
justify decisions (that result in more-formal proofs). There will be evidence of analyzing the
situation in mathematical terms and extending prior knowledge. The Expert will communicate a
Halloween Quilted Tablecloths
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sense of audience and purpose. Arguments will be supported by mathematical properties, and
precise and symbolic math language will be used. Mathematical observations will extend the
solution and representations will clarify phenomenon.
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More Accessible Version Worksheet
A quilter designed tablecloths to fit square tables for Halloween parties. The tablecloths were
designed using the 3 colors in the designs shown below.
Design 1: is made using 9 quilt squares.
Design 2: is made using 16 quilt squares.
Design 3: is made using 25 quilt squares.
How many quilt squares would be needed for designs 4, 5 and 10?
Halloween Quilted Tablecloths
Copyright 2008, Exemplars, Inc. All rights reserved.
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More Challenging Version Worksheet
A quilter designed tablecloths to fit square tables for Halloween parties. The tablecloths were
designed using the 3 colors in the designs shown below.
Design 1: fits a 1’ x 1’ table (with 1 ft overhanging on each side)
Design 2: fits a 2’ x 2’ table (with 1 ft overhanging on each side)
Design 3: fits a 3’ x 3’ table (with 1 ft overhanging on each side)
How many of each color quilt square will the quilter need to make a quilt to fit a 4’ x 4’ table? A
5’ x 5’ table? How big is each quilt? How many of each color square will she need to make a
quilt to fit any size table, and how big will any size quilt be?
If the quilter is putting together a display of her quilts 1 through 10, how many square yards of
fabric of each color would she need to purchase to make the quilts for this display?
Halloween Quilted Tablecloths
Copyright 2008, Exemplars, Inc. All rights reserved.
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Novice
Halloween Quilted Tablecloths
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Apprentice
Halloween Quilted Tablecloths
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Practitioner
Halloween Quilted Tablecloths
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Practitioner
Halloween Quilted Tablecloths
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Expert
Halloween Quilted Tablecloths
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Expert
Halloween Quilted Tablecloths
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