The following 19 Sample Student Responses represent a range of score points.

Score for Sample Student Response #1: Rubric Score 1

Annotation: This response demonstrates little application of a reasonable strategy. The hexagon is incorrectly divided but the table is correctly completed. A general relationship between the number of sides of each polygon and non-overlapping triangles is given (The More sides it has the greater # of Non-overlaping triangles that fit inside), but the student does not describe the relationship between the number of sides of any polygon and its number of non-overlapping triangles. A justification is not provided. The student provides a relationship (and the greater the number of triangles the greater the total degree of the polygon), but does not describe the relationship between the number of non-overlapping triangles of any polygon and the sum of its angle measures. A justification is not given. This response demonstrates a minimal understanding and analysis of the problem. (Compare to this Level 1 anchor paper.)

Score for Sample Student Response #2: Rubric Score 3

Annotation: This response demonstrates application of a reasonable strategy that leads to some correct solutions within the context of the problem. The hexagon is incorrectly divided into non-overlapping triangles. The table is correctly completed. The relationship between the number of sides and non-overlapping triangles is correct (You subtract 2 from the number of sides and your difference is the number of non-overlapping triangles) but a justification is not provided. The relationship between the number of non-overlapping triangles in a polygon and the sum of its angle measures is correct (You take the number of non-overlapping triangles and multiply it by 180°). A justification is not given. This response demonstrates a clear understanding and analysis of the problem. (Compare to this Level 3 anchor paper.)

Score for Sample Student Response #3: Rubric Score 4

Annotation: This response demonstrates application of a reasonable strategy that leads to correct solutions within the context of the problem. The hexagon is correctly divided into non-overlapping triangles and the table is correctly completed. The relationship between the number of sides of each polygon and the number of non-overlapping triangles is correct (The number of sides minus 2 will give you the number of non-overlaping triangles. The formula is S-2=T, S=sides and T is non-overlaping triangles) and the justification is fully developed (Triangle [3-2=1], Quadrilateral [4-2=2], pentagon [5-2=3], Hexagon [6-2=4], etc). The relationship between the number of non-overlaping triangles in a polygon and the sum of its angle measures is correct (The formula is T·180=A. T is non-overlapping triangles and A is the sum of all the angles measured). The justification is clearly presented (Triangle [1·180=180] Quad. [2·180=360], Pentagon [3·180=540)], and Hexagon [4·180=720]). This response demonstrates a complete understanding and analysis of the problem.

Score for Sample Student Response #4: Rubric Score 1

Annotation: This response demonstrates little application of a reasonable strategy. The hexagon is incorrectly divided. While the table's column for the sum of angle measures is not completed, the number of sides and over-lapping triangles of a hexagon are correct. The relationship between the number of sides and non-overlapping triangles is correct (The non overlapping triangles are always 2 below the # of sides of the shape) but a justification is not given. The student did not address the fourth part of the problem. This response demonstrates a minimal understanding and analysis of the problem.

Score for Sample Student Response #5: Rubric Score 2

Annotation: This response demonstrates an incomplete application of a reasonable strategy. The hexagon is incorrectly divided into non-overlapping triangles. The table is correctly completed. The relationship between the number of sides and non-overlapping triangles is correct (If you subtract 2 from the number of sides of each polygon, you get the number of non-overlaping triangles) but a justification is not provided. The relationship between the number of non-overlapping triangles in a polygon and the sum of its angle measures is not provided and a justification is not given. This response demonstrates a conceptual understanding and analysis of the problem. (Compare to this Level 2 anchor paper.)

Score for Sample Student Response #6: Rubric Score 4

Annotation: This response demonstrates application of a reasonable strategy that leads to correct solutions within the context of the problem. The hexagon is correctly divided into non-overlapping triangles and the table is correctly completed. The relationship between the number of sides of each polygon and the number of non-overlapping triangles is correct (The number of non-overlapping triangles is always 2 less than the number of sides). The justification is fully developed (For example the triangle has 3 sides thes only 1 overlapping triangle. Also quadrilateral has four sides well it has two triangles). The relationship between the number of non-overlapping triangles in a polygon and the sum of its angle measures is correct (However many triangles there are you multiply it by 180° [number degrees a triangle equals] and thats your sum of angles measures). The justification is fully developed (For example the hexagon had 4 non-overlapping triangles so take 4x180°=720°). This response demonstrates a complete understanding and analysis of the problem.

Score for Sample Student Response #7: Rubric Score 3

Annotation: This response demonstrates application of a reasonable strategy that leads to some correct solutions within the context of the problem. The hexagon is incorrectly divided into non-overlapping triangles but the table is correctly completed. The relationship between the number of sides and non-overlapping triangles is correct (the total # of sides minus 2 is the total # of triangles there are) but a justification is not provided. The relationship between the number of non-overlapping triangles in a polygon and the sum of its angle measures is correct (how ever many total triangles there are you multiply that by 180°). A justification is not given. This response demonstrates a clear understanding and analysis of the problem. (Compare to this Level 3 anchor paper.)

Score for Sample Student Response #8: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy. The hexagon is incorrectly divided into non-overlapping triangles but the table is correctly completed. The relationship between the number of sides and non-overlapping triangles is correct (The number of non-overlapping triangles is always the number of sides minus 2) but a justification is not provided. The student provides a relationship (Each non-overlapping triangle is 180°), but does not describe the relationship between the number of non-overlapping triangles of any polygon and the sum of its angle measures. A justification is not provided. This response demonstrates a conceptual understanding of the problem.

Score for Sample Student Response #9: Rubric Score 3

Annotation: This response demonstrates application of a reasonable strategy that leads to some correct solutions within the context of the problem. The hexagon is not divided but the table is correctly completed. The relationship between the number of sides of each polygon and non-overlapping triangles is correct (The number of non-overlapping triangles is always 2 less than the number of sides). The justification supports the solution (The triangle has 3 sides. Subtract 2 and you get 1, the number of non-overlapping triangles in a triangle. The same is applied for the other polygons. The quadrilateral has 4 sides, subtract 2 from 4 and you get two, which is equal to the number of non-overlapping triangles. The pentagon has 3 sides, 5-2 is 3, which is the number of triangles. Finally, the hexagon has 6 sides, 6-2 is 4, which I figured to be the number of triangles). The relationship between the number of non-overlapping triangles in a polygon and the sum of its angle measures is correct (There is an equation for finding the sum of angle measures. Let s equal the sum of angle measures and t equal the number of non-overlapping triangles. The equation would be s=180t. 180 is 180° which is the sum of the angle measures of a triangle. You are simply multiplying 180 by the number of triangles). The justification supports the solution (For example: The pentagon has 3 triangles. 180·3=540). This response demonstrates a clear understanding and analysis of the problem. (Compare to this Level 3 anchor paper.)

Score for Sample Student Response #10: Rubric Score 4

Annotation: This response demonstrates application of a reasonable strategy that leads to correct solutions within the context of the problem. The hexagon is correctly divided into non-overlapping triangles and the table is correctly completed. The relationship between the number of sides of each polygon and the number of non-overlapping triangles is correct (subtract two from the sides of the polygon) and the justification is fully developed and clearly presented in a labeled diagram. The relationship between the number of non-overlapping triangles in a polygon and the sum of its angle measures is correct (One triangle has a sum of 180°, therefore if there are many triangles you have to multiply 180 by that amount). The justification is fully developed and clearly presented (One triangle is 180° and two triangles which equal a quadrialateral is 360° because there are two triangles, and each has a measure of 180 degrees), including a labeled diagram. This response demonstrates a complete understanding and analysis of the problem.

Score for Sample Student Response #11: Rubric Score 2

Annotation: This response demonstrates an incomplete application of a reasonable strategy. The hexagon is correctly divided into non-overlapping triangles and the table is correctly completed. The relationship between the number of sides and non-overlapping triangles is correct (If you take the number of sides of the polygons + you subtrat 2 from it you would have the number of non-overlaping Triangles) but a justification is not provided. The relationship between the number of non-overlapping triangles in a polygon and the sum of its angle measures is not provided and a justification is not given. This response demonstrates a conceptual understanding and analysis of the problem.

Score for Sample Student Response #12: Rubric Score 3

Annotation: This response demonstrates application of a reasonable strategy that leads to some correct solutions within the context of the problem. The hexagon is correctly divided into non-overlapping triangles and the table is correctly completed. The relationship between the number of sides and non-overlapping triangles is correct (However many number of sides you have, take that number and subtract it by two and you will have the number of non-overlapping triangles). A justification is not provided. The relationship between the number of non-overlapping triangles in a polygon and the sum of its angle measures is correct (you take the number of non-overlapping triangles and you multiply it by 180 and you will get the sum of Angle measures). A justification is not given. This response demonstrates a clear understanding and analysis of the problem. (Compare to this Level 3 anchor paper.)

Score for Sample Student Response #13: Rubric Score 1

Annotation: This response demonstrates little application of a reasonable strategy. The hexagon is correctly divided into non-overlapping triangles. The number of sides and overlapping triangles for a hexagon are correct, but the column for the sum of angle measures is incorrect. The student did not address the third or fourth parts of the question. This response demonstrates a minimal understanding and analysis of the problem.

Score for Sample Student Response #14: Rubric Score 2

Annotation: This response demonstrates an incomplete application of a reasonable strategy. The hexagon is incorrectly divided but the table is correctly completed. The student provides a relationship (When the number of sides a polygon has increases so does the number of overlapping triangles), but does not describe the relationship between the number of sides of any polygon and its number of non-overlapping triangles. A justification is not provided. The relationship between the number of non-overlapping triangles in a polygon and the sum of its angle measures is correct (Every time the number of non overlapping tirangles increases you multiply that number by 180°) but a justification is not given. This response demonstrates a conceptual understanding and analysis of the problem. (Compare to this Level 2 anchor paper.)

Score for Sample Student Response #15: Rubric Score 4

Annotation: This response demonstrates application of a reasonable strategy that leads to correct solutions within the context of the problem. The hexagon is correctly divided into non-overlapping triangles and the table is correctly completed. The relationship between the number of sides of each polygon and the number of non-overlapping triangles is correct (The number of non-overlapping triangles is two less than the number of sides that figure has). The justification is fully developed (I know this because for the triangle 3-2 is 1. The quadrilateral 4-2 is 2 and so on). The relationship between the number of non-overlapping triangles in a polygon and the sum of its angle measures is correct (all you have to do is multiply the number of non-overlapping triangles by 180°) and the justification is clearly presented (Like for a quadrilateral 2·180=360). This response demonstrates a complete understanding and analysis of the problem.

Score for Sample Student Response #16: Rubric Score 3

Annotation: This response demonstrates application of a reasonable strategy that leads to some correct solutions within the context of the problem. The hexagon is correctly divided into non-overlapping triangles and the table is correctly completed. The relationship between the number of sides and non-overlapping triangles is correct (The number of non-overlapping triangles is 2 less then the number of sides the shape has). A justification is not provided. The relationship between the number of non-overlapping triangles in a polygon and the sum of its angle measures is correct (The number of non-overlapping triangles is multiplied by 180 to get the sum of angle measures.) A justification is given (Each triangle's angle measures equal 180 so if you multiply 180 to the number of triangles you get the sum). This response demonstrates a clear understanding and analysis of the problem. (Compare to this Level 3 anchor paper.)

Score for Sample Student Response #17: Rubric Score 1

Annotation: This response demonstrates little application of a reasonable strategy. The hexagon is not divided. The number of sides and overlapping triangles for a hexagon are correct, but the column for the sum of angle measures is incorrect. The relationship between the number of sides and non-overlapping triangles is correct (The number of sides each polygon has the number of non-overlapping triangles is 2 less) but a justification is not given. The relationship between the number of non-overlapping triangles in a polygon and the sum of its angle measures is incorrect, but consistent with the student's table (For the sum of Angle Measures is 2 time greater for each side). A justification is not provided. This response demonstrates a minimal understanding and analysis of the problem.

Score for Sample Student Response #18: Rubric Score 3

Annotation: This response demonstrates application of a reasonable strategy that leads to some correct solutions within the context of the problem. The hexagon is incorrectly divided but the table is correctly completed. The relationship between the number of sides of each polygon and non-overlapping triangles is correct (the number of sides is 2 numbers higher than the non-overlapping triangle number; so inorder to find the number of side you add 2 to the number of non-overlapping triangles or vise versa). The justification supports the solution (For example, the triangle. It has 1 non-overlapping triangle and 3 side. 3 is 2 numbers higher than 1). The relationship between the number of non-overlapping triangles in a polygon and the sum of its angle measures is correct (In order to find the sum you multiply 180 by the number of non-overlapping triangles because 180° is the sum of one triangle). The justification supports the solution (So if there was 4 non-overlapping Triangles, inorder to get the sum of the angle measurements, you would multiply 180° by 4 and get 720°, which is the sum of the angle measures). This response demonstrates a clear understanding and analysis of the problem. (Compare to this Level 3 anchor paper.)

Score for Sample Student Response #19: Rubric Score 4

Annotation: This response demonstrates application of a reasonable strategy that leads to correct solutions within the context of the problem. The hexagon is correctly divided into non-overlapping triangles and the table is correctly completed. The relationship between the number of sides of each polygon and the number of non-overlapping triangles is correct (you subtract 2 from the # of sides). The justification is fully developed (Ex. Quadralateral's got 4 sides. 4-2=2. It's got 2 triangles. Pentagon: 5-2=3. It has 3 triangles). The relationship between the number of non-overlapping triangles in a polygon and the sum of its angle measures is correct (since one triangle's angles measure, in total, 180°, then, to find the degree of another polygon you just have to find how many triangles it has and multiply that # by 180°). The justification is clearly presented (Ex: That's what I did for the Hexagon: multiply 4 x 180° and got 720°. Quadralateral: 2 triangles x 180°=360°). This response demonstrates a complete understanding and analysis of the problem.

Anchor Papers used in scoring