1. A Date with Data
IATP – November 9, 2016

2. Item #1
Which of these is the number 3,060,007?
a. thirty, six thousand, seven
b. three billion, six million, seven
c. three million, six thousand, seven
d. three million, sixty thousand, seven
Analysis of responses:
(d) Correct response
Distractors
(a) Writes out the numbers as separate values
(b) Does not realize that there are 10 place values in 1 billion.
(c)* Mistakes 60,0007 as “six thousand, seven” because there are four “0” before the number “7”

3. Item #2
The estimated cost to build a new football stadium is eighty-six million dollars. What is the cost of building the new stadium written in standard form?
a. $80,600
b. $86,000
c. $80,600,000
d. $86,000,000
Analysis of responses: (d) Correct response Distractors (a) Does not realize that 86 million contains 8 place values – does not know how to represent 86, writes it as “80” and “6”. (b)* Does not realize that 86 million contains 8 place values. (c) Does not realize that 86 million contains 8 place values.

4. Item #3
Which means the same as three hundred four thousand, forty-two?
a. 34,042
b. 304,042
c. 304,420
d. 340,042
Analysis of responses: (b) Correct response Distractors (a), (c), and (d) Does not know where to place digits relative to written form

5. Overall Impressions All items target the same learning objective
Item 1 is about expressing a numeric value into written form
Items 2 and 3 are about expressing the written form of numbers into numeric values
Questions to consider about the content and student performance
About the Items
Were all items equal in difficulty?
Was the content for one more difficult than the others?
About student performance
Was the performance of students expected, i.e., students perform better on items that assess easier content than on those that assess more difficult content?
For students who incorrectly answered any question, which was the most common incorrect response selected? How would you correct this misunderstanding through instruction?
Is the overall performance of students on this learning objective satisfactory?

6. Item #5
Which means the same as 72, , ?
a. 672,102
b. 672,120
c. 721,620
d. 726,102
Analysis of responses: (a) Correct response Distractors (b)* Mistakes “2” with “20” (c) Does not realize that each number represents a different value – adds numbers in order of appearance (d) Does not understand that 600,000 is greater than 72,000; has some understanding of where to place numbers up to hundreds place

7. Item #6
Solve:
66,275
+ 3,918
a. 62,357
b. 69,183
c. 70,193
d. 105,455
Analysis of responses: (c) Correct response Distractors (a) Subtracted 3,918 from 66,275 (b)* Added the numbers but does not carry over from columns on right to those on left (d) Added the numbers but shifts numbers on the bottom row a column over to the left – 39,180

8. Item #7
What number do you get when you perform the following calculation? Subtract 291,420, from the number 303,615.
a. 12,195
b. 39,195
c. 112,295
d. 595,035
Analysis of responses: (a) Correct response Distractors (b) ?? (c) Did not apply borrowing rules from the left column (d)* Added the numbers instead of subtracting

9. Item #8
What number do you get when you perform the following calculation on the number 3,529? First, add 627, then subtract 2,068, and lastly, subtract 88.
746
b. 2,000
c. 3,529
d. 6,312
Analysis of responses: (b) Correct response Distractors (a)* Subtracted all the numbers from 3,529 (c) Did not add or subtract from 3,529 (d) Added all the all the numbers

10. Item #9
Solve:
16,112
2,979
+ 11,053
a. 14,032
b. 19,091
c. 29,034
d. 30,144
Analysis of responses: (d) Correct response Distractors (a)* Only added the bottom two rows of numbers (b) Only added the top two rows of numbers (c) Added all the numbers but did not carry over from right columns over into left columns

11. Overall Impressions All items target the same learning objective
Items 6, 9, 5 assesses students’ ability to add numbers with varying numbers of digits
Items 7 and 8 assesses students’ ability to express the word problems as
Questions to consider about the content and student performance
About the Items
Were all items equal in difficulty?
Was the content for one more difficult than the others?
About student performance
Was the performance of students expected, i.e., students perform better on items that assess easier content than on those that assess more difficult content?
For students who incorrectly answered any question, which was the most common incorrect response selected? How would you correct this misunderstanding through instruction?
Is the overall performance of students on this learning objective satisfactory?