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 Copyright 2008, Exemplars, Inc. All rights reserved. 1 of 15 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 Copyright 2008, Exemplars, Inc. All rights reserved. 2 of 15 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 Copyright 2008, Exemplars, Inc. All rights reserved. 3 of 15 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 Copyright 2008, Exemplars, Inc. All rights reserved. 4 of 15 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 Copyright 2008, Exemplars, Inc. All rights reserved. 5 of 15 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 Copyright 2008, Exemplars, Inc. All rights reserved. 6 of 15 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. Halloween Quilted Tablecloths Copyright 2008, Exemplars, Inc. All rights reserved. 7 of 15 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. 8 of 15 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. 9 of 15 Novice Halloween Quilted Tablecloths Copyright 2008, Exemplars, Inc. All rights reserved. 10 of 15 Apprentice Halloween Quilted Tablecloths Copyright 2008, Exemplars, Inc. All rights reserved. 11 of 15 Practitioner Halloween Quilted Tablecloths Copyright 2008, Exemplars, Inc. All rights reserved. 12 of 15 Practitioner Halloween Quilted Tablecloths Copyright 2008, Exemplars, Inc. All rights reserved. 13 of 15 Expert Halloween Quilted Tablecloths Copyright 2008, Exemplars, Inc. All rights reserved. 14 of 15 Expert Halloween Quilted Tablecloths Copyright 2008, Exemplars, Inc. All rights reserved. 15 of 15

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