Tile 1 would have an area of 1 square inch and a perimeter of 4 inches. Tile 2 would have an area of 3 square inches and a perimeter of 8 inches.

Transcription

1 Sarah s little sister asked her to decorate a wall in her bedroom. Sarah decided to make 15 cardboard tiles so that her little sister could put pictures on them. Each tile would be a different size. Tile 1 would have an area of 1 square inch and a perimeter of 4 inches. Tile 2 would have an area of 3 square inches and a perimeter of 8 inches. Tile 3 would have an area of 5 square inches and a perimeter of 12 inches. Tile 4 would have an area of 7 square inches and a perimeter of 16 inches. Sarah decided to continue this pattern for the remaining tiles. Sarah knew her little sister loved pink and purple, so she decided to paint each tile purple and put a pink ribbon around its perimeter. Sarah found purple paint at the hobby shop that costs $3.75 a jar. Each jar covers 125 square inches. Pink ribbon costs 60 1 of 13

2 cents for 1 yard, or $1.50 for 3 yards. Sarah had $20.00 to spend. Will she have enough money to complete her project for decorating her little sister s wall? Explain your mathematical thinking. 2 of 13

3 Suggested Grade Span 3 5 Grade(s) in Which Task Was Piloted 4 and 5 Task Sarah s little sister asked her to decorate a wall in her bedroom. Sarah decided to make 15 cardboard tiles so that her little sister could put pictures on them. Each tile would be a different size. Tile 1 would have an area of 1 square inch and a perimeter of 4 inches. Tile 2 would have an area of 3 square inches and a perimeter of 8 inches. Tile 3 would have an area of 5 square inches and a perimeter of 12 inches. Tile 4 would have an area of 7 square inches and a perimeter of 16 inches. Sarah decided to continue this pattern for the remaining tiles. Sarah knew her little sister loved pink and purple, so she decided to paint each tile purple and put a pink ribbon around its perimeter. Sarah found purple paint at the hobby shop that costs $3.75 a jar. Each jar covers 125 square inches. Pink ribbon costs 60 cents for 1 yard, or $1.50 for 3 yards. Sarah had $20.00 to spend. Will she have enough money to complete her project for decorating her little sister s wall? Explain your mathematical thinking. Alternative Versions of Task More Accessible Version: Change the tile size so that each tile is the same size, for example, each tile is 1 square inch. Ask students to find only the amount of ribbon needed to tie around the outside of each tile. 3 of 13

4 More Challenging Version: After completing the original version of the task, ask students to create a diagram to scale (using graph paper) representing the 15 completed tiles. 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 find the size of 15 growing tiles. 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 amount of area, perimeter and cost of painting and decorating all 15 tiles. Time/Context/Qualifiers/Tip(s) From Piloting Teacher This task was piloted with fourth- and fifth-grade students who were practicing multistep problems. It took one 45-minute period. This task allows students to apply the concepts of area and perimeter, cost comparison, and patterns and functions as well as to have experience with a multistep problem. This task is similar to "Roger s Roofing" and Meg s Muffins" also published by Exemplars, in that it has more than one step/part. This task is a little more complex in the mathematics involved. Students become used to tasks that do not require the juggling of different components. They need experiences like these to become more well-rounded problem solvers. To get students ready to handle this type of task, some instruction will need to occur in teaching students strategies such as underlining the important parts of the task, listing the required outcomes and organizing solutions. You can use "Roger s Roofing" and "Meg s Muffins" as teaching pieces and then present students with this tiles task to practice what they learned. 4 of 13

5 Links This task links well to creating tiles in art class or learning about tile art in other cultures. Common Strategies Used to Solve This Task Students will create a table to find the area and perimeter for all 15 tiles. Provide students with paper (lined and graph), pencil and calculators (optional). Possible Solutions Tile Number Area (square inches) Perimeter (inches) Total Paint: 225 square inches 125 square inches = 1.8 jars of paint. So, 2 jars x $3.75 = $7.50. Ribbon: 480 inches needed 12 inches = 40 feet 40 feet 3 = approx yards Approx yards 3 yards = approx. 5 for $1.50 = $ of 13

6 $ $7.50 = $15.00 So yes, she has enough money for the project. More Accessible Version Solution: Answers will vary depending on the tile size used and the design. Ribbon should be purchased for the perimeter of the design. Using one square inch tiles would be the easiest to determine perimeter especially if they used graph paper where one block equals the tile size. More Challenging Version Solution: The diagram will appropriately display the relative size of each tile. Task-Specific Assessment Notes Novice The Novice will not be able to correctly complete the problem. Work will lack organization and labels. Little or no math language or representations will be used. Apprentice The Apprentice will have a correct solution to part of the problem. Not all work will be shown or labeled, and communication will be unclear. The Apprentice will have some math language and representations present. Practitioner The Practitioner will achieve a correct solution for all parts of the problem with work labeled and shown. Math language and representations will be used to communicate. The Practitioner may think that the three yards of ribbon can be purchased in fractional parts and may base the answer on this premise. Expert The Expert will have all parts of the solution correct with work shown, labeled and clearly organized. Math language and representations will be used to communicate. Mathematically relevant comments and observations will also be made about the solution (such as doing a cost comparison between the two ways to buy ribbon). 6 of 13

7 Novice 7 of 13

8 Apprentice 8 of 13

9 Practitioner 9 of 13

10 Practitioner 10 of 13

11 Expert 11 of 13

12 Expert 12 of 13

13 Expert 13 of 13