Download BSA Item Guide-2016-G8_21816

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