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exemplars.com 1© 2014
Gingerbread Men
Gina is making six gingerbread men. Gina needs raisins for each gingerbread man’s eyes. How many raisins does Gina need to make six gingerbread men? Show and tell how you know.
Grade K: Counting and Cardinality Unit Assessment Math Task
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Gingerbread Men
TaskGina is making six gingerbread men. Gina needs raisins for each gingerbread man’s eyes. How many raisins does Gina need to make six gingerbread men? Show and tell how you know.
TEKS Unit of Study and Evidence
Counting and Cardinality UnitThe Counting and Cardinality Unit involves understanding numbers and how they are used to name quantities and to answer questions, such as:
• How many balls is the clown juggling?• Do you have enough cups for each member of your group to have one?
Exemplars Task-Specific EvidenceThis task requires students to combine, count on and have number sense to 12. It also requires students to recognize that a gingerbread man has two eyes.
Underlying Mathematical Concepts• Number sense to 12• 2 to 1 (2 raisins to 1 gingerbread man)• Addition/Counting on• Patterns
Possible Problem-Solving Strategies• Model (manipulatives)• Diagram/Key• Table• Tally chart• Equation
Possible Mathematical Vocabulary/Symbolic Representation• Model• Diagram/Key• Table• Tally chart• Per
Counting and Cardinality UnitMathematical Processes: K.1A, K.1E
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Possible Mathematical Vocabulary/Symbolic Representation (cont.)• Pair• Total/Sum• Double• Sets• Pattern• Dozen• Odd/Even
Possible SolutionsGina needs 12 raisins.
Possible ConnectionsBelow are some examples of mathematical connections. Your students may discover some that are not on this list.
• Eyes are pairs.• Patterns: Raisins +2, Gingerbread man +1.• 12 raisins are a dozen.• 6 is half of 12.• One gingerbread man has 2 eyes.• Student adds more gingerbread men/eyes to extend the task.• Double the number of gingerbread men to get the total number of raisins.• There is always an even number of raisins used.• If Gina made noses, she would need six more raisins.• Youcancountbytwostofindthenumberofraisineyes.
Key
is 1 Raisin
Key
is 1 Raisin
is 1 Gingerbread Man
1 2 3 4 5 6
2 4 6 8 10 12
Gingerbread Man
TotalRaisin
1 2
2 4
3 6
4 8
5 10
6 12
Gingerbread Man Raisins
1
2
3
4
5
6
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Novice Scoring Rationales, Student 1
Criteria and Performance Level
Assessment Rationales
Problem SolvingNovice
The student’s strategy of drawing only one gingerbread man and himself does not work to solve the problem.
Reasoning ProofNovice
The student’s solution does not demonstrate understanding of the underlying mathematics of the problem. The student does not indicate Gina’s six gingerbread men and a total of 12 raisins for eyes.
CommunicationNovice
The student is not given credit for the mathematical term diagram. The student is drawing a picture of his gingerbread man and himself. The scribing supports that the student is not addressing Gina’s six gingerbread men.
ConnectionsNovice
The student does not include a connection in her/his solution.
RepresentationNovice
The student does not provide any representation to support the underlying mathematics in the problem.
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Novice, Student 1P/S R/P Com Con Rep A/LevelN N N N N N
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Novice Scoring Rationales, Student 2
Criteria and Performance Level
Assessment Rationales
Problem SolvingPractitioner
The student’s strategy of making a diagram of six ginger-bread men with 12 raisin eyes works to solve the problem. The student indicates a correct answer, “12,” and states, “This is my answer, 12 raisins.” A student will often use the letter “A” to represent the word answer.
Reasoning ProofPractitioner
The student’s diagram is adequate and systematic to support her/his reasoning and proof.
CommunicationNovice
The student does not use any mathematical language in her/his solution.
ConnectionsNovice
The student does not include a connection in her/his solution.
RepresentationPractitioner
The student’s diagram is appropriate and accurate. Necessary labels for gingerbread man and raisins are provided in the scribing.
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Novice, Student 2P/S R/P Com Con Rep A/LevelP P N N P N
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Apprentice Scoring Rationales, Student 1
Criteria and Performance Level
Assessment Rationales
Problem SolvingPractitioner
The student’s strategy of making a diagram of six ginger-bread men and using 12 raisins for eyes works to solve the problem. The student states a correct answer,”Gina has 12 raisins.”
Reasoning ProofPractitioner
The student’s diagram is adequate and systematic to support her/his reasoning and proof.
CommunicationApprentice
The student correctly uses the mathematical term diagram.
ConnectionsNovice
The student does not include a connection in her/his solution. The comment, “I do not like raisins,” is not mathematically relevant and cannot be considered an attempt at a mathematical connection.
RepresentationPractitioner
The student’s diagram is appropriate and accurate. Necessary labels for gingerbread “people” and raisins are provided in the scribing.
Notes The overall achievement level for this piece of student work falls under Exemplars exception to the rule category. If a student has all Apprentice scores or above, but a Novice in “Connections,” the student may still receive an achievement level score of Apprentice.
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Apprentice, Student 1P/S R/P Com Con Rep A/LevelP P A N P A
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Apprentice Scoring Rationales, Student 2
Criteria and Performance Level
Assessment Rationales
Problem SolvingPractitioner
The student’s strategy of making a diagram of six ginger-bread men with 12 raisin eyes works to solve the problem. The student states a correct answer, “12 raisins.” Students often put a circle around an “A” to indicate the word answer.
Reasoning ProofPractitioner
The student’s diagram is adequate and systematic to support her/his reasoning and proof. A key and scribing is provided todefinethegingerbreadmenandtheraisins.
CommunicationPractitioner
The student correctly uses the mathematical terms diagram, key.
ConnectionsNovice
The student does not include a connection in her/his solution.
RepresentationPractitioner
The student’s diagram is appropriate and accurate. A key is provided for the gingerbread men, and the raisins for eyes are provided in the scribing.
Notes The overall achievement level for this piece of student work falls under Exemplars exception to the rule category. If a student has all Apprentice scores or above, but a Novice in “Connections,” the student may still receive an achievement level score of Apprentice.
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Apprentice, Student 2P/S R/P Com Con Rep A/LevelP P P N P A
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Apprentice Scoring Rationales, Student 3
Criteria and Performance Level
Assessment Rationales
Problem SolvingPractitioner
The student’s strategy of making a diagram of six ginger-bread men on a plate and using 12 raisins for eyes works to solve the problem. The student indicates a correct answer, “12,” and states, “She needs 12 raisins.”
Reasoning ProofPractitioner
The student’s diagram is adequate and systematic to support her/his reasoning and proof.
CommunicationApprentice
The student correctly uses the mathematical term diagram.
ConnectionsPractitioner
The student makes a mathematically relevant connection by findingthenumberofraisinsneededforsevengingerbreadmen and stated, “If she makes a new one it is 13, 14—14 raisins.”
RepresentationPractitioner
The student’s diagram is appropriate and accurate. Necessary labels for gingerbread men and raisins are provided in the scribing.
Notes The overall achievement level for this piece of student work falls under Exemplars exception to the rule category. If a student has all Apprentice scores or above, but a Novice in “Connections,” the student may still receive an achievement level score of Apprentice.
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Apprentice, Student 3P/S R/P Com Con Rep A/LevelP P A P P A
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Practitioner Scoring Rationales, Student 1
Criteria and Performance Level
Assessment Rationales
Problem SolvingPractitioner
The student’s strategy of making a diagram of six ginger-bread men faces and 12 raisin eyes works to solve the prob-lem. The student indicates a correct answer, “dozen, 12,” and states, “I got 12 raisins.”
Reasoning ProofPractitioner
The student has a systematic approach and the diagram sup-ports her/his thinking.
CommunicationPractitioner
The student correctly uses the mathematical terms diagram, dozen, pair.
ConnectionsPractitioner
The student makes the relevant observations, “It’s a dozen,” and, “This says pair. They have a pair of eyes. We do too.”
RepresentationPractitioner
The student’s diagram is appropriate and accurate. Necessary labels for the gingerbread men and the raisins for eyes are provided in the scribing.
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Practitioner, Student 1P/S R/P Com Con Rep A/LevelP P P P P P
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Practitioner Scoring Rationales, Student 2
Criteria and Performance Level
Assessment Rationales
Problem SolvingPractitioner
The student’s strategy of making a diagram of six ginger-bread men and 12 raisin eyes works to solve the problem. The student indicates a correct answer, “12” and states, “See, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 raisins for the eyes,” in scribing.
Reasoning ProofPractitioner
The student has a systematic approach and the diagram sup-ports her/his thinking.
CommunicationPractitioner
The student correctly uses the mathematical terms diagram, key, more than.
ConnectionsPractitioner
The student recreates the problem by adding raisin buttons and states, “I made raisin buttons, I got 18. That is more than the eyes.”
RepresentationPractitioner
The student’s diagram is appropriate and accurate. A key is provided for the gingerbread men, and the raisins are definedinthescribing
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Practitioner, Student 2P/S R/P Com Con Rep A/LevelP P P P P P
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Practitioner Scoring Rationales, Student 3
Criteria and Performance Level
Assessment Rationales
Problem SolvingPractitioner
The student’s strategy of gluing paper “gingerbread men,” on her/his paper and adding the raisin eyes works to solve this problem. The student states a correct answer, “My an-swer is 12 raisins.”
Reasoning ProofPractitioner
The student has a systematic approach and the diagram sup-ports her/his thinking.
CommunicationPractitioner
The student correctly uses two mathematical terms diagram, more.
ConnectionsPractitioner
The student makes the mathematical relevant observation, “She gots more raisins than gingerbread mans.”
RepresentationPractitioner
The student’s diagram is appropriate and accurate. A key is provided for the raisins and the gingerbread men in the scribing.
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Practitioner, Student 3P/S R/P Com Con Rep A/LevelP P P P P P
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Expert Scoring Rationales
Criteria and Performance Level
Assessment Rationales
Problem SolvingExpert
The student’s strategy of making a diagram of six ginger-bread men and 12 raisins for eyes works to solve the prob-lem. The student indicates a correct answer, “12.” The stu-dent then uses an alternative strategy of a table to show the six gingerbread men and 12 raisins for eyes. The student relates this problem to a previous, completed problem.
Reasoning ProofExpert
The student creates a table to verify her/his answer of twelve raisins. The student also relates the problem to a previous, completed problem and links the mathematical similarities.
CommunicationExpert
The student correctly uses the mathematical terms diagram, key, dozen, pair, table, pattern.
ConnectionsExpert
The student makes the mathematically relevant Practitioner observations, “Pair of eyes,” “Dozen is 12.” The student states “2 raisins is a pair,” and “I did the add 2 pattern.” The student also recreates the problem by adding her/his own gingerbread man for a total of “14,” and states, “I did one for me. Now it is 14 raisins.” The student makes an Expert connection by verifying her/his own answer by creating a table and stating, “This is called correct because I got 12 again.” The student makes an additional Expert connection by relating the Gingerbread Man problem to a problem done in the past that involved counting dog legs. “We did that when we counted 3 dogs legs. That table was hard because I did 4, 8, 12 on it.”
RepresentationExpert
The student’s diagram is appropriate and accurate. The key and the scribings provide all necessary labels. The student’s table is appropriate and accurate with all necessary labels included.
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ExpertP/S R/P Com Con Rep A/LevelE E E E E E
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Expert (cont.)