Right angles do not have to be marked, but should appear to be right angles. Two right angles must be on the inside of the figure.

2

In this question, a student needed to interpret the meaning of a remainder in a division problem. Dividing 34 by 8 gives an answer of 4 with a remainder of 2. Therefore, Ms. Hernandez would form 4 teams with 8 students on each and have 2 students left as substitutes.

If the student was not able to interpret the meaning of a remainder and gave an answer of 4 (or 4 remainder 2 or any other response), without the correct interpretation of the remainder 2, then the response was scored incorrect.

Must mention both P and Q or neither P nor Q plus N is a square or give other characteristics of N.

In this question, a student needed to compare the shapes with respect to a common attribute such as number of sides or angles or vertices. The student could choose which attribute he or she wished to use.

* The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of the incorrect categories earned no credit.

In this question, a student needed to visualize where to place 4 of the 6 given shapes (2 squares, 2 isosceles triangles, and 2 right triangles) so that they formed a 6-sided shape that was already given to the student.

* The use of more than one correct category in this question enabled NAEP to gather data on different ways in which students responded correctly to this question. Any response that fell into one of these correct categories earned full credit.

In this question, a student needed to visualize how to form a square using two isosceles right triangles.

Examples of correct response #1 (see note below score & description)

Examples of a correct response #2 (see note below score & description)

Space between pieces is acceptable.
Freehand drawings are acceptable.

In this question, a student needed to take 2 isosceles triangles and construct a 4-sided figure that was not a square or a rhombus. A student had to manipulate 2 figures, form a shape other than a square or rhombus, and draw a line of separation in order to earn a score of correct #1. To earn a correct #2, a student had to manipulate 2 figures with some overlapping possible, form a shape that was not a square or rhombus, but did not have to drawn a line of separation.

* The use of more than one correct category in this question enabled NAEP to gather data on different ways in which students responded correctly to this question. Any response that fell into one of these correct categories earned full credit.

"Majority" is acceptable (taken to mean most) If student says the most classes, do not accept.

In this question, a student has to read and interpret information from a chart. A student then has to make a decision on which of the shapes should be the choice for the class. To earn full credit the student has to tell which of the three pieces should be the choice for the class and then explain why he or she chose that shape.

* The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of the incorrect categories earned no credit.

Parts of P overlaps N, and part sticks out.
The sticking out part is equal to the left out part of N.

Two P's match two N's therefore they have the same area. (Therefore, one N has the same area as one P.)

Areas are equal because height of P is the same as the height of N, and the base of P is twice the base of N.

Either of these two figures alone are acceptable.

Scoring Guide:

In this question, a student has to compare two given shapes with respect to their area. A student needed to realize that area meant the amount of surface a shape covers. They also needed to know how to compare the areas of the shapes. Using pictures and words to make the comparison between the areas of N and P, a student could have given a variety of explanations such as two shape P’s match with two shape N’s; therefore, one N has the same area as one P. They also could have used the geometric shapes placed one on top of the other to see how their areas compared.

* The use of more than one incorrect category in this question enabled NAEP to gather data on different ways on common student errors. Any response that fell into one of the incorrect categories earned no credit.

Scoring Guide:

In the first part of the question a student needed to know that the meaning of the word "sum"is the result of adding numbers. The sum of the two numbers is 752. The second part of the question focused on aspects of number sense, specifically on magnitude of numbers. Students are expected to realize that a result in the hundred thousands would occur only when 489 and 263 are multiplied.

Answer may be given pictorially.

In this question a student needed to add together the cost of a juice, the cost of a sandwich, and the cost of a piece of fruit for one day. The total cost for lunch each day is $1.75. Once the total is found for each day, the student needs to multiply the total for each day by 5 days. This gives a total for the week of $8.75. The least number of dollar bills that Sam's mother needs to give him is 9. To earn full credit the student needed to give an answer of nine $1 bills (or one $5 bill and four $1 bills). Partial credit could be earned in a variety of ways, such as giving only the total for 5 days ($8.75), or rounding the per day total to $2 and multiplying by 5 days, which would have given an answer of $10. The question presented students with an opportunity to demonstrate their understanding of money in a real-world situation.

This question focused on aspects of measurement sense and geometric reasoning. No ruler is available to the student. A possible full credit explanation would have described folding the string in half and cutting it and then folding each of the two pieces in half and cutting them again. Clear written communication is an essential part of a full-credit response on this question.