Appendix 14C: TIMSS 2015 Eighth Grade Mathematics Item Descriptions Developed During the TIMSS 2015 Benchmarking Items at Low International Benchmark (400) Number M04_01 M07_01 Recognizes a 7-digit number given in words Evaluates the power of a whole number Data and Chance M01_13 M06_13 Uses information in a table to complete a bar graph Identifies the table that matches the information shown in a pictograph Items at Intermediate International Benchmark (475) Number M01_04 M02_01 M03_01 M05_01 M07_03 M07_04A M08_04 M09_01 M09_02 M10_01 M11_03 M11_04 M13_02A Identifies equivalent ratios Recognizes the commutative property Identifies the decimal number closest in size to a given fraction Identifies the divisor by moving the decimal point Uses knowledge of the whole being 100 percent to solve a simple word problem Completes a table of equivalent proportions Shades a percent of a figure Evaluates an expression involving negative whole numbers and parentheses Solves a word problem involving subtraction of negative numbers Solves a word problem involving subtraction of negative numbers Solves a two-step word problem involving whole numbers Determines what fraction of a 10 10 grid is shaded Solves a word problem involving addition of time METHODS AND PROCEDURES IN TIMSS 2015 14.27
Algebra M11_06 M12_08 M14_05 Evaluates the power of an expression given its value Uses values for a linear function to determine an extrapolated value Solves a linear equation in two-variables given the value of one variable Geometry M02_08 M04_09 M05_12 M12_09 M12_11 Identifies opposite faces of a cube given its net Recognizes congruent quadrilaterals Identifies a true statement based on the properties of parallel and perpendicular lines Identifies the reflection of a partly shaded shape Determines the total number of stacked unit cubes Data and Chance M05_15 M06_12A M07_12 M07_14 M08_14A M09_12 M09_14 M11_12A M11_12B M13_12 Given a table of percentages, selects the pie chart that could represent the given data Compares the chances of two outcomes shown pictorially Reads values from two line graphs to solve a problem Given a situation, judges the chance of an outcome as unlikely Estimates an expected value given an observed sample Finds and compares the unit prices of four objects Identifies the bar graph that matches the information shown in a table Reads data from a line graph Compares data from two line graphs to solve a problem Solves a problem given the chance of an outcome Items at High International Benchmark (550) Number M01_01 M01_06B M02_02 Solves a word problem involving multiplication of a fraction and a decimal Selects and combines information from two sources to solve a multi-step word problem (2 of 2 points) Solves a two-step word problem involving subtraction of whole numbers and multiplication of a fraction METHODS AND PROCEDURES IN TIMSS 2015 14.28
M02_03A M03_04 M03_05 M05_02 M05_03 M05_04 M06_01 M06_04 M07_04B M08_01 M08_03 M09_04 M09_05A M10_02 M10_04 M11_01 M11_02 M12_01 M12_02 M13_01 M13_03 M13_04 M14_01 M14_02 M14_04 Determines the percentage for a section of a pie chart Orders decimals with different numbers of decimal places Solves a proportion problem involving decimals Recognizes the fraction equivalent to a percentage Approximates the sum of five three-digit numbers to the nearest hundred Identifies the larger of two fractions with different numerators and different denominators and explains why it is larger Uses the distributive law to identify an expression equivalent to a given one Determines fractions equivalent to a given fraction Finds the unknown term in a proportion in a given situation Identifies an expression equivalent to a given division expression Finds the missing value in an addition problem with both fractions and decimals Given the two parts of a whole in a word problem, identifies the fraction which represents one part Solves a word problem involving multiplication and addition of whole numbers Identifies equivalent ratios Uses four different digits to write two two-digit numbers with the smallest product Solves a word problem involving ratios Identifies a prime number Solves a word problem involving a fraction of a whole Solves a word problem involving division of whole numbers with a remainder Identifies the representation of a fraction equivalent to a given representation of a fraction Understands a property of adding multiples Writes a decimal with three places as a fraction Identifies an expression equivalent to a given multiplicative expression Solves a two-step word problem involving subtraction of whole numbers and multiplication of a fraction Solves a word problem involving ratios and decimals METHODS AND PROCEDURES IN TIMSS 2015 14.29
Algebra M01_03 M01_05 M01_07 M01_08 M01_09 M03_06 M03_08 M03_09 M05_06 M05_07 M05_08 M05_11A M06_08A M07_07 M08_07 M08_08 M09_07 M09_08 M10_05 M12_06 M12_07 M13_06 M13_07A M14_07 Recognizes the distributive property in evaluating an algebraic expression Identifies the algebraic expression that represents a fraction of a variable Identifies the ordered pair of numbers that satisfies a given linear equation Identifies the equation that models a situation given in a word problem Identifies values of two variables, each satisfying a simple inequality Evaluates an algebraic expression involving a fraction Identifies the solution to an equation involving a square root Identifies the formula that represents a situation involving area Solves a simple linear equation in one variable with a mixed number solution Finds a missing term in a non-arithmetic and non-geometric number sequence Identifies the linear equation satisfied by two given values Adds two algebraic expressions and simplifies Extends a pattern to find the area of a square Finds the value of an algebraic expression involving parentheses and negative terms Identifies an algebraic expression that represents the perimeter of an irregular shape Determines a missing coordinate for a linear relationship given in a table Evaluates an algebraic expression involving fractions and integers Uses a given formula involving fractions to solve a word problem Identifies an expression that represents a situation Identifies an equation that models a situation Identifies an expression for the area of part of a geometric figure Identifies the equivalent algebraic expression involving exponents and multiplication Extends a given geometric pattern to find the value of the 10th term Identifies the true statement about a linear relationship given in a graph METHODS AND PROCEDURES IN TIMSS 2015 14.30
Geometry M01_11 M02_07 M03_11 M03_12 M05_13 M06_09 M06_10 M07_09 M08_10 M09_10 M09_11 M11_10 M13_11 M14_08A Identifies the number of remaining unit cubes Draws the reflection of a shape over a diagonal line on a grid Identifies a net of a rectangular solid Solves a problem involving angles of a triangle and parallel lines Uses the angle properties of triangles and rectangles to find a missing angle Uses the Pythagorean theorem to solve a word problem Solves a problem involving angles of a triangle Draws a symmetrical shape given half of it and its line of symmetry Finds the coordinates of a midpoint given two points in the Cartesian plane Identifies the value of an angle involving properties of corresponding and supplementary angles Draws an angle of a given measure on a square grid Solves a problem involving similar triangles Solves a problem involving angles of a triangle Solves a word problem involving the length around a hexagonal prism Data and Chance M01_14 M02_13 M05_16 M06_12B M07_02 M07_13 M10_13A M11_13 M11_14 Explains why a conclusion drawn from a given bar graph is incorrect Identifies the probability of an event Interpolates from a line graph to provide an estimated value Compares the chances of two outcomes Reads the value indicated by an unlabeled mark on a speedometer Identifies a possible description of a part of a time-speed graph Computes the mean of four given values Interprets data in a pictograph to solve a multi-step problem Justifies a conclusion resulting from comparing two distributions METHODS AND PROCEDURES IN TIMSS 2015 14.31
M12_13 M12_14 M13_13B M14_11 M14_13 Interprets a histogram to identify a proportion Draws a spinner that has given probabilities Uses and interprets data sets in pie charts to solve a problem involving percentages Evaluates information given by a time/distance graph Identifies the probability of an event Items at Advanced International Benchmark (625) Number M01_02 M01_06A M02_03B M03_02 M03_03 M04_02 M04_03 M04_04 M06_02 M06_03 M06_05 M08_02 M09_03 M09_05B M10_03 M11_05 M12_03 M12_04 Uses knowledge of place value to express a sum as a decimal Selects and combines information from two sources to solve a multi-step word problem (2 of 2 points) Determines the whole given the amount of a percentage Solves a non-routine problem involving whole numbers Reasons about divisibility in an algebraic expression Given the volume of a fraction of a container, determines the total volume for multiple containers of the same size Solves a word problem involving price per unit and explains reasoning Given four different containers, identifies the container with the greatest fraction filled Solves a word problem involving comparison of fractions and percentages and explains answer Solves a non-routine word problem involving reasoning with whole numbers (2 of 2 points) Reasons about fractional parts of a whole in a word problem and explains answer Solves a two-step word problem involving whole numbers Solves a two-step word problem involving percentages Solves a non-routine word problem involving whole numbers Determines the dimensions of a rectangle that is similar to a given rectangle Identifies a true statements about percentages of given numbers Completes a table of equivalent proportions and percentages (2 of 2 points) Solves a word problem involving ratios METHODS AND PROCEDURES IN TIMSS 2015 14.32
M13_02B M14_03 Solves a word problem involving percentages and elapsed time Identifies a percentage using a given ratio Algebra M01_10 M02_04 M02_05 M02_06 M04_05 M04_06 M04_08 M05_05 M05_09 M05_10 M05_11B M06_06 M06_07 M07_05 M07_06 M07_08A M07_08B M07_08C M08_06 M09_06 M09_09 M10_06 Uses a given formula to solve a word problem Solves a pair of simultaneous linear equations in two variables Computes values of a function given values of the variable Identifies a linear equation given the y-intercept Simplifies an algebraic expression Retrieves coordinate points from a graph of a function Constructs a linear equation for the perimeter of a triangle and solves for the length of one side Writes a rule for a multiplicative number pattern involving negative numbers Solves a proportion expressed algebraically Constructs and uses the solution of a linear equation to solve a word problem (2 of 2 points) Subtracts one algebraic expression from another and simplifies Identifies an equivalent equation Identifies a pair of simultaneous linear equations that model a given situation Identifies the equation of a line that passes through points shown on a graph Identifies the equation that models a situation involving distance, speed, and time Finds a specific term in a pattern presented numerically and geometrically Explains how to find a specific term in a pattern presented numerically and geometrically Expresses the general term algebraically in a pattern presented numerically and geometrically Identifies a line with positive slope Identifies an equivalent algebraic expression Demonstrates an understanding of slope by relating graphs and their equations Constructs a linear equation to represent a situation METHODS AND PROCEDURES IN TIMSS 2015 14.33
M10_08 M11_08 M13_05 M13_07B M13_08 M14_06 Constructs a linear equation for the perimeter of a rectangle and finds the area (2 of 2 points) Solves a pair of simultaneous linear equations Identifies an algebraic expression that represents the area of a given rectangle Gives a rule for the nth term of a geometric pattern Identifies the graph of a linear equation Identifies the slope of a line given its equation Geometry M01_12 M02_09 M04_10 M05_14 M06_11 M07_10 M07_11 M08_09 M08_12 M10_09 M10_10 M10_11 M12_10 M13_10 M14_08B Uses the Pythagorean theorem in finding the area of a triangle Identifies two different arrangements of trapezoids with the same perimeter Finds the coordinates of a vertex of a rectangle given the other three vertices Uses properties of similar triangles to identify equal angles Identifies the point equidistant from two given points in the Cartesian plane Uses the Pythagorean theorem in finding the perimeter of a trapezoid Identifies two shapes that make a square Uses properties of triangles and quadrilaterals to solve for an angle Draws a rectangle on square grid given area and perimeter (2 of 2 points) Estimates area of an irregular shape on a square grid Finds vertices of triangles created from trapezoids in the Cartesian plane (2 of 2 points) Uses properties of supplementary angles to solve for an angle Determines the number of faces of a regular solid with unit cubes removed Determines the surface area of a prism given its net Solves a word problem involving the lateral surface area of a hexagonal prism Data and Chance M01_15 M02_11 Uses understanding of average to solve a problem Identifies the statement that best describes a data set given in a table METHODS AND PROCEDURES IN TIMSS 2015 14.34
M02_12 M03_13 M03_14 M03_15 M04_12A M08_14B M10_12 M10_13B M12_12 M13_13A Estimates probability given an observed sample Explains why a data representation could be misleading Interprets data in a pie chart to solve a word problem Uses understanding of mean and range to solve a problem Calculates mean and median for two ordered lists of data (2 of 2 points) Compares observed and expected values Estimates the number of objects in a given probability sample Determines the change in a mean given changes in individual scores Solves a word problem involving averages Uses and interprets data sets in pie charts to solve a problem involving percentages Items Above the Advanced International Benchmark (625) Number M01_06C Compares results derived from two sources and provides a justification for the conclusion (2 of 2 points) Algebra M03_07 M04_07 M06_08B M08_05 M11_07 M12_05 Writes an expression for the area of part of a geometric figure Determines a collinear point given another point on the line and the slope Writes the algebraic expression for the nth term in a series Identifies the equivalent form of a linear inequality in one variable Identifies an algebraic expression involving parentheses and negative terms Identifies equivalent rational expressions Geometry M02_10 M03_10 M04_11 M08_11 M11_09 Explains how to find the area of an irregular shape on a grid (2 of 2 points) Solves a word problem using properties of similar triangles Explains why two shaded areas of overlapping congruent triangles are equal Solves for a missing side length given two similar triangles Draws all lines of symmetry on a regular polygon METHODS AND PROCEDURES IN TIMSS 2015 14.35
M11_11 M13_09 M14_09 M14_10 Solves a multi-step word problem involving ratios between volumes Identifies the image of a shape after rotation and reflection Determines the number of exposed faces for unit-cubes that make up a larger cube (2 of 2 points) Solves a word problem involving the Pythagorean theorem Data and Chance M04_13 M08_13 M09_13 Solves a multi-step problem involving probability Compares characteristics of two dot plots to justify a conclusion Explains why a data representation could be misleading METHODS AND PROCEDURES IN TIMSS 2015 14.36