Scoring Tasks

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Task: Ben’s Poster

Ben loves the Red Sox and wants to buy a poster of Dustin Pedroia. Ben's parents said Ben can earn five cents a day feeding the dog and twenty cents a day feeding the pony. Ben needs to earn two dollars and twenty-five cents to buy the poster. Ben thinks it will take seven days to earn enough money. Is Ben correct? Show all your mathematical thinking.

Aligned to the 3.NBT.A.3 Standard

More on the 3.NBT.A.3 Standard

Possible Solutions

No, Ben is not correct. He will not have earned enough money in 7 days to buy the poster.

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3.NBT.A.3

Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations.

Assess Student Performance

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Assess Student #1’s work according to the following category:

No strategy is chosen, or a strategy is chosen that will not lead to a solution.

Little or no evidence of engagement in the task present.

A partially correct strategy is chosen, or a correct strategy for only solving part of the task is chosen.

Evidence of drawing on some relevant previous knowledge is present, showing some relevant engagement in the task.

A correct strategy is chosen based on the mathematical situation in the task.

Planning or monitoring of strategy is evident.

Evidence of solidifying prior knowledge and applying it to the problem-solving situation is present.

Note: The Practitioner must achieve a correct answer.

An efficient strategy is chosen and progress towards a solution is evaluated.

Adjustments in strategy, if necessary, are made along the way, and/or alternative strategies are considered.

Evidence of analyzing the situation in mathematical terms and extending prior knowledge is present.

Note: The Expert must achieve a correct answer.

Arguments are made with no mathematical basis.

No correct reasoning nor justification for reasoning is present.

Arguments are made with some mathematical basis.

Some correct reasoning or justification for reasoning is present.

Arguments are constructed with adequate mathematical basis.

A systematic approach and/or justification of correct reasoning is present.

Deductive arguments are used to justify decisions and may result in formal proofs.

Evidence is used to justify and support decisions made and conclusions reached.

No awareness of audience or purpose is communicated.

No formal mathematical terms or symbolic notations are evident.

Some awareness of audience or purpose is communicated.

Some communication of an approach is evident through verbal/written accounts and explanations.

An attempt is made to use formal math language. One formal math term or symbolic notation is evident.

A sense of audience or purpose is communicated.

Communication of an approach is evident through a methodical, organized, coherent, sequenced and labeled response.

Formal math language is used to share and clarify ideas. At least two formal math terms or symbolic notations are evident, in any combination.

A sense of audience and purpose is communicated.

Communication of an approach is evident through a methodical, organize, coherent, sequenced and labeled response. Communication of an argument is supported by mathematical properties.

Formal math language and symbolic notation is used to consolidate math thinking and to communicate ideas. At least one of the two formal math terms or symbolic notations is beyond grade level.

No connections are made or connections are mathematically or contextually irrelevant.

A mathematical connection is attempted but is partially incorrect or lacks contextual relevance.

A mathematical connection is made. Proper contexts are identified that link both the mathematics and the situation in the task.

Some examples may include one or more of the following:

  • clarification of the mathematical or situational context of the task
  • exploration of mathematical phenomenon in the context of the broader topic in which the task is situated
  • noting patterns, structures and regularities

Mathematical connections are used to extend the solution to other mathematics or to a deeper understanding of the mathematics in the task.

Some examples may include one or more of the following:

  • testing and accepting or rejecting of a hypothesis or conjecture
  • explanation of phenomenon
  • generalizing and extending the solution to other cases

No attempt is made to construct a mathematical representation.

An attempt is made to construct a mathematical representation to record and communicate problem solving but is not accurate.

An appropriate and accurate mathematical representation is constructed and refined to solve problems or portray solutions.

An appropriate mathematical representation is constructed to analyze relationships, extend thinking and clarify or interpret phenomenon.

This Achievement Level demonstrates little or no evidence of understanding the math concepts of the task.

This Achievement Level has the broadest range, from a student who is just beginning to demonstrate mathematical understanding to a student who almost meets the standard.

This Achievement Level meets the standard and is proficient in understanding the underlying mathematics of the task. A correct solution must be achieved.

This Achievement Level goes beyond the standard and shows a deeper understanding of the underlying mathematics.

Exemplars has assessed Student #1’s work in the following way:

Problem Solving:
Expert

The student's strategy of making a table to show seven days, the money earned for walking the dog, feeding the pony, the total money, and comparing that total to $2.25 works to solve this task. The student's answer, "not correct," is correct. The student uses an alternative strategy of generalizing and applying rules to solve the same task and verifies that her/his answer is correct.

Reasoning & Proof:
Expert

The student demonstrates correct understanding of the underlying concepts of the task. The student's table shows seven days, a running total of feeding the dog earnings, feeding the pony earnings and total money. The student also compares her/his total money to $2.25. The student then generalizes two rules, 5 * d = g and 20 * d = p and uses the two rules to extend the task to other days and to verify that the data on her/his table and answer is correct.

Communication:
Expert

The student correctly uses the mathematical terms money and days from the task. The student also correctly uses the terms table, "totol" (total), week, more, "paterns" (patterns), dollar, quarter, nickel, dime, rules, key. The student correctly uses the mathematical notation $.05, $.10, $.15, $.20, $.25, $.30, $.35, $.20, $.40, $.60, $.80, $1.00, $1.20, $1.40, $.50, $.75, $1.25, $1.50, $1.75, $2.00, $2.25, 1/4, 3/4, 1/2. The student correctly uses the symbolic notation 5 * d = g, and, 20 * d = p, with all variables defined in a key.

Connections:
Expert

The student solves the task and makes the mathematically relevant Practitioner observations, "7 days is a week," "day 8 is $2.00," "day 9 is $2.25," "Ben needs $.50 more money," "paterns day +1, dog +$.05, pony +$.20, total money +$.25." The student also states, "It ($.25) is a quarter," and, "$.05 is a nickel." The student makes Expert connections. The student relates money to fractions by stating, "I Know $.25 is 1/4 of a dollar," "$.50 is 1/2 of a dollar," "$.75 is 3/4 of a dollar," "... a nickel and 1/2 of a dime." The student states, "rules to how I am right." The student generalizes the rule, 5 * d = g, defines the variables in a key, and uses the rule to find the total dog money earned for days two, seven, and 10. The student generalizes the rule, 20 * d = p, defines the variables in a key, and uses the rule to find the total pony money for days four, seven, and one hundred.

Representation:
Expert

The student's use of a table is appropriate and accurate. All necessary labels and money notation are provided and the entered data is correct. The student uses the table to determine two rules that would work to find the total money earned for any number of days that Ben walks the dog or feeds the pony. All variables are defined.

Score Card:
Student #1

Problem Solving:

Unassigned

Reasoning & Proof:

Unassigned

Communication:

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Connections:

Unassigned

Representation:

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Overall Achievement Level:

Unassigned

Score Card:
Student #2

Problem Solving:

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Reasoning & Proof:

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Communication:

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Connections:

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Representation:

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Overall Achievement Level:

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Score Card:
Student #3

Problem Solving:

Unassigned

Reasoning & Proof:

Unassigned

Communication:

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Connections:

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Representation:

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Overall Achievement Level:

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Score Card:
Student #4

Problem Solving:

Unassigned

Reasoning & Proof:

Unassigned

Communication:

Unassigned

Connections:

Unassigned

Representation:

Unassigned

Overall Achievement Level:

Unassigned