# Northborough

Districts Schools

# 2023 Item by Item Results for GRADE 08 MATHEMATICS

## Number of Students Included: 176     Participation Rate = 100.00%

 Northborough - GRADE 08 MATHEMATICS ITEM INFORMATION PERCENT OF DISTRICT'S POSSIBLE POINTS ITEM TYPE REPORTING CATEGORY STANDARD ITEM DESC POSSIBLE POINTS NORTHBOROUGH STATE DISTRICT-STATE DIFFERENCE 1 SR NSEE 8.EE.C.7 Solve a linear equation by collecting like terms. 1 62% 59% 3 2 SR GE 8.G.C.9 Find the volume of a cylinder given its diameter and height. 1 51% 45% 6 3 SR GE 8.G.A.2 Given several transformations on a triangle, determine whether the resulting images are congruent to the original figure. 1 59% 55% 4 4 SR NSEE 8.NS.A.2 Approximate the value of a square root by showing how to find its location on a number line. 1 67% 59% 8 5 CR FN 8.F.B.4 Use the linear relationship represented in a table to determine the y-intercept and slope; to write the equation of the line; and to determine whether a given point falls on the line. 4 48% 32% 16 6 SR NSEE 8.EE.A.4 Solve a real-world problem that involves performing operations on two numbers expressed in scientific notation. 1 47% 49% -2 7 SR NSEE 8.EE.C.8 Determine the number of solutions to a system of equations. 1 38% 40% -2 8 SR NSEE 8.EE.A.1 Apply the properties of negative integer bases and exponents to identify the signed values of expressions. 1 32% 38% -6 9 SR NSEE 8.NS.A.1 Match decimal expansions with their fraction equivalents. 1 56% 49% 7 10 SR NSEE 8.EE.A.2 Evaluate the cube root of a small perfect cube. 1 53% 46% 7 11 SR NSEE 8.EE.B.5 Determine which graph represents a proportional relationship in a real-world context. 1 88% 74% 14 12 SR GE 8.G.B.7 Use the Pythagorean theorem to find the missing side length of a right triangle in a real-world problem. 1 57% 53% 4 13 CR SP 8.SP.A.1 Given a scatter plot, determine if there are outliers in the data, describe the association represented by the data, and make a prediction based on the data. 4 83% 70% 13 14 SR GE 8.G.B.6 Given the lengths of two sides of a right triangle, determine the possible length of the third side by using the Pythagorean Theorem. 1 31% 27% 4 15 SA NSEE 8.EE.C.8 Create two linear equations, each involving the same two variables, to solve a real-world problem. 1 58% 48% 10 16 SA GE 8.G.A.1 Determine the length of a line segment after a series of transformations. 1 76% 65% 11 17 SA GE 8.G.B.8 Use the Pythagorean Theorem to create an equation to represent the length of a line segment that is graphed on a coordinate plane. 1 55% 45% 10 18 SR GE 8.G.A.5 Determine the angle measures of a triangle that is congruent to a given triangle. 1 64% 43% 21 19 SR FN 8.F.A.3 Interpret the equation y=mx+b, and decide whether given functions are linear or not linear. 2 60% 48% 12 20 SR GE 8.G.A.3 Determine the coordinates of the image of a vertex of a quadrilateral after it has been rotated about the origin. 1 78% 63% 15 21 SR NSEE 8.NS.A.2 Determine between which pair of integers the square root of a given number lies. 1 76% 72% 4 22 SA SP 8.SP.A.3 Use the equation of a linear model derived from data to solve a real-world problem. 1 68% 58% 10 23 CR NSEE 8.EE.A.1 Use the properties of exponents to find equivalent expressions. 4 54% 44% 10 24 SR NSEE 8.NS.A.1 Identify an irrational number from a list of numbers. 1 71% 59% 12 25 SR NSEE 8.EE.C.8 Determine the coordinates of the solution of a system of equations. 1 60% 54% 6 26 SR NSEE 8.EE.A.1 Use the properties of exponents to identify equivalent expressions. 1 33% 30% 3 27 SR NSEE 8.EE.B.5 Interpret a proportional relationship on a graph, and identify and interpret the slope of the graph. 1 61% 51% 10 28 SR NSEE 8.EE.A.2 Classify radical expressions as rational or irrational numbers. 1 51% 38% 13 29 SA GE 8.G.A.1 Determine the effects of a translation and a rotation on the angles and sides of a quadrilateral. 2 75% 66% 9 30 SR NSEE 8.NS.A.1 Identify rational numbers from a list of radical expressions. 1 52% 52% 0 31 SR FN 8.F.B.4 Use the linear relationship represented in a table of values to solve a real-world problem that involves determining the y-value for a given x-value. 1 73% 70% 3 32 SR SP 8.SP.A.3 Use the equation of a linear model derived from data to solve a real-world problem. 1 76% 70% 6 33 SR SP 8.SP.A.2 Justify why a line drawn through data on a scatter plot is suitable as a line of best fit. 1 68% 48% 20 34 SR FN 8.F.B.4 Given a real-world context, interpret the rate of change from an equation. 1 76% 65% 11 35 CR GE 8.G.A.1 Given a polygon and its image after a transformation, verify congruence by analyzing properties of both polygons; describe a series of transformations that would result in the same image of the polygon. 4 51% 36% 15 36 SA FN 8.F.A.1 Given a set of points on a coordinate plane, determine which point should be removed in order to create a function. 1 55% 43% 12 37 SR FN 8.F.A.1 Determine which set of coordinate pairs represents a function. 1 77% 60% 17 38 SR FN 8.F.A.2 Compare properties of two functions represented algebraically and in a table, and interpret each function's rate of change and initial value. 1 77% 67% 10 39 SA GE 8.G.C.9 Find the volume of a sphere given its radius. 1 53% 35% 18 40 SR GE 8.G.A.4 Given several transformations of a figure, determine whether the image created by each transformation is congruent or similar but not congruent to the original figure. 1 56% 38% 18