Bag of Beads
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?
Bag of Beads
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Bag of Beads
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 ...
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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
1
6
0
2
5
1
3
4
2
4
3
3
5
2
4
6
1
5
7
0
6
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More Accessible Version Solution:
Bag Number
Round Beads
Square Beads
1
4
0
2
3
1
3
2
2
4
1
3
5
0
4
Bag Number
Round Beads
Square Beads
1
6
0
2
5
1
3
4
2
4
3
3
5
2
4
6
1
5
7
0
6
Total
21
21
More Challenging Version Solution:
21 + 21 = 42 beads in all
Task-Specific Assessment Notes
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.
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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.
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Novice
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Apprentice
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Practitioner
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Practitioner
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Expert
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Expert
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