Assessment Items (Sample)

1. Sample pretest assessment items with corresponding Common Core (CC) standards and Mathematical Practices (MP) and item sources

Assessment Item

Prior Knowledge and Common Core Standards

Source

Add: ½ + 2/3 =

 

 

 

Rational Number Operation CC6CA2, CC6NS2, 7NS1 MP1, MP6

Alexander & Ambrose, 2010

Solve: 12 children shared 9 giant cookies. How much cookie did each child get?

 

CC6CA2, 7NS2, 7NS3 MP1, MP2, MP4

Carpenter, et al. (1999)

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.

 

PK Similar triangles and Explanation CC7G1-3 MP1, MP2, MP3, MP4

Connecticut State Department of Education, www.sde.ct.gov/ /cmtgrade8.

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.

 

Read graphs

CC5OA3, 5G2,

6EE9, 7RP2b, CC7CA1 (Critical Area), 8CA1 MP1, MP2, MP3, MP4

NAEP, 2013, Grade 8, Block

M3 Q#8, Medium difficulty

(52% correct).

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?

PK-Modeling CC6NS3, 7EE3 MP1, MP2, MP3, MP4

Connecticut State Department of Education, www.sde.ct.gov/ /cmtgrade8, # S-3.

 

 

2. Sample interim assessment items with corresponding standards and sources

Assessment Item

Common Core

Standards

Source

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?

Identify a graph that shows how speed changed

NAEP, 2011; Grade 8,

Block M9 Question #3, Multiple

Choice, Easy (70% correct)

 

 

3. Sample posttest assessment items with corresponding standards and sources Sample items from the Pre Test Rubric with Error Analysis and Next Steps

Assessment Item

Common Core Standards

Source

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?

 

Identify algebraic expression modeling a scenario

NAEP, 2013; Grade 8, Block M6 Question #2 (originally multiple choice with easy difficulty level)

Which of the following is the graph of the line with equation y = –2 x + 1?

 

Identify the graph of a linear equation

NAEP, 2007; Grade 8, Block M11 Question #11, Multiple Choice, Difficult (25% correct)

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.

Write story that could be described by graph

NAEP, 2003; Grade 8, Block M10 Question #19, Extended Constructed Response, Difficult (15% correct)

 

 

4. Sample items from the Pre Test Rubric with Error Analysis and Next Steps

Question & Solution

Error Analysis: Possible Misconceptions

Next Steps

Add: 1/2 + 2/3 =

 

Correct Solution:

7/6 = 1 1/6

Rubric Point Value: 1 point

* 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.

 

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.)

 

In which of the following are the three fractions arranged from least to greatest?

 

Correct Solution:

A.

 

a) , ,

 

Rubric Point Value: 1 point

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.

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.