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

### Possible Solutions

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

#### 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 Click to enlarge
##### 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:
Practitioner

The student's strategy of making an equation and a table to show seven days and a running total of the money that Ben earns works to solve this task. The student's answer, "not enough money," is correct.

Reasoning & Proof:
Practitioner

The student's arguments are constructed with adequate mathematical basis. The student's table demonstrates correct understanding of the underlying concepts of the task. The student uses seven days, has a correct running total of money, and correctly compares that total to \$2.25.

Communication:
Practitioner

The student correctly uses the mathematical terms day and money from the task. The student also correctly uses the mathematical term table. The student does not earn credit for the term number chart, because one is not indicated in the student's solution. The student correctly uses the mathematical notation \$.25, \$1.75.

Connections:
Practitioner

The student solves the task and makes the mathematically relevant observations, "If he worked 2 more day he would have enough money," "he need 50 more cents to buy the poster," and, "If he worked 18 days he would be 'alde' (able) to buy two posters. 225 + 225 = 450."

Representation:
Apprentice

The student's use of a table is appropriate but not accurate. The student does not include the money notation for days two through nine. ### Score Card:Student #1

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