Item 28 Anchor Papers  

Anchor Papers ~ Algebra/Data Analysis ~ Item 28
Score Level 1 Anchor Paper 

This response demonstrates little application of a reasonable strategy. The table is correctly completed. The student has not responded to the first, third and fourth parts of the question. This response demonstrates a minimal understanding and analysis of the problem. 
Score Level 1 Anchor Paper 

This response demonstrates little application of a reasonable strategy. The hexagon is incorrectly divided into nonoverlapping triangles but the table is correctly completed. A general relationship between the number of sides of each polygon and nonoverlapping triangles is given (As the number of sides went up so did the number of nonoverlapping triangles). The student does not describe the relationship between the number of sides of any polygon and its number of nonoverlapping triangles and does not provide a justification. The student provides a relationship (Also every time the number of non overlapping triangles goes up so does the sum of the angles), but does not describe the relationship between the number of nonoverlapping triangles of any polygon and the sum of its angle measures. A justification is not provided. This response demonstrates a minimal understanding and analysis of the problem. 
Score Level 2 Anchor Paper 

This response demonstrates an incomplete application of a reasonable strategy. The hexagon is incorrectly divided into nonoverlapping triangles. The table is correctly completed. The student provides a relationship (The more sides you have, the more nonoverlapping triangles you going have), but does not describe the relationship between the number of sides of any polygon and its number of nonoverlapping triangles. A justification is not provided. The relationship between the number of nonoverlapping triangles in a polygon and the sum of its angle measures is correct (To get the sum of angle measures, you have to multiply the number of non overlapping triangles times 180°) but a justification is not given. This response demonstrates a conceptual understanding and analysis of the problem. 
Score Level 2 Anchor Paper 

This response indicates an incomplete application of a reasonable strategy. The hexagon is correctly divided into nonoverlapping 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 relationship between the number of sides and nonoverlapping triangles is correct (If you take the number of sides and subtract 2 you get the # of nonoverlapping triangles) and the justification supports the solution (32=1 triangle; 42=2 Quad; 52=3 pentagon). The relationship between the number of nonoverlapping triangles in a polygon and the sum of its angle measures is not given and a justification is not provided. This response demonstrates a conceptual understanding of the problem. 
Score Level 2 Anchor Paper 

This response demonstrates an incomplete application of a reasonable strategy. The hexagon is incorrectly divided into nonoverlapping triangles. The table is correctly completed. The student provides a relationship (the numbers in both go up one number each time), but does not describe the relationship between the number of sides of any polygon and its number of nonoverlapping triangles. A justification is not provided. The relationship between the number of nonoverlapping triangles in a polygon and the sum of its angle measures is correct (you take the number of nonoverlapping triangles and you multiply 180 by that number) but a justification is not given. This response demonstrates a conceptual understanding and analysis of the problem. 
Score Level 3 Anchor Paper 

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 nonoverlapping triangles and the table is correctly completed. The relationship between the number of sides and nonoverlapping triangles is correct (how many sides there were you would subtract 2 away from it to get the number of over lapping triangles) but a justification is not provided. The omission of the prefix "non" in "over lapping triangles" constitutes a minor error. The relationship between the number of nonoverlapping triangles in a polygon and the sum of its angle measures is correct (You could multiply the number of non overlapping triangles times 180°). The justification is given (because 180° is one triangle, so you would multiply 180° by the # of triangles). This response demonstrates a clear understanding and analysis of the problem. 
Score Level 3 Anchor Paper 

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 and nonoverlapping triangles is correct (if you subtract 2 to the number of sides, you get the number of NonOverlapping triangles) and the justification supports the solution (32=1. 42=2. 52=3. 62=4.). The relationship between the number of nonoverlapping triangles in a polygon and the sum of its angle measures is correct (multiplied by 180 to get the sum of its angle measures) but a justification is not provided. This response demonstrates a clear understanding and analysis of the problem. 
Score Level 3 Anchor Paper 

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 nonoverlapping triangles is correct (you subract 2 from the number of sides on that shape) and the justification supports the solution (On a triangle it has three sides  two=1 overlapping triangle. In the quadrilateral it had 4 sides  two= 2 overlapping sides). The use of "sides" rather than triangles constitutes a minor error. The relationship between the number of nonoverlapping triangles in a polygon and the sum of its angle measures is correct (multiplying the number of triangles times 180°) and the justification supports the solution (Hexagon 4 triangles x 180°=720°). This response demonstrates a clear understanding and analysis of the problem. 
Score Level 4 Anchor Paper 

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 nonoverlapping triangles and the table is correctly completed. The relationship between the number of sides of each polygon and the number of nonoverlapping triangles is correct (There are 2 less overlapping triangles than there are # of sides) and the justification is fully developed and clearly presented (31=2,42=2,53=2,64=2). The relationship between the number of nonoverlapping triangles in a polygon and the sum of its angle measures is correct (The sum of angle measures 180° times the # of non overlapping triangles), and the justification is fully developed (1x180°=180°, 2x180°=360°, 3x180°=540°, 4x180°=720°). This response demonstrates a complete understanding and analysis of the problem. 
Score Level 4 Anchor Paper 

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 nonoverlapping triangles and the table is correctly completed. The relationship between the number of sides of each polygon and the number of nonoverlapping triangles is correct (To find the # of triangles using the # of sides you simply minus 2 to the # of sides) and the justification is fully developed (32=1; 42=2; 52=3; 62=4). The relationship between the number of nonoverlapping triangles in a polygon and the sum of its angle measures is correct (To find the sum of angle measurements yo times # of triangle times 180). The justification is fully developed and clearly presented (1·180=180; 2·180=360; 3·180=540; 4·180=720). This response demonstrates a complete understanding and analysis of the problem. 