魅影直播 1999 Benchmarking Report Appendix D

Lower Quarter Benchmark Items

Fractions and Number Sense
H09	Rounds to estimate the sum of two three-digit numbers
R07	Subtracts a three-decimal-place number from another with multiple regrouping.
R13	Subtracts a four-digit number from another involving zeroes.
Data Representation, Analysis, and Probability
A06	Calculates and compares the averages of two sets of data.
P16	Reads a thermometer and locates the reading in a table.
Algebra
P09	Selects an expression in exponential notation for repeated multiplication.

Median Benchmark Items

Fractions and Number Sense
B08	Solves a word problem by finding the missing term in a proportion.
C06	Determines which is the most unreasonable estimate for two 3-digit numbers.
D12	Estimates the value, to one decimal place, of a point on a number line marked at whole number intervals.
E04	Arranges four given digits in descending and ascending order and finds the difference between those two numbers.
H08	Selects a figure with shaded parts that represents a familiar fraction.
I05	Solves a word problem involving subtraction of a two-place decimal number from another.
K01	Identifies a circular model of a fraction that best approximates a given rectangular model of the same fraction.
K02	Solves a word problem by adding numbers with up to three decimal places.
K06	Selects the approximate quantity remaining after an amount is decreased by a given percent.
L09	Given an object of one length, to one decimal place, estimates the length of a second object in a diagram.
L10	Identifies the numerical equivalent of a decimal number given in words.
M04	Selects the smallest fraction from a set of familiar fractions.
N11	Rounds a number less than 100,000 to the nearest hundred.
P13	In a word problem, uses rounding to identify the number sentence that gives the best estimate for the product.
Measurement
D11	Selects appropriate metric unit to measure weight (mass).
G02	Identifies an unlabeled midway point on a number line marked in tenths.
L13	Recognizes the inverse relation between length of nonstandard units and the number of those units required to cover a distance.
Data Representation, Analysis, and Probability
B07	Given two line graphs, identifies the relevant one and determines the interval showing the greatest increase.
C02	Reads and interprets information from a pie graph.
E01	Solves problem by interpreting information from a graph of two intersecting lines.
H07	Reads data from a bar graph to solve a word problem.
J13	Determines how many items are represented by one symbol in a pictogram.
M03	Recognizes that the probability of an outcome of a single event is inversely related to the number of elements in the population of events
M09	Given a table of values for two variables, selects the graph that could represent the given data.
Q04	Solves a comparison problem by associating elements of a bar graph with a verbal description.
Geometry
C03	Identifies corresponding parts of congruent trapezoids.
J15	Selects the pair of similar triangles from a set of triangles.
J16	Locates the point on a grid with 5-unit divisions when the point lies between the grid lines.
K03	Identifies the diagrammatic representation of a three- dimensional object after rotation.
Algebra
A02	Using properties of a balance, reasons to find an unknown weight (mass).
B12	Identifies the linear equation corresponding to a given verbal statement involving a variable.
D08	Solves for missing number in a proportion.
G04	Solves equation for missing number in a proportion.
H12	Selects the expression that represents a situation involving multiplication.
J17	Finds a missing y value in a table relating x and y values.
V04A	Given a sequence of diagrams growing in one-dimension and a partially completed table, finds the next two terms in the table.

Upper Quarter Benchmark Items

Fractions and Number Sense
A01	Finds 4/5 of a region divided into 10 equal parts.
A04	Solves a word problem by finding the missing term in a proportion.
B09	Given two equivalent fractions, identifies the pictorial representation showing they are equivalent.
B10	Selects the smallest of a set of numbers with differing numbers of decimal places.
D09	Selects the smallest fraction from a set of familiar fractions.
E03	Identifies the fraction of an hour representing a time interval.
F09	Identifies a decimal number given in thousandths between two decimal numbers given in hundredths.
F12	Identifies the interval containing the fraction that represents the shaded part of a circle.
G05	Selects a fraction representing the comparison of part to whole, given each of two parts in a word-problem setting.
I02	Solves a multi-step word problem involving multiplication of whole numbers by fractions.
I06	Writes a fraction less than a given fraction.
J12	Divides one fraction by another with unlike denominator.
J18	Uses a map scale to find the approximate distance between two towns.
K09	Adds three fractions with denominators less than 10.
L18	Subtracts fractions with unlike denominators.
N14	Selects a set of equivalent fractions.
N19	Shades squares in a rectangular grid to represent a given fraction.
O04	Rounds a four-place decimal to the nearest hundredth.
O09	Solves a one-step word problem involving division of a whole number by a unit fraction.
P14	Estimates the product of two whole numbers in a word problem.
Q05	Selects the statement that describes the effect of adding the same amount to both terms of a ratio.
Q06	Estimates the product of a multiple of 1000 and a two-digit number in a word problem involving knowledge of units of time.
Q09	Multiplies and adds fractions with different denominators in the correct order.
R15	Solves a multi-step word problem that involves dividing a quantity in a given ratio.
T04	Solves a word problem that involves multiplying a decimal in thousandth by a multiple of a hundred.
V01	Provides an example of a measure that would round to a given value.
V03	Determines the ratio of part to total in a word problem.
Measurement
A03	Given a length rounded to the nearest centimeter, identifies what the actual length could have been in centimeters to one decimal place.
C01	Compares volume by visualizing and counting cubes.
I07	Finds the area between two rectangles when one is inside the other and their sides are parallel.
M01	Reads the value indicated by an unlabeled tick mark on a circular scale.
N15	Identifies an angle of a given size in a diagram.
O06	Given the start time, and the duration of an event expressed as a fraction of an hour, determines the end time.
S02A	Finds a fraction of a given area of an irregular figure composed of squares of equal sides.
T03	Finds the area of a rectangle contained in a parallelogram of given dimensions.
Data Representation, Analysis, and Probability
F08	Understands independence in a probability setting.
H11	In a word problem, finds the missing number in a proportion.
I09	Given the set of possible outcomes expressed as fractions of all outcomes, recognizes that probability is associated with the size of a fraction.
K07	In a word problem, when given the possible number of outcomes and the probability of successful outcomes, solves for the number of successful outcomes.
L11	Determines the number of values on the horizontal axis of a line graph that correspond with a given value on the vertical axis.
N18	Identifies the number of successful outcomes of a simple experiment and calculates the probability of success.
O01	On a given graph, interpolates to find a value between graduations on one axis matching a given value on the other axis.
O05	In a word problem, when given the possible number of outcomes and the probability of successful outcomes, solves for the number of successful outcomes.
R09	Solves a word problem by extrapolating a graph of a non-linear relationship.
Geometry
A05	Identifies pairs of congruent triangles.
B11	Visualizes the arrangement of the faces of a cube given its net.
D07	Applies knowledge of symmetry to select the measure of an angle.
E02	Uses properties of congruent triangles to find the measure of an angle.
G03	Solves a problem involving adjacent and vertical angles.
J11	Identifies a false statement about the properties of rectangles.
M07	Uses knowledge of a straight angle to find the measure of an angle.
O03	Given two parallel lines cut by a transversal, selects a pair of supplementary angles.
O08	Selects the center of rotation when shown a diagram of a triangle and its image under a quarter turn.
R11	Determines the number of triangles of given dimensions needed to cover a given rectangle.
Algebra
C05	Finds a specified term in a sequence given the first three terms pictorially.
D10	Identifies algebraic equation (formula) corresponding to a verbal description involving a constant and two variables.
E05	Identifies the linear relationship between the first and second terms in a set of ordered pairs.
F11	Solves a two-step problem involving multiplication and division of whole numbers and fractions.
G06	Finds the value of an algebraic expression involving multiplication of negative integers.
H10	Identifies the linear equation that describes the relationship between two variables given a table of values.
L12	Translates a word problem into a short finite arithmetic sequence and sum the sequence.
L14	Identifies the linear equation that describes the relationship between two variables given a table of values.
L17	Solves a linear equation involving transposing.
N13	Evaluates a rational expression in one variable for a given value of the variable.
O07	Solves a linear equation involving parentheses.
P11	Selects a multiplicative expression for repeated addition.
Q02	Subtracts algebraic fractions with the same numeric denominator.
Q07	Selects the formula satisfied by the given values of the variables.
R12	Selects a simple, multiplicative expression in one variable that is positive for all negative values of that variable.
S01A	Given a sequence of diagrams growing in two dimensions and a partially completed table, finds the next two terms in the table.
V04B	Knowing the first five terms of a sequence growing in one dimension, finds the seventh term.

Top 10% Benchmark Items

Fractions and Number Sense
C04	Identifies the pair of numbers satisfying given conditions involving ordering integers, decimals, and common fractions.
F07	Solves a time-distance-rate problem that involves division of decimals and conversion of minutes to seconds.
J14	Identifies the correct position for the decimal point in the quotient in a division of a decimal written in hundredths by a decimal written in thousandths.
M06	Given the total number and the ratio of the two parts, finds the value of one part.
M08	Multiplies a two-place decimal by a three-place decimal.
N16	Solves multi-step problem with fractions requiring analysis of the verbal relations described.
N17	Solves a word problem involving multiplication of two-digit one-place decimals and subtraction of decimals.
O02	Finds the percent change given the original and the new quantities.
P15	Solves a word problem involving both addition and subtraction of familiar fractions.
P17	Writes a decimal expressed in hundredths as a fraction in lowest terms.
Q08	Orders a set of decimals of up to three decimal places.
R08	In a word problem, finds an average by dividing a decimal by a multiple of 100.
R14	Solves a two-step problem involving multiplication of a whole number by a fraction.
T02A	In a multi-step word problem, finds how many of each of two groups of different sizes are required to produce a given number.
Measurement
E06	Identifies the length of a rectangle given its perimeter and width.
F10	Recognizes that precision of measurement is related to the size of the unit of measurement.
I03	Applies knowledge of number of milliliters in a liter to solve a word problem.
J10	Finds the area between two rectangles when one is inside the other and their sides are parallel.
K05	Finds the perimeter of a square given that its area is a square number less than 150.
P12	Estimates the length of a curved piece of string adjacent to a ruler.
Q03	From a set of times expressed variously in days, hours, minutes, and seconds, determines which is least.
S02B	Finds the length of a side of a square, given that its area is a square number.
U02A	Uses computation with fractions to find the length and width of a rectangle and draws and labels that rectangle on a grid.
U02B	Given the dimensions of two rectangles, expresses the ratio of their areas.
U03	Finds the area of a triangle, on the same base and with the same height as a square, when the length of a side of the square is known.
Data Representation, Analysis, and Probability
G01	Reads data from a frequency table to solve a problem.
Geometry
I08	Given only the coordinates of two points on the line, selects the coordinates of a third point on that line.
K08	Uses properties of congruent triangles and the sum of the angles of a triangle to find the measure of an angle.
L16	Identifies the measure of an angle of a quadrilateral given the measures of the other three angles.
M05	Identifies the image of a triangle under a rotation about a point in the plane.
N12	Locates a point on a number line given its distance from two given points.
P10	Uses properties of similar triangles to find the length of a corresponding side.
Q10	Solves a problem involving measures of overlapping angles.
Algebra
K04	Solves a linear inequality involving a fraction.
L15	Uses proportion to find missing values in a table.
R10	Recognizes properties of operations on real numbers represented in symbolic form.
S01B	Knowing the first five terms of a sequence growing in one dimension, finds the seventh term.
T01	Solves a multi-step word problem in which there are two unknowns and displays the method of solution.
V04C	Given the initial terms in a sequence and, for example, the 50th term of that sequence, generalizes to find the next term.

Items Above the Top 10% Benchmark

Fractions and Number Sense
S03	Solves a word problem involving multiplication and subtraction of decimals.
T02B	Uses information in a word problem to determine numerator and denominator and writes the relevant common fraction.
U01	Estimates the total time in minutes for an event made up of a series of events, each given in minutes and seconds.
Measurement
P08	Finds the ratio of width to perimeter for a rectangle when given the ratio of length to width of a rectangle.
S02C	Finds the perimeter of a figure made up of squares with known length of sides.
Data Representation, Analysis, and Probability
V02	Selects relevant information from two advertisements to solve a complex word problem involving decimals.
Algebra
I01	Identifies what the variable represents in an equation for a given situation.
I04	Identifies numbers common to two different arithmetic sequences.
Q01	Selects an algebraic expression to answer a question about a set of linked verbal statements.
S01C	Generalizing from the first several terms of a sequence growing in two dimensions, explains a way to find a specified term, e.g. the 50th.

魅影直播 1999 is a project of the International Study Center
Boston College, Lynch School of Education