Grade 2: Place Value Unit
Assessment Math Task
One Thousand Sea Shells
Emily and Kayla collect sea shells. Emily has 400 + 90 + 2
sea shells. Kayla has four hundred ninety-four sea shells.
Emily and Kayla put all the sea shells on a large tray and
start to count them. Emily wants to have a total of one
thousand sea shells. After counting for a while, Kayla
thinks they will each have to find seven more sea shells. Is
Kayla correct? Show all your mathematical thinking.
© 2013
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1
One Thousand Sea Shells
Place Value Unit
Mathematical Processes: 2.1A, 2.1B, 2.1E, 2.1G
TEKS Covered in Unit:
2.2B, 2.2C, 2.3A, 2.7B
Task
Emily and Kayla collect sea shells. Emily has 400 + 90 + 2 sea shells. Kayla has four hundred
ninety-four sea shells. Emily and Kayla put all the sea shells on a large tray and start to count
them. Emily wants to have a total of one thousand sea shells. After counting for a while,
Kayla thinks they will each have to find seven more sea shells. Is Kayla correct? Show all your
mathematical thinking.
TEKS Unit of Study and Evidence
Place Value Unit
The Place Value Unit involves understanding the relative position, magnitude and
relationships within the numeration system in order to answer questions such as:
• How could you use base-10 blocks to show what the numerals in this number mean?
• How can you use the additive property of place value to decompose this number?
• What other way(s) can you use thousands, hundreds, tens, and ones to show this
number without changing its value?
Exemplars Task-Specific Evidence
Students are expected to use different representations of whole numbers to find sums and
differences.
Underlying Mathematical Concepts
• Additive Property of the Base-10 Number System
• Finding sums when the parts are known and differences when the whole and one
part is known.
• Number sense to 1,000
• Addition/Subtraction
• Comparison
Possible Problem-Solving Strategies
•
•
•
•
Model (manipulatives)
Table
Diagram/Key
Number line
Possible Mathematical Vocabulary/Symbolic Representation
• Model
• Table
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Possible Mathematical Vocabulary/Symbolic Representation (cont.)
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Diagram/Key
Number line
Total/Sum
Part/Whole
Odd/Even
Subtrahend
Minuend
Difference
Amount
Expanded notation/Standard notation
Rule
Per
Equivalent/Equal to
Equal share
Ones, tens, hundreds, thousands
Possible Solutions
Yes, Kayla is correct.
Girl
Shells
Total Shells
Emily
492
492
Kayla
494
986
800
0
1000 - 1 =
- 986
999
- 986
13
180
492
+ 494
+ 1 = 14
800
180
+ 6
6
100 200 300 400 500 600 700 800 900 1000
1
of 14 = 7
2
986
Seashells
Possible Connections
Below are some examples of mathematical connections. Your students may discover some
that are not on this list.
• Kayla has 2 more sea shells than Emily.
• Both girls have the same number of hundreds and tens, but different numbers in the
ones place.
• They both have an even number of shells. Even + Even = Even
• 494 = 400 + 90 + 4
• Both girls had an estimation of 500 sea shells.
• Solve more than one way to verify the answer.
• Relate to a similar task and state a math link.
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Novice Scoring Rationales
4
Criteria and
Performance Level
Assessment Rationales
Problem Solving
Novice
The student does not write 492 correctly from the expanded
notation or the number in words, 494. The student does not
address the second part of the problem to determine if each
girl needs to find seven more seashells. The student’s answer, “no,” is not correct.
Reasoning Proof
Novice
The student does not demonstrate correct reasoning of
place value. The student correctly notates the ones and tens
place but is not able to notate the hundreds place correctly
in the number 492. The student does not solve the second
part of the problem.
Communication
Novice
The student does not use any mathematical language to
communicate her/his reasoning and proof.
Connections
Novice
The student does not make a mathematically relevant
observation about her/his solution.
Representation
Novice
The student does not attempt a mathematical representation
to solve or portray her/his solution.
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Novice
P/S R/P Com Con Rep A/Level
N
5
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N
N
N
N
N
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Apprentice Scoring Rationales
6
Criteria and
Performance Level
Assessment Rationales
Problem Solving
Practitioner
The student’s strategy of using a table to find the total number of shells the girls have and counting up to 1,000 works to
solve the problem. The student’s answer, “Kayla is correct,”
is correct.
Reasoning Proof
Practitioner
The student demonstrates correct reasoning of place value.
The student correctly notates 492 and 494. The student also
correctly reasons that 14 seashells are still needed for a total
of 1,000 seashells.
Communication
Apprentice
The student correctly uses the mathematical term table.
Connections
Practitioner
The student makes the mathematically relevant observation,
“They both have almost 500 shells. That is almost 1,000
shells.”
Representation
Apprentice
The student’s table is appropriate but not accurate. The
student has the labels Kayla and Emily on top of the wrong
columns. Kayla collects 494 shells and Emily 492 shells.
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Note: Verbs are not considered as communication terms
because they represent an action a student uses in her/his
solution.
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Apprentice
P/S R/P Com Con Rep A/Level
P
7
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P
A
P
A
A
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Practitioner Scoring Rationales, Student 1
8
Criteria and
Performance Level
Assessment Rationales
Problem Solving
Practitioner
The student’s strategy of using a number line to find the total
number of shells the girls have and counting up to 1,000
works to solve the problem. The student’s answer, “Kayla is
correct is the answer,” is correct.
Reasoning Proof
Practitioner
The student demonstrates correct reasoning of place value.
The student correctly notates 492 and 494. The student also
correctly reasons that 14 seashells or “14 is 7 + 7,” are needed for a total of 1,000 seashells.
Communication
Practitioner
The student correctly uses the mathematical terms number
line, even
, odd number, more.
Connections
Practitioner
The student makes the mathematically relevant observation,
“I notisced both start with a even number but end with a
odd number, 492 + 7 = 499, 494 + 7 = 501. Kayla finds 2
more shells.”
Representation
Practitioner
The student’s number line is appropriate and accurate. The
shells are labeled and the student adds additional support,
“I put 400 + 400 on first. then 90 + 90. then 4 + 2 then I
subtract 1000 – 986 = 14—put on last.”
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Practitioner, Student 1
P/S R/P Com Con Rep A/Level
P
9
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P
P
P
P
P
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Practitioner Scoring Rationales, Student 2
10
Criteria and
Performance Level
Assessment Rationales
Problem Solving
Practitioner
The student’s strategy of using a table to find the total number of shells the girls have, subtracting that total from 1,000,
and determining that each girl needs to find seven more
shells works to solve the problem. The student’s answer,
“yes,” is correct.
Reasoning Proof
Practitioner
The student demonstrates correct reasoning of place value.
The student correctly notates 492 and 494. The student also
correctly uses subtraction to reason that each girl needs to
find seven more seashells.
Communication
Practitioner
The student correctly uses the mathematical term total from
the problem. The student also correctly uses the terms table,
even numbers, hundreds, tens, more than.
Connections
Practitioner
The student makes the mathematically relevant observations,
“The shells they find are even numbers,” “I see both have 4
in the hundreds and 9 in the tens,” and, “Kayla finds 2 more
shells than Emily.”
Representation
Practitioner
The student’s table is appropriate and accurate. All columns
are labeled and the entered data is correct.
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Practitioner, Student 2
P/S R/P Com Con Rep A/Level
P
11
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P
P
P
P
P
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Practitioner, Student 2 (cont.)
12
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Expert Scoring Rationales
13
Criteria and
Performance Level
Assessment Rationales
Problem Solving
Expert
The student’s strategy of creating a table of each girl, the
seashells they collect, and total seashells works to solve
part of the problem. The student also applies subtraction to
determine that each girl needs to find seven more seashells.
The student’s answer, “yes Kayla is correct,” is correct. The
student uses two number lines to verify that her/his answer is
correct.
Reasoning Proof
Expert
The student demonstrates correct reasoning of the underlying concepts in the problem. The student’s table indicates
correct data and the student also uses subtraction correctly.
The student discusses the concept of equal share/fair share
and the Odd + Odd = Even rule. The student provides an
additional strategy of number lines to verify that her/his answer is correct.
Communication
Expert
The student correctly uses the mathematical terms total
and more from the problem. The student also uses the
mathematical terms even number, hundreds, tens, sets,
rule, odd, even, number line, place value, half, expanded
notation.
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Expert Scoring Rationales (cont.)
14
Criteria and
Performance Level
Assessment Rationales
Connections
Expert
The student makes the mathematically relevant Practitioner
observations, “Kayla has 2 more shells to start,” “both have
even number of shells,” “both have same hundreds and tens
numbers,” “both have sets of shells,” “both are close to
500 so have to find not to many more shells.” The student
makes Expert connections. The student explains how a rule
supports, 7 + 7 = 14. The student states, “rule-odd + odd =
even.” The student also explores the concept of equal share/
fair share. “I know 14 can be a fair share. It is a even number.
7 + 7 = 14. You do half of 14.” The student verifies her/
his answer by creating number lines. “I can make a number
line with place value to get to 1000.” The student shows
two different groupings of totals to indicate how 14 more
seashells need to be found by the girls. The student states,
“I am correct. It is 14 shells or 7 shells each to get to 1000
shells. Kayla is correct. I thout a lot.”
Representation
Expert
The student’s table is appropriate to the problem and
accurate. All labels are included and the data is accurate.
The student’s number lines are appropriate and accurate.
The label “shells,” is correct. The student uses the two
number lines to verify that her/his answer is correct.
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Expert
P/S R/P Com Con Rep A/Level
E
15
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E
E
E
E
E
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Expert (cont.)
16
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