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BSA CBT Item Guide 2015-6 Grade 8 As of 2/18/16 ItissuggestedthatteacherslookattheTestItemAnalysisreportfortheirstudentsusingIBTP.They cancomparetheirstudentpercentcorrecttothepercentcorrectonthisreportandseehowtheir studentsdidoneachitemandwhatwasdifferentabouttheitemthatmayhavegiventhestudents issues.Itisalsosuggestedthatstaffdeterminewhathasbeentaughtandlookatthosestandards withaneyetowardsreteachingandalsolookatthestandardsthathavenotbeentaughttoseeif thefuturetimelineforinstructionshouldbemodified. Legend MC-Multiple Choice GR-Gridded Response MS-Multi-select DD-Drag and Drop HS-Hot Spot Red-Students scored less than 40% correct MAFS.8.NS.1.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion, which repeats eventually into a rational number. Item Percent Item Item Description Most Common Error Type Correct 1-83% 1 Categorize numbers as rational or irrational DD 2-59% Confused about meaning of an irrational number 3-71% Did not understand the significance of the bar 5 Convert a decimal expansion, which repeats over a repeating decimal-Given student 16 MC 19% eventually, into a rational number 12 selected 0.416 instead of 0.416 BSA CBT Item Guide 2015-6 Grade 8 As of 2/18/16 MAFS.8.NS.1.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., 𝜋2) Item Percent Item Item Description Most Common Error Type Correct Not able to approximate the value of a square Place an irrational number in its approximate root and locate it on a number line-for example, 2 HS 40% location on a number line 45 would be placed between 6 and 7 Unable to compare the size of numbers when 15 Compare the size of irrational numbers MC 41% presented using π, square roots, or fractions MAFS.8.EE.1.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. Item Percent Item Item Description Most Common Error Type Correct Identify equivalent fractions involving integer 1 1 1 13 MC 57% Thought = 2 instead of 3 exponents 27 3 3 Apply the properties of integer exponents to 14 MC 27% Thought (x 3 )2 i x 2 = x 7 instead of x 8 generate equivalent numerical expressions 23 Identify the value of integer exponents with values between 0 and 1 MS 1-40% 2-37% Thought value of 74 would be between 0 and 1 7 −3 MAFS.8.EE.1.2 Use square root and cube root symbols to represent solutions to equations of the form x2=p and x3=p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. Item Percent Item Item Description Most Common Error Type Correct 1-47% Categorize given numbers as perfect squares, Identified a number that was a perfect square as 41 DD 2-56% perfect cubes, or both a perfect square and a perfect cube 3-60% Use knowledge of square roots to find solutions to 51 MC 10% Thought 0.64 was 0.08 instead of 0.8 equations of the form x 2= p Use knowledge of square roots to find solutions to 72 GR 20% Thought 256 was 64 equations of the form x 2= p BSA CBT Item Guide 2015-6 Grade 8 As of 2/18/16 MAFS.8.EE.1.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. Item Percent Item Item Description Most Common Error Type Correct Use numbers in the form of a single digit times an 25 integer power of 10 to express how many times as GR 22% Incorrect answer much one is than the other in a real-world problem Use numbers in the form of a single digit times an 26 integer power of 10 to express how many times as MC 43% Incorrect answer much one is than the other Use numbers in the form of a single digit times an 27 integer power of 10 to express how many times as MC 18% Incorrect answer much one is than the other in a real-world problem MAFS.8.EE.1.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. Item Percent Item Item Description Most Common Error Type Correct Perform operations where numbers expressed in Correct math but unable to convert answer into 5 MC 17% scientific notation and decimals are used scientific notation Solve word problem which includes operations Rounded each number to the nearest tenth 7 using numbers expressed in scientific notation MC 29% before calculations instead of after and decimals Solve word problem which includes operations Difficulty in converting numbers written in 10 using numbers expressed in scientific notation MC 42% scientific notation and decimals BSA CBT Item Guide 2015-6 Grade 8 As of 2/18/16 MAFS.8.EE.2.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. Item Item Item Item Item Could not determine unit rate when presented in 58 Interpret the unit rate as the slope of a graph MC 68% a graph Compare different proportional relationships 1-47% Incorrect comparison of unit rates when 60 MS represented in different ways 2-51% presented in different ways 62 Identify a graph representing a real-world situation MC 34% Confused value of x- and y-coordinate values MAFS.8.EE.2.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. Item Percent Item Item Description Most Common Error Type Correct Use similar triangles to explain why the slope m is 65 the same between any two distinct points on a MC 25% Could not identify the correct values of the slope non-vertical line in the coordinate plane Derive the equation y = mx + b for a line Equation had the incorrect value for the slope 69 intercepting the vertical axis at b from a MC 38% (change of x over change of y, instead of vicecoordinate grid versa) Derive the equation y = mx + b for a line Did not include the slope when deriving the 71 intercepting the vertical axis at b when given a MC 43% equation real-world problem and graph BSA CBT Item Guide 2015-6 Grade 8 As of 2/18/16 MAFS.8.EE.3.7 Solve linear equations in one variable. MAFS.8.EE.3.7a Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x=a, a=a, or a=b, results (where a and b are different numbers). MAFS.8.EE.3.7b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Item Percent Item Item Description Most Common Error Type Correct Explain why a linear equation with one variable Could not select correct explanation of why an 59 MC 42% has no solution equation would have no solution Identify linear equations with one variable that 1-45% Could not identify equations with infinite 63 MS have an infinite number of solutions 2-41% solutions When arriving at the final step, 10=4x, the 64 Solve a linear equation with one variable MC 51% student subtracted instead of dividing MAFS.8.EE.3.8 Analyze and solve pairs of simultaneous linear equations. MAFS.8.EE.3.8a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. MAFS.8.EE.3.8b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. MAFS.8.EE.3.8c Solve real-world and mathematical problems leading to two linear equations in two variables. Item Percent Item Item Description Most Common Error Type Correct Identify a system of two linear equations on a Did not identify a set of parallel lines as having 66 MC 48% graph and know there is no solution no solution Solve real-world problems leading to two linear Selected the x-intercept instead of the 67 GR 9% equations and find the solution to both intersection of the 2 lines Understand that solutions to a system of two Could not identify the set of equations that would 70 linear equations correspond to points of MC 33% intersect at given points intersection of their graphs BSA CBT Item Guide 2015-6 Grade 8 As of 2/18/16 MAFS.8.F.1.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. Item Percent Item Item Description Most Common Error Type Correct Understand a function is a rule that assigns to Could not identify graph with a relation that is a 11 each input exactly one output as displayed in a MC 40% function graph Understand a function is a rule that assigns to Could not identify a table with a relation that is a 17 each input exactly one output as displayed in a MC 39% function table Identify an equation representing a function Could not identify the equation of a function 38 MC 48% displayed in a table when given the table MAFS.8.F.1.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Item Percent Item Item Description Most Common Error Type Correct Compare properties of functions represented in Could not identify which set of information had 36 MC 32% different ways (which has greatest rate of change) the greatest rate of change Compare properties of two functions represented Could not correctly compare the values to find 39 in different ways (numerically in tables and by MC 34% the greatest change verbal descriptions) Given a function displayed on a graph, student 1-37% Could not correctly identify the equation showing 40 MS identifies equation with a greater rate of change 2-48% a greater rate than the given graph BSA CBT Item Guide 2015-6 Grade 8 As of 2/18/16 MAFS.8.F.1.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. Item Percent Item Item Description Most Common Error Type Correct 1-54% Could not identify which equations were linear 35 Identify which equation is a linear function MS 2-47% functions Could not identify which table was a linear 42 Identify which table displays a linear function MC 45% function Identify the linear function when presented as Could not identify which equation, table or graph 44 MC 30% equations, tables, and graphs was a linear function MAFS.8.F.2.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or table of values. Item Percent Item Item Description Most Common Error Type Correct Identify the linear function that models a realCould not identify the correct linear function 3 MC 31% world situation when given a verbal description Identify a linear function that represents a Could not identify the correct linear function 18 MC 33% relationship shown in a table when given a table 1-39% Difficulty identifying which graph went with which 24 Match linear functions with the correct graph DD 2-33% equation; given equations were in the form of y + 3-48% mx = b BSA CBT Item Guide 2015-6 Grade 8 As of 2/18/16 MAFS.8.F.2.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. Item Percent Item Item Description Most Common Error Type Correct Identify a graph that exhibits the qualitative While the situation changed rates the student 12 features of a function that has been described MC 65% picked the graph with a straight line verbally Identify a graph that exhibits the qualitative Student picked the graph that was the opposite 20 features of a function that has been described MC 60% of what was described (increased when it should verbally have been declining) Given two graphs the student describes Could not correctly identify what was happening 21 MC 59% qualitatively the functional relationship shown in the given graphs MAFS.8.G.1.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. Also Assessed: MAFS.8.G.1.1 Verify experimentally the properties of rotations, reflections, and translations: MAFS.8.G.1.1a Lines are taken to lines, and line segments to line segments of the same length. MAFS.8.G.1.1b Angles are taken to angles of the same measure. MAFS.8.G.1.1c Parallel lines are taken to parallel lines. Item Percent Item Item Description Most Common Error Type Correct Understand that a two-dimensional figure is congruent to another if the second can be 1-36% Did not understand that a dilation would not 28 MS obtained from the first by a sequence of rotations, 2-43% maintain congruence reflections, and translations Given two congruent figures, describe a sequence 30 MC 59% Did not identify the correct transformation that exhibits the congruence between them Could not identify how a shape should be moved Verify experimentally the properties of rotations, 31 MC 27% to a new location (included a 90º reflections, and translations counterclockwise rotation) BSA CBT Item Guide 2015-6 Grade 8 As of 2/18/16 MAFS.8.G.1.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Item Item Item Item Item Identify the effect of a translation on a twoConfused x- and y-coordinates when given 33 MC 44% dimensional figure using a coordinate grid directions 43 Describe the effect of a rotation on a twodimensional figure using a coordinate grid MC 35% 46 Identify the effect of translations and reflections on a two-dimensional figure using a coordinate grid MC 41% Could not identify how a shape should be moved to a new location which included the terms 90º, 45º, clockwise, and counterclockwise Confused x- and y-coordinates when given directions MAFS.8.G.1.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. Also Assessed: MAFS.8.G.1.1 Verify experimentally the properties of rotations, reflections, and translations: MAFS.8.G.1.1a Lines are taken to lines, and line segments to line segments of the same length. MAFS.8.G.1.1b Angles are taken to angles of the same measure. MAFS.8.G.1.1c Parallel lines are taken to parallel lines. Item Percent Item Item Description Most Common Error Type Correct Understand that a two-dimensional figure is similar to another if the second can be obtained Did not understand that a dilation would not 29 MC 39% from the first by a sequence of reflections and maintain congruence dilations Identify a sequence of transformations that would Did not understand that a dilation would not 32 MC 36% result in figures that are similar but not congruent maintain congruence Understand the difference between similarity and Did not understand the difference between 34 MC 42% congruence similarity and congruence BSA CBT Item Guide 2015-6 Grade 8 As of 2/18/16 MAFS.8.G.1.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angle created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. Item Percent Item Item Description Most Common Error Type Correct Find the measure of the missing values of a 47 triangle using what is known about angle sums GR 13% Incorrect answer and exterior angles of triangles Identify the measure of angles and associated parallel lines using what is known about angles Confused about the meaning of transversals, 49 MC 41% created when parallel lines are cut by a parallel lines and equivalent angles transversal Find the measure of the missing values of a 50 GR 7% Incorrect calculations triangle using what is known about angle sums MAFS.8.G.2.6 Explain a proof of the Pythagorean Theorem and its converse. Item Percent Item Item Description Most Common Error Type Correct Given sets of three lengths, the student identifies 1-42% Could not use the Pythagorean Theorem to 57 MS which can be used to make a right triangle 2-28% identify a right triangle Cold not identify an explanation of the Given a real-world scenario, the student explains 61 MC 19% Pythagorean Theorem as the reason three why the triangle described is a right triangle locations were arranged as a right triangle Given 2 lengths of a triangle, the student finds the Added two side lengths to determine the length 68 MC 28% measure of the third to make a right triangle of the third side BSA CBT Item Guide 2015-6 Grade 8 As of 2/18/16 MAFS.8.G.2.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. Also Assessed: MAFS.8.G.2.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. Item Percent Item Item Description Most Common Error Type Correct Apply the Pythagorean Theorem to find the 45 distance between two points in a coordinate GR 2% Most students added the given points system Apply the Pythagorean Theorem to determine the Students selected the shortest possible length 52 hypotenuse in a right triangle in a mathematical MC 24% for the third side instead of the longest possible problem length as required Apply the Pythagorean Theorem to determine an Added the measures of one leg and the 53 unknown side length of a right triangle in a realMC 34% hypotenuse to find the length of the other leg world problem MAFS.8.G.3.9 Know the formulas for the volumes of, cones cylinders, and spheres and use them to solve real-world and mathematical problems. Item Percent Item Item Description Most Common Error Type Correct Know the formula for the volume of a sphere and Students used the measure of the radius to find 54 GR 1% use to solve a mathematical problem the diameter Students used correct formula but made an error Know the formula for the volume of a cylinder and 55 MC 39% algebraically by subtracting instead of dividing to use to solve a real-world problem find final answer Know the formula for the volume of a cone and Students used correct formula but forgot to 56 GR 1% use it solve a mathematical problem include π in the calculations BSA CBT Item Guide 2015-6 Grade 8 As of 2/18/16 MAFS.8.SP.1.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. Item Percent Item Item Description Most Common Error Type Correct Interpret a scatter plot and investigate patterns Students interpreted a negative correlation on a between two quantities and describe patterns scatter plot as having no correlation 4 MS 56% such as outliers, positive or negative associations, linear association, and nonlinear associations Interpret a scatter plot and investigate patterns Students interpreted a positive correlation between two quantities such as positive or 1-41% surrounding a line of best fit on a scatter plot as 6 MC negative associations, linear association, and 2-59% having no correlation nonlinear associations MAFS.8.SP.1.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. Item Percent Item Item Description Most Common Error Type Correct 8 Given a scatter plot identify the line of best fit MC 53% Selected line that began in origin but was too low 19 Given a scatter plot identify the line of best fit MC 51% Selected line that began in origin but was too low MAFS.8.SP.1.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. Item Percent Item Item Description Most Common Error Type Correct Given a real-world scenario with an equation and Identified the slope as representing the fixed 9 MC 55% graph, interpret the meaning of the slope cost instead of rate of change Given a real-world scenario with an equation and 22 MC 56% Confused the x-intercept with the rate of change graph, interpret the meaning of the x-intercept BSA CBT Item Guide 2015-6 Grade 8 As of 2/18/16 MAFS.8.SP.1.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. Item Percent Item Item Description Most Common Error Type Correct Given information about a survey, identify the Could not identify the correct two-way table for 37 MC 22% correct two-way table summarizing data data given in a real-world problem Given a completed two-way table, use relative Unable to correctly select summary statements 1-73% 48 frequencies calculated for rows/columns to MS about the information presented in the table 2-57% describe associations between the two variables