Jeff's Marble Collection
Jeff’s grandfather taught him how to play marbles. Jeff likes to
play marbles so much that he saves his spending money to buy
marbles. Every time Jeff buys 4 marbles for 40 cents, his
grandfather buys him 3 marbles for 30 cents. After a while Jeff
has 42 marbles.
How many marbles did Jeff buy, and how many marbles did his
grandfather buy?
Jeff's Marble Collection
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Jeff's Marble Collection
Suggested Grade Span
3–5
Grade(s) in Which Task Was Piloted
3
Task
Jeff’s grandfather taught him how to play marbles. Jeff likes to play marbles so much that he
saves his spending money to buy marbles. Every time Jeff buys 4 marbles for 40 cents, his
grandfather buys him 3 marbles for 30 cents. After a while Jeff has 42 marbles.
How many marbles did Jeff buy, and how many marbles did his grandfather buy?
Alternative Versions of Task
More Accessible Version:
Jeff’s grandfather taught him how to play marbles. Every time Jeff buys 4 marbles, his
grandfather buys him 3 marbles. After a while Jeff has 21 marbles.
How many marbles did Jeff buy, and how many marbles did his grandfather buy?
More Challenging Version:
Jeff’s grandfather taught him how to play marbles. Jeff likes to play marbles so much that he
saves his spending money to buy marbles. Every time Jeff buys 4 marbles, his grandfather
buys him 3 marbles. After a while Jeff had 42 marbles.
How many marbles did Jeff buy, and how many marbles did his grandfather buy? Marbles cost
$0.05 each, or a bag containing a dozen costs $0.50. How much did Jeff spend on marbles?
How much did his grandfather spend?
NCTM Content Standards and Evidence
Number and Operations Standard for Grades 3–5: Instructional programs from prekindergarten through grade 12 should enable students to ...
Jeff's Marble Collection
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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 add, multiply and
divide to determine the number of marbles bought.
Time/Context/Qualifiers/Tip(s) From Piloting Teacher
This is a medium-length task.
Links
This task could link to the other collecting marbles task featured in the Pre K–2 tasks. Students
could first be given the Pre K–2 task as a practice task and then this task as an assessment
piece.
Common Strategies Used to Solve This Task
Many students will make lists of numbers to determine the number of 7s there are in 42. Once
this is determined, the students will multiply or use repeated addition to determine the total
bought by Jeff and his grandfather.
Possible Solutions
4 marbles + 3 marbles = 7 marbles
42 marbles ÷ 7 marbles = 6 sets
6 x 4 marbles = 24 marbles bought by Jeff
6 x 3 marbles = 18 marbles bought by his grandfather
More Accessible Version Solution:
4 marbles + 3 marbles = 7 marbles
21 marbles ÷ 7 marbles = 3 sets
3 x 4 marbles = 12 marbles bought by Jeff
3 x 3 marbles = 9 marbles bought by his grandfather
Jeff's Marble Collection
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More Challenging Version Solution:
4 marbles + 3 marbles = 7 marbles
42 marbles ÷ 7 marbles = 6 sets
6 x 4 marbles = 24 marbles bought by Jeff
6 x 3 marbles = 18 marbles bought by his grandfather
Jeff: 24 marbles = 2 dozen at 50 cents a dozen = 1 dollar
Grandfather: 18 marbles = 1 dozen at 50 cents + 6 at 5 cents = 80 cents
Task-Specific Assessment Notes
General Notes
Computation will be included throughout the solution to this task. This task requires
computation but no other math language.
Novice
The Novice will demonstrate little or no understanding of the task. The Novice will not be able to
get beyond restating the data presented in the task, if even that. No math language will be
used, and no representations attempted.
Apprentice
The Apprentice will have a partially correct solution with a strategy that will work for solving part
of the task. The Apprentice will not achieve a correct solution, because of a computation or a
reasoning error. The Apprentice may achieve a correct solution by guessing, but there will be
little or no work to support the solution.
Practitioner
The Practitioner will achieve a correct solution using an effective approach. Appropriate
representation and clear communication will be present.
Expert
The Expert will not only achieve a correct solution but will also utilize other good problemsolving strategies, such as creating a rule to solve the task [(total marbles ÷ 7) x 3 for marbles
grandfather bought, or times 4 for marbles Jeff bought], verifying the solution, or going above
and beyond the task requirements to extend the solution.
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Novice
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Apprentice
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Practitioner
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Expert
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