Help With Our School Store Order

Transcription

1 The table below shows mechanical pencil sales in a recent week at our school store. Type of Pencil Number Sold Neon Grip Mechanical Pencil 124 Looney Tunes Mechanical Pencil 64 Rainbow Mechanical Pencil 49 Disney Mechanical Pencil 42 NFL Mechanical Pencil 42 Next week, the school store plans to order 36 dozen mechanical pencils. Use the data to determine how many dozen of each type of mechanical pencil the store should order. 1 of 13

2 Suggested Grade Span 6 8 Grade(s) in Which Task Was Piloted 6 Task The table below shows mechanical pencil sales in a recent week at our school store. Type of Pencil Number Sold Neon Grip Mechanical Pencil 124 Looney Tunes Mechanical Pencil 64 Rainbow Mechanical Pencil 49 Disney Mechanical Pencil 42 NFL Mechanical Pencil 42 Next week, the school store plans to order 36 dozen mechanical pencils. Use the data to determine how many dozen of each type of mechanical pencil the store should order. Alternative Versions of Task More Accessible Version: The table below shows mechanical pencil sales in a recent week at our school store. Type of Pencil Number Sold Neon Grip Mechanical Pencil 120 Looney Tunes Mechanical Pencil 60 Rainbow Mechanical Pencil 48 Disney Mechanical Pencil 36 NFL Mechanical Pencil 24 Next week, the school store plans to order 48 dozen mechanical pencils. Use the data to determine how many dozen of each type of mechanical pencil the store should order. 2 of 13

3 More Challenging Version: The table below shows mechanical pencil sales in a recent week at our school store. Type of Pencil Number Sold Neon Grip Mechanical Pencil 124 Looney Tunes Mechanical Pencil 64 Rainbow Mechanical Pencil 49 Disney Mechanical Pencil 42 NFL Mechanical Pencil 21 Next week, the school store plans to order 36 dozen mechanical pencils. Use the data to determine how many dozen of each type of mechanical pencil the store should order. If it is predicted that pencil sales will increase 33% the following week, how many pencils of each type will be sold? NCTM Content Standards and Evidence Number and Operations Standard for Grades 6 8: Instructional programs from prekindergarten through grade 12 should enable students to Understand numbers, ways of representing numbers, relationships among numbers and number systems. NCTM Evidence: Understand and use ratios and promotions to represent quantitative relationships. Exemplars Task-Specific Evidence: This task requires students to find the ratio of each type of pencil bought to the 36 dozen to be purchased. Time/Context/Qualifiers/Tip(s) From Piloting Teacher This is a medium-length task in that it took one class period of 45 minutes for students to complete. A few students had to finish for homework. To print a copy of the more accessible version of the task with the chart, refer to page 6. To print a copy of the more challenging version of the task with the chart, refer to page 7. Links This task could be adapted to items sold at your school store. 3 of 13

4 Common Strategies Used to Solve This Task Many students will find what percentage each type of pencil contributes to the total and will then use those results to reach conclusions. Other students will adjust the numbers to make them more compatible with 36 dozen. Possible Solutions Solutions will vary depending on student decision making. The following shows the approximate percentage each type of pencil contributes to the order: Type of Pencil Number Sold % of Total Neon Grip Mechanical Pencil % Looney Tunes Mechanical Pencil 64 21% Rainbow Mechanical Pencil 49 16% Disney Mechanical Pencil 42 14% NFL Mechanical Pencil 21 7% 41% of 36 dozen = 15 dozen Neon Grip Mechanical Pencils 21% of 36 dozen = 8 dozen Looney Tunes Mechanical Pencils 16% of 36 dozen = 6 dozen Rainbow Mechanical Pencils 14% of 36 dozen = 5 dozen Disney Mechanical Pencils 7% of 36 dozen = 3 dozen NFL Mechanical Pencils The store can order 37 dozen pencils or subtract one dozen from any of the orders above. More Accessible Version Solution: Type of Pencil # Sold # Dozen # Dozen to Order Neon Grip Mechanical Pencil Looney Tunes Mechanical Pencil Rainbow Mechanical Pencil Disney Mechanical Pencil NFL Mechanical Pencil of 13

5 More Challenging Version Solution: The original solution, and Type of Pencil Number Sold 33% Increase Neon Grip Mechanical Pencil Looney Tunes Mechanical Pencil Rainbow Mechanical Pencil Disney Mechanical Pencil NFL Mechanical Pencil Task-Specific Assessment Notes General Notes This task does not lend itself well to students needing to create math representations as a problem-solving strategy, so students should not be penalized for not doing so. Novice The Novice will have no understanding of the underlying mathematics in the task and so will be unable to make any progress toward a solution. Apprentice The Apprentice may have some understanding of the underlying mathematics in the task but will not achieve a correct solution because of computation or reasoning errors. Some math language may be used to communicate the approach used. Practitioner The Practitioner will have an approach that works and a correct solution that is supported with mathematical evidence. Math language and an organized solution will assist in communicating with the audience. Expert The Expert will have an accurate solution that is supported mathematically. The approach and reasoning used will be explained fully. The Expert will extend the solution beyond the task requirements. 5 of 13

6 More Accessible Version Worksheet The table below shows mechanical pencil sales in a recent week at our school store. Type of Pencil Number Sold Neon Grip Mechanical Pencil 120 Looney Tunes Mechanical Pencil 60 Rainbow Mechanical Pencil 48 Disney Mechanical Pencil 36 NFL Mechanical Pencil 24 Next week, the school store plans to order 48 dozen mechanical pencils. Use the data to determine how many dozen of each type of mechanical pencil the store should order. 6 of 13

7 More Challenging Version Worksheet The table below shows mechanical pencil sales in a recent week at our school store. Type of Pencil Number Sold Neon Grip Mechanical Pencil 124 Looney Tunes Mechanical Pencil 64 Rainbow Mechanical Pencil 49 Disney Mechanical Pencil 42 NFL Mechanical Pencil 21 Next week, the school store plans to order 36 dozen mechanical pencils. Use the data to determine how many dozen of each type of mechanical pencil the store should order. If it is predicted that pencil sales will increase 33% the following week, how many pencils of each type will be sold? 7 of 13

8 Novice 8 of 13

9 Apprentice 9 of 13

10 Apprentice 10 of 13

11 Practitioner 11 of 13

12 Practitioner 12 of 13

13 Expert 13 of 13