MATHEMATICS
OPEN-ENDED ITEM
A.1
17. Theresa is making cookies.
A.
The recipe Theresa is using calls for 2 1} cups of ßour. She only has a container that
3
holds }1 of a cup. How many times should she Þll the container with ßour? Show
3
or explain all your work.
548746
GO TO THE NEXT PAGE TO FINISH THE QUESTION.
Grade 6 Mathematics Item Sampler Supplement 2009–2010
12
MATHEMATICS
17.
Continued. Please refer to the previous page for task explanation.
Theresa made 42 chocolate chip cookies and 28 oatmeal cookies. She put all of
the cookies into bags. She Þlled each bag with only chocolate chip cookies or only
oatmeal cookies. Each bag contains the same number of cookies.
B.
What is the greatest number of cookies Theresa could have put into each bag?
Show or explain all your work.
Score
Point 4
Score
Point 3
Score
Point 2
Score
Point 1
Score
Point 0
14%
16%
35%
19%
16%
548746
Grade 6 Mathematics Item Sampler Supplement 2009–2010
13
MATHEMATICS
ITEM-SPECIFIC SCORING GUIDELINE
Item #17
This item is reported under Category A, Numbers and Operations.
Assessment Anchor:
A.1– Demonstrate an understanding of numbers, ways of representing numbers, relationships among
numbers, and number systems.
SpeciÞc Eligible Content addressed by this item:
A.1.1.4– Represent a mixed number as an improper fraction.
A.1.3.1– Find the Greatest Common Factor (GCF) of two numbers (through 50) and/or use the GCF to
simplify fractions.
Scoring Guide:
Score
In response to this item, the student—
4
demonstrates a thorough understanding of representing a mixed number as an
improper fraction and Þnding the GCF of two numbers by correctly solving
problems and clearly explaining procedures.
3
demonstrates a general understanding of representing a mixed number as an
improper fraction and Þnding the GCF of two numbers by clearly explaining
procedures with only minor errors or omissions.
2
demonstrates a partial understanding of representing a mixed number as an
improper fraction and Þnding the GCF of two numbers by correctly performing
a signiÞcant portion of the required task.
1
demonstrates minimal understanding of representing a mixed number as an
improper fraction and Þnding the GCF of two numbers.
0
The response has no correct answer and insufÞcient evidence to demonstrate
any understanding of the mathematical concepts and procedures as required by
the task. Response may show only information copied from the question.
Nonscorable
BLK
OT
IL
LOE
– Blank, entirely erased, or written refusal to respond
– Off Task
– Illegible
– Response in a language other than English
Grade 6 Mathematics Item Sampler Supplement 2009–2010
14
MATHEMATICS
Item #17
Top Scoring Response:
Part A Answer
Support
2×3+1=7
OR
7 (times)
Each cup contains three }1 cups. So two cups have
3
6 one-third cups.
Six plus another 1} cup equals 7.
3
(2 score points)
1 point for correct answer
1 point for complete support (.5 points for correct, but incomplete, support)
Part B Answer
Support
Factors of 42:
1, 2, 3, 6, 7, 14, 21, 42
Factors of 28:
1, 2, 4, 7, 14, 28
Greatest Common Factor = 14
OR
14 (cookies)
42 = 7 • 6 = 7 • 2 • 3
28 = 7 • 4 = 7 • 2 • 2
7 • 2 = 14
OR
Since she put the same number of cookies in each
bag, I found the greatest common factor of 42 and
28. I listed the factors of each of these numbers and
found 14 to be the greatest.
(2 score points)
1 point for correct answer
1 point for complete support (.5 points for correct, but incomplete, support)
Grade 6 Mathematics Item Sampler Supplement 2009–2010
15
MATHEMATICS
OPEN-ENDED ITEM RESPONSES
A.1
Response Score: 4
17. Theresa is making cookies.
A.
The recipe Theresa is using calls for 2 1} cups of ßour. She only has a container that
3
holds }1 of a cup. How many times should she Þll the container with ßour? Show
3
or explain all your work.
The student has given a correct answer.
The student has shown complete support.
548746
GO TO THE NEXT PAGE TO FINISH THE QUESTION.
Grade 6 Mathematics Item Sampler Supplement 2009–2010
16
MATHEMATICS
17.
Continued. Please refer to the previous page for task explanation.
Theresa made 42 chocolate chip cookies and 28 oatmeal cookies. She put all of
the cookies into bags. She Þlled each bag with only chocolate chip cookies or only
oatmeal cookies. Each bag contains the same number of cookies.
B.
What is the greatest number of cookies Theresa could have put into each bag?
Show or explain all your work.
The student has given a correct answer.
The student has shown complete support.
548746
Grade 6 Mathematics Item Sampler Supplement 2009–2010
17
MATHEMATICS
A.1
Response Score: 3
17. Theresa is making cookies.
A.
The recipe Theresa is using calls for 2 1} cups of ßour. She only has a container that
3
holds }1 of a cup. How many times should she Þll the container with ßour? Show
3
or explain all your work.
The student has given a correct answer.
The student has shown complete support.
548746
GO TO THE NEXT PAGE TO FINISH THE QUESTION.
Grade 6 Mathematics Item Sampler Supplement 2009–2010
18
MATHEMATICS
17.
Continued. Please refer to the previous page for task explanation.
Theresa made 42 chocolate chip cookies and 28 oatmeal cookies. She put all of
the cookies into bags. She Þlled each bag with only chocolate chip cookies or only
oatmeal cookies. Each bag contains the same number of cookies.
B.
What is the greatest number of cookies Theresa could have put into each bag?
Show or explain all your work.
The student has given a correct answer.
The student has shown incomplete support.
548746
Grade 6 Mathematics Item Sampler Supplement 2009–2010
19
MATHEMATICS
A.1
Response Score: 3
17. Theresa is making cookies.
A.
The recipe Theresa is using calls for 2 1} cups of ßour. She only has a container that
3
holds }1 of a cup. How many times should she Þll the container with ßour? Show
3
or explain all your work.
The student has given a correct answer.
The student has shown complete support.
548746
GO TO THE NEXT PAGE TO FINISH THE QUESTION.
Grade 6 Mathematics Item Sampler Supplement 2009–2010
20
MATHEMATICS
17.
Continued. Please refer to the previous page for task explanation.
Theresa made 42 chocolate chip cookies and 28 oatmeal cookies. She put all of
the cookies into bags. She Þlled each bag with only chocolate chip cookies or only
oatmeal cookies. Each bag contains the same number of cookies.
B.
What is the greatest number of cookies Theresa could have put into each bag?
Show or explain all your work.
The student has given a correct answer.
The student has shown incomplete support.
548746
Grade 6 Mathematics Item Sampler Supplement 2009–2010
21
MATHEMATICS
A.1
Response Score: 2
17. Theresa is making cookies.
A.
The recipe Theresa is using calls for 2 1} cups of ßour. She only has a container that
3
holds }1 of a cup. How many times should she Þll the container with ßour? Show
3
or explain all your work.
The student has given a correct answer.
The student has shown complete support.
548746
GO TO THE NEXT PAGE TO FINISH THE QUESTION.
Grade 6 Mathematics Item Sampler Supplement 2009–2010
22
MATHEMATICS
17.
Continued. Please refer to the previous page for task explanation.
Theresa made 42 chocolate chip cookies and 28 oatmeal cookies. She put all of
the cookies into bags. She Þlled each bag with only chocolate chip cookies or only
oatmeal cookies. Each bag contains the same number of cookies.
B.
What is the greatest number of cookies Theresa could have put into each bag?
Show or explain all your work.
The student has given an incorrect answer.
The student has shown incorrect support.
548746
Grade 6 Mathematics Item Sampler Supplement 2009–2010
23
MATHEMATICS
A.1
Response Score: 2
17. Theresa is making cookies.
A.
The recipe Theresa is using calls for 2 1} cups of ßour. She only has a container that
3
holds }1 of a cup. How many times should she Þll the container with ßour? Show
3
or explain all your work.
The student has given a correct answer.
The student has shown complete support.
548746
GO TO THE NEXT PAGE TO FINISH THE QUESTION.
Grade 6 Mathematics Item Sampler Supplement 2009–2010
24
MATHEMATICS
17.
Continued. Please refer to the previous page for task explanation.
Theresa made 42 chocolate chip cookies and 28 oatmeal cookies. She put all of
the cookies into bags. She Þlled each bag with only chocolate chip cookies or only
oatmeal cookies. Each bag contains the same number of cookies.
B.
What is the greatest number of cookies Theresa could have put into each bag?
Show or explain all your work.
The student has given an incorrect answer.
The student has shown incomplete support.
548746
Grade 6 Mathematics Item Sampler Supplement 2009–2010
25
MATHEMATICS
A.1
Response Score: 1
17. Theresa is making cookies.
A.
The recipe Theresa is using calls for 2 1} cups of ßour. She only has a container that
3
holds }1 of a cup. How many times should she Þll the container with ßour? Show
3
or explain all your work.
The student has given an incorrect answer.
The student has shown complete support.
548746
GO TO THE NEXT PAGE TO FINISH THE QUESTION.
Grade 6 Mathematics Item Sampler Supplement 2009–2010
26
MATHEMATICS
17.
Continued. Please refer to the previous page for task explanation.
Theresa made 42 chocolate chip cookies and 28 oatmeal cookies. She put all of
the cookies into bags. She Þlled each bag with only chocolate chip cookies or only
oatmeal cookies. Each bag contains the same number of cookies.
B.
What is the greatest number of cookies Theresa could have put into each bag?
Show or explain all your work.
The student has given an incorrect answer.
The student has shown incorrect support.
548746
Grade 6 Mathematics Item Sampler Supplement 2009–2010
27
MATHEMATICS
A.1
Response Score: 1
17. Theresa is making cookies.
A.
The recipe Theresa is using calls for 2 1} cups of ßour. She only has a container that
3
holds }1 of a cup. How many times should she Þll the container with ßour? Show
3
or explain all your work.
The student has given an incorrect answer.
The student has shown correct, but
incomplete, support (receiving ½ a point).
548746
GO TO THE NEXT PAGE TO FINISH THE QUESTION.
Grade 6 Mathematics Item Sampler Supplement 2009–2010
28
MATHEMATICS
17.
Continued. Please refer to the previous page for task explanation.
Theresa made 42 chocolate chip cookies and 28 oatmeal cookies. She put all of
the cookies into bags. She Þlled each bag with only chocolate chip cookies or only
oatmeal cookies. Each bag contains the same number of cookies.
B.
What is the greatest number of cookies Theresa could have put into each bag?
Show or explain all your work.
The student has given an incorrect answer.
The student has shown correct, but
incomplete, support (receiving ½ a point).
548746
Grade 6 Mathematics Item Sampler Supplement 2009–2010
29
MATHEMATICS
A.1
Response Score: 0
17. Theresa is making cookies.
A.
The recipe Theresa is using calls for 2 1} cups of ßour. She only has a container that
3
holds }1 of a cup. How many times should she Þll the container with ßour? Show
3
or explain all your work.
The student has given an incorrect answer.
The student has shown incorrect support.
548746
GO TO THE NEXT PAGE TO FINISH THE QUESTION.
Grade 6 Mathematics Item Sampler Supplement 2009–2010
30
MATHEMATICS
17.
Continued. Please refer to the previous page for task explanation.
Theresa made 42 chocolate chip cookies and 28 oatmeal cookies. She put all of
the cookies into bags. She Þlled each bag with only chocolate chip cookies or only
oatmeal cookies. Each bag contains the same number of cookies.
B.
What is the greatest number of cookies Theresa could have put into each bag?
Show or explain all your work.
The student has given an incorrect answer.
The student has shown incorrect support.
548746
Grade 6 Mathematics Item Sampler Supplement 2009–2010
31