Bag of Beads. What are all the different ways Maria can fill the bags with 6 beads? Bag of Beads. 1 of 11

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1 Maria has a lot of square and round beads. She wants to bring some to school to share. She has decided to put 6 beads in a bag. She wants the contents of every bag to be different. What are all the different ways Maria can fill the bags with 6 beads? 1 of 11

2 Suggested Grade Span K 2 Grade(s) in Which Task Was Piloted 1 Task Maria has a lot of square and round beads. She wants to bring some to school to share. She has decided to put 6 beads in a bag. She wants the contents of every bag to be different. What are all the different ways Maria can fill the bags with 6 beads? Alternative Versions of Task More Accessible Version: Maria has a lot of square and round beads. She wants to bring some to school to share. She has decided to put 4 beads in a bag. She wants the contents of every bag to be different. What are all the different ways Maria can fill the bags with 4 beads? More Challenging Version: Maria has a lot of square and round beads. She wants to bring some to school to share. She has decided to put 6 beads in a bag. She wants the contents of every bag to be different. What are all the different ways Maria can fill the bags with 6 beads? If Maria makes all of the different combinations, how many square and round beads will she need in all? NCTM Content Standards and Evidence Data Analysis and Probability Standard for Grades Pre K 2: Instructional programs from prekindergarten through grade 12 should enable all students to... 2 of 11

3 Understand and apply basic concepts of probability. NCTM Evidence: Understand and apply basic concepts of probability. Exemplars Task-Specific Evidence: This task requires students to understand the concept of finding all possible combinations. Time/Context/Qualifiers/Tip(s) From Piloting Teacher This is a short- to medium-length task. You may want to make round and square beads available for students who need to use manipulatives to solve the task. The task could be easily adapted to themes you may be studying, such as the ocean. You could use starfish and seashells instead of round and square beads, for instance. Links This task could link to a study of collections or hobbies. It could also link to studies of cultures where beads play an integral role. Students could also make their own beads and necklaces. Common Strategies Used to Solve This Task Most students will create diagrams. Students who are most successful in finding all the combinations will use an organized and systematic approach. Some will use math sentences and tables instead. Possible Solutions Bag Number Round Beads Square Beads of 11

4 More Accessible Version Solution: More Challenging Version Solution: = 42 beads in all Task-Specific Assessment Notes Bag Number Round Beads Square Beads Bag Number Round Beads Square Beads Total General Notes Students may need experience with combination problems to be successful solving this task. Novice The Novice will demonstrate a rudimentary understanding of the task, but it will not lead to even a partially correct solution. There will be little or no correct reasoning or justification of work shown. Little or no math language will be used, or it will be used incorrectly. Apprentice The Apprentice will achieve a partially correct solution, but omissions may lead to an incorrect solution. For instance, all combinations may not be found, or repeats may be present. An Apprentice will use some math language correctly, and some correct reasoning may be present. There will be an attempt at using math representations to communicate the solution and assist with understanding. 4 of 11

5 Practitioner The Practitioner will achieve a correct solution and all work will be shown and labeled. All parts of the task will be successfully addressed, and representations will help organize and display the solution. A Practitioner will use math language to communicate the solution, and mathematically relevant observations will be made. Expert The Expert s work will be clearly labeled and organized, and math representations and language will clarify thinking and communicate to the audience the approach and reasoning used. A correct solution will be achieved, and math connections will extend the solution. 5 of 11

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