Ls for Linda. The 1st L took 3 tiles to make. The 2nd L took 5 tiles to make. The 3rd L took 7 tiles to make. Ls for Linda.

Transcription

1 Linda likes to do art projects. She also likes the letter L because it is the 1st letter of her name. Linda decided to decorate her bedroom with Ls made from colored plastic tiles. The 1st L took 3 tiles to make. The 2nd L took 5 tiles to make. The 3rd L took 7 tiles to make. 1 of 16

2 Linda didn t know how many Ls she would make, but she was sure she would make at least 10. She might even make 50! If Linda continues to make Ls in the same pattern established above, how many tiles would Linda need to make the 10th L? How many tiles would Linda need to make the 50th L? Linda went to the hobby store and discovered that a bag of 50 colored tiles cost $1.30 (that included tax). She also noticed that a bag of 65 colored tiles cost $1.50 (that also included tax). If Linda makes just the 50th L, what bags of tiles should she buy that will give her the best deal? Show your math thinking. 2 of 16

3 Suggested Grade Span 3 5 Grade(s) in Which Task Was Piloted 5 Task Linda likes to do art projects. She also likes the letter L because it is the 1st letter of her name. Linda decided to decorate her bedroom with Ls made from colored plastic tiles. The 1st L took 3 tiles to make. The 2nd L took 5 tiles to make. The 3rd L took 7 tiles to make. Linda didn t know how many Ls she would make, but she was sure she would make at least 10. She might even make 50! If Linda continues to make Ls in the same pattern established above, how many tiles would Linda need to make the 10th L? How many tiles would Linda need to make the 50th L? 3 of 16

4 Linda went to the hobby store and discovered that a bag of 50 colored tiles cost $1.30 (that included tax). She also noticed that a bag of 65 colored tiles cost $1.50 (that also included tax). If Linda makes just the 50th L, what bags of tiles should she buy that will give her the best deal? Show your math thinking. Alternative Versions of Task More Accessible Version: Refer to the original version of the task and the pattern above, and substitute: Linda did not know how many Ls she would make, but she was sure she would make at least 10. She might even make 50! If Linda continues to make Ls in the same pattern established above, how many tiles would Linda need to make the 4th L? How many tiles will it take to make the 5th L? How many tiles will it take to make the 10th L? Show your math thinking. Teacher Note: See page 8 of the PDF to print a complete worksheet with graphics. More Challenging Version: Refer to the original version of the task and the pattern above, and substitute: Linda didn t know how many Ls she would make, but she was sure she would make at least 10. She might even make 50! If Linda continues to make Ls in the same pattern established above, how many tiles would Linda need to make the 10th L? How many tiles would Linda need to make the 15th L? Make a rule for determining the number of tiles for any number L. Linda went to the hobby store and discovered that a bag of 50 colored tiles cost $1.30 (that included tax). She also noticed that a bag of 65 colored tiles cost $1.50 (that also included tax). If Linda makes just the 50th L, what bags of tiles should she buy that will give her the best deal? Show your math thinking. Teacher Note: See page 9 of the PDF to print a complete worksheet with graphics. NCTM Content Standards and Evidence Algebra Standard for Grades 3 5: Instructional programs from pre-kindergarten through grade 12 should enable students to... 4 of 16

5 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 identify how the pattern in tiles is increasing and then to extend the pattern for the 10th and 50th L. 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 use computation to determine which tiles are the better deal. Time/Context/Qualifiers/Tip(s) From Piloting Teacher This is a medium-length task. 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. Links This task could link to units about "me." Students could investigate letters in their own names to study symmetry, open and closed figures and other geometric attributes. Common Strategies Used to Solve This Task Most students make a chart in which to record data. They analyze the data to identify a pattern and then extend it to draw conclusions. Students then use a computational approach to determine the better deal on tiles. 5 of 16

6 Possible Solutions L # # of Tiles $ = $0.026 each $ = $0.023 each So, $ = $0.023 each. This is the least expensive bag when you compare the cost per tile. More Accessible Version Solution: More Challenging Version Solution: $ = $0.026 each $ = $0.023 each L # # of Tiles L # # of Tiles n 2n of 16

7 So, $ = $0.023 each. This is the least expensive bag when you compare the cost per tile. Task-Specific Assessment Notes General Notes This task lends itself well to students identifying a pattern and then generalizing it. Students who do so accurately will achieve Expert status. Novice The Novice will demonstrate little or no understanding of the task. Some attempt may be made at drawing one or more L s, but the response needs to show evidence of leading to a partially correct solution to score beyond Novice. Reasoning errors in initial understanding limit the student s response. Apprentice The Apprentice will have a partially correct solution with a strategy that will work for solving the task. The Apprentice may draw some correct L s that are free from reasoning errors. The Apprentice may also correctly solve one part of the task, but not all. Practitioner The Practitioner will achieve a correct solution to both parts of the task with supporting work. Math representations such as charts or diagrams will be used as strategy and communication tools. Expert The Expert will not only achieve a correct solution to both parts of the task but will also utilize other good problem-solving strategies, such as creating a rule to solve the task (2n + 1 with n equal to the l number) or verifying the solution by showing a comparison between rules and diagrams. 7 of 16

8 More Accessible Version Worksheet Linda likes to do art projects. She also likes the letter L because it is the 1st letter of her name. Linda decided to decorate her bedroom with L s made from colored plastic tiles. The 1st L took 3 tiles to make. The 2nd L took 5 tiles to make. The 3rd L took 7 tiles to make. Linda did not know how many L s she would make, but she was sure she would make at least 10. She might even make 50! If Linda continues to make L s in the same pattern established above, how many tiles would Linda need to make the 4th L? How many tiles will it take to make the 5th L? How many tiles will it take to make the 10th L? Show your math thinking. 8 of 16

9 More Challenging Version Worksheet inda likes to do art projects. She also likes the letter L because it is the 1st letter of her name. Linda decided to decorate her bedroom with L s made from colored plastic tiles. The 1st L took 3 tiles to make. The 2nd L took 5 tiles to make. The 3rd L took 7 tiles to make. Linda didn t know how many L s she would make, but she was sure she would make at least 10. She might even make 50! If Linda continues to make L s in the same pattern established above, how many tiles would Linda need to make the 10th L? How many tiles would Linda need to make the 15th L? Make a rule for determining the number of tiles for any number L. Linda went to the hobby store and discovered that a bag of 50 colored tiles cost $1.30 (that included tax). She also noticed that a bag of 65 colored tiles cost $1.50 (that also included tax). If Linda makes just the 50th L, what bags of tiles should she buy that will give her the best deal? Show your math thinking. 9 of 16

10 Novice 10 of 16

11 Novice 11 of 16

12 Apprentice 12 of 16

13 Apprentice 13 of 16

14 Practitioner 14 of 16

15 Expert 15 of 16

16 Expert 16 of 16