1. Sample pretest assessment
items with corresponding Common Core (CC) standards and Mathematical Practices
(MP) and item sources
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Assessment Item
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Prior Knowledge and Common Core
Standards
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Source
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Add: ½ + 2/3 =
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Rational Number Operation CC6CA2,
CC6NS2, 7NS1 MP1, MP6
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Alexander & Ambrose, 2010
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Solve:
12 children shared 9 giant cookies.
How much cookie did each child get?
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CC6CA2, 7NS2, 7NS3 MP1, MP2, MP4
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Carpenter, et al. (1999)
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Barry traced the outline of two
different floor tiles, the picture below shows his outlines. Do the tiles
appear to be similar? (Yes/No) Explain how you could tell for sure whether or not they were similar.
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PK Similar triangles and Explanation
CC7G1-3 MP1, MP2, MP3, MP4
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Connecticut State Department of
Education, www.sde.ct.gov/ …/cmtgrade8.
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Marina is filling a rectangular fish
tank using two hoses that fill the tank at the same flow rate.
When the tank is about half full, she
turns off one hose but does not change the flow rate of the other hose.
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Read graphs
CC5OA3, 5G2,
6EE9, 7RP2b, CC7CA1 (Critical Area), 8CA1 MP1, MP2, MP3, MP4
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NAEP, 2013, Grade 8, Block
M3 Q#8, Medium difficulty
(52% correct).
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N x 8.3 = □ Explain what would happen to the
solution if N was a fraction less than 1 such as ¼. For example, would the solution be
more than, less than or equal to 8.3?
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PK-Modeling CC6NS3, 7EE3 MP1, MP2,
MP3, MP4
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Connecticut State Department of
Education, www.sde.ct.gov/ … /cmtgrade8, # S-3.
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2. Sample interim assessment
items with corresponding standards and sources
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Assessment Item
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Common Core
Standards
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Source
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For 2 minutes, Casey runs at a constant speed.
Then she gradually increases her speed. Which of the following graphs could
show how her speed changed over time?
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Identify a graph
that shows how speed changed
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NAEP, 2011;
Grade 8,
Block M9
Question #3, Multiple
Choice, Easy (70% correct)
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3. Sample posttest assessment items
with corresponding standards and sources Sample items from the Pre Test Rubric
with Error Analysis and Next Steps
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Assessment Item
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Common Core Standards
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Source
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A car can seat c adults. A van can
seat 4 more than twice as many adults as the car can. In terms of c, how many
adults can the van seat?
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Identify algebraic expression
modeling a scenario
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NAEP, 2013; Grade 8, Block M6
Question #2 (originally multiple choice with easy difficulty level)
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Which of the following is the graph
of the line with equation y = –2 x + 1?
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Identify the graph of a linear
equation
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NAEP, 2007; Grade 8, Block M11
Question #11, Multiple Choice, Difficult (25% correct)
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The graph above represents Marisa's
riding speed throughout her 80-minute bicycle trip. Use the information in
the graph to describe what could have
happened on the trip, including her speed throughout the trip.
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Write story that could be described
by graph
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NAEP, 2003; Grade 8, Block M10
Question #19, Extended Constructed Response, Difficult (15% correct)
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4. Sample items from the Pre
Test Rubric with Error Analysis and Next Steps
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Question & Solution
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Error Analysis: Possible
Misconceptions
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Next Steps
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Add: 1/2 + 2/3 =
Correct Solution:
7/6 = 1 1/6
Rubric Point Value: 1 point
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* 3/5: Student adds numerators and
denominators straight across. This treats a fraction as two separate whole
numbers rather than as a single rational number.
* ½: Student remembers common denominators, and correctly chooses
6, and does not change numerators: ½ + 2/3 = 1/ 6 + 2/ 6 = 3/6. Student correctly reduces fraction,
3/6 = ½.
* 1/3: Student cross cancels with
multiplication ½ + 2/3 = 1/3 where the 2’s cross out. This does not work with
addition.
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When answers are < 1, students
have not used reasoning to realize that the answer will be >1.
Spend time reviewing the meaning of
fractions before going to symbol manipulation. Allow for discussion and
discovery. Review the “why” of cancellation and other shortcuts. Ask students
to explain
(a over b) + (c over d) = (ad + bc)
over (b*d.)
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In which of the following are the
three fractions arranged from least to greatest?
Correct Solution:
A.
a) , ,
Rubric Point Value: 1 point
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Many of the incorrect answers are
based on a separation of the numerators and denominators, treating them as
independent whole numbers, and/or dismissing the role of the numerator.
If the student answered:
B. ½ is always the smallest fraction. Or, ½ is smallest because there is only 1
left (when you subtract the numerator from the denominator, or cut the pie
into pieces. With 5/9, there are 4 pieces left, so 5/9 is biggest. OR, 2/7 on
the number line is close to 2, and 5/9 is close to 5 or 9, and ½ is between 0 and 1; thus ½ is the smallest. OR, the numerators
are getting bigger, OR the denominators are getting bigger. In fractions, the
smaller number is larger.
C. ½ is always the biggest fraction. Half a pie is a lot!
D. Incorrect order. Student may
confuse least to greatest with greatest to least. Or, student believes that
in fractions, the smallest is largest. This could be true for unit fractions,
not all fractions.
E. 5/9 is judged smallest when a
student misapplies the unit fraction notion that a large denominator makes a
small fraction, forgetting the numerators. Numerators and denominators,
judged separately, are in descending order. Or, ½ is judged to be big.
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Spend time reviewing the meaning of
fractions before going to symbol manipulation. Allow for discussion and
discovery of fraction magnitude. Discuss why fractions look like they are
ordered differently than whole numbers.
If student answered B, C or E: Ask
student to draw the different sizes of fractions and visually compare. Or,
change all to decimals and compare decimal equivalents. And, use number line
representations to plot points and compare distance to 0.
If student answered “D”: If students
confused least to greatest with greatest to least, they may understand
magnitude, and got confused with where to start. Use techniques above to
check understanding of magnitude.
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