Fourth Grade – Mathematics

Items at Low International Benchmark (400)
Number
M08_01 Subtracts a three-digit number from another three-digit
number.

M09_01 Adds a four-digit and a three-digit whole number.

M10_01 Identifies the number sentence that models a word problem
involving subtraction.

M11_04 Finds the missing number in a number sentence involving
multiplication.

M13_05 Solves a word problem involving addition of three-digit
whole numbers.

M14_01 Identifies a four-digit number given in words.

Geometric Shapes and Measures

M01_09 Identifies two triangles with the same size and shape in a
complex figure.

M07_09 Recognizes the inverse relationship between the size of a
unit shown in a figure and the number of units required to
cover an area.

M08_07 Identifies a pair of parallel lines.

M10_07A Given the position, gives the informal coordinates of the
position .

M10_07B Given the informal coordinates, determines the position.

Data Display

M08_12 Completes a table from given information by counting.

M09_12 Completes a bar graph that represents a table of data.

M14_12 Identifies the largest increase shown in a bar graph.

Items at Intermediate International Benchmark (475)
Number

M01_08 Solves a measurement word problem involving subtraction
of two-digit numbers.

M02_01 Identifies a set of two-digit numbers ordered from largest to
smallest.

M02_05 Subtracts a number with one decimal place from another
with one decimal place.

M04_01 Identifies a three-digit number described in units, 10s, and
100s.

M05_01 Identifies the appropriate operation to solve a word problem
involving multiplication.

M05_04A Extends entries in two tables according to numerical rules
described in a situation.

M06_01 Identifies the value of a digit in a four-digit number.

M09_05 Selects the expression that represents a situation involving
addition.

M10_06A Extends a given geometrical pattern to determine a
specified term.

M11_03 Generalizes from the first several terms of a numeric
sequence to select another number that is also in the
sequence.

M11_06 Extends a numeric sequence based on a geometric pattern.

M12_01 Identifies the rectangular model for a unit fraction.

M13_01A Selects appropriate information and uses it to solve a simple
proportion problem .

M14_02 Solves a word problem involving multiplication of one-digit
numbers.

M14_03 Identifies multiples of a given number.

Geometric Shapes and Measures

M04_06 Identifies an object with its line of symmetry shown.

M04_07 Draws a rectangle given two adjacent sides.

M06_08 Writes the names of three familiar geometrical shapes.

M07_06 Recognizes that area does not change when the parts of a
figure are rearranged.

M07_10 Recognizes the triangles in a set of polygons.

M09_10 Orders four angles by size.

M09_11 Identifies a pattern generated by quarter turns clockwise.

M10_08 Draws the line of symmetry on a symmetrical polygon.

M11_10 Locates a point on an informal coordinate grid and
identifies the moves to get there.

M13_06 Identifies a three-dimensional object given the pictorial
representation of its faces.

M14_06A Identifies the shape made by connecting specified dots on a
circle .

M14_06B Draws a specified geometrical shape by connecting dots on
a circle.

M14_06C Draws a specified geometrical shape by connecting dots on
a circle.

Data Display

M01_11 Identifies the pie chart that matches the information shown
in a table.

M03_10 Completes a two-by-two table to summarize information.

M04_11 Completes a bar graph from information given in a table.

M05_09 Uses information to identify the number of symbols needed
to complete a pictograph when the symbol represents more
than one.

M06_13 Identifies the bar graph that shows a given piece of
information.

M06_14 Identifies the bar chart that matches the information shown
in a pie chart.

M07_12 Identifies the pie chart that matches a given bar graph.

M10_11 Identifies information from a pie chart.

M10_12 Identifies the bar chart that matches the information shown
in a table.

M12_11 Interprets a bar chart to solve a problem.

M14_11 Interprets information in a table to solve a problem.

Items at High International Benchmark (550)
Number

M01_01 Solves a word problem involving division of a three-digit
number by a one-digit number.

M01_02 Determines the missing digit to give a specified difference
in a three-digit subtraction problem.

M01_05 Solves a multistep word problem involving time and
temperature.

M01_06 Solves a multistep word problem involving du ration of time .

M01_07 Solves a word problem involving conversion of metric units
of capacity.

M02_02 Identifies the operation needed to solve a problem involving
division.

M02_03 Multiplies 2 two-digit numbers.

M03_06 Identifies a number that satisfies a number sentence
involving division.

M04_04 Solves a word problem involving addition of two fractions
with the same denominator .

M04_05 Identifies the operation needed to solve a problem involving
division.

M05_02 Solves a word problem involving division of a three-digit
number by a one-digit number.

M05_07 Solves a multistep word problem involving addition and
multiplication of whole numbers.

M06_03 Shades half of a geometrical figure divided into four equal
parts.

M06_04 Given five different digits , determines the smallest possible
three-digit number.

M06_05 Writes a number between two consecutive whole numbers.

M07_01 Identifies the difference between two fractions with the
same denominator.

M07_03 Selects the two-place decimal closest to a given whole
number.

M07_04 Identifies the next term in a sequence of whole numbers
formed by doubling.

M07_05 Identifies a number sentence that represents a situation
involving division.

M07_07 Identifies the value of an unlabelled mark on a circular
scale.

M08_02 Identifies the whole number closest to a given multiple of a
hundred.

M09_06 Identifies the two-step rule for a linear relationship between
the first and second numbers in a set of ordered pairs of
numbers.

M09_07 Identifies the value of an unlabelled mark on a circular
scale.

M09_09 Identifies the appropriate operation to solve a word problem
involving division.

M10_02 Identifies the number that is a hundred more than a given
four-digit number.

M10_04 Identifies appropriately rounded numbers in a
multiplication situation.

M10_05 Identifies equivalent familiar fractions in a context.

M10_06B Extends a given geometrical pattern to find the value of a
specified term.

M11_02 Solves a multistep word problem involving halving,
doubling, and adding.

M11_08 Solves a word problem involving addition of time and
conversion between hours and minutes.

M12_02 Uses knowledge of place value to solve a problem involving
a five-digit number.

M12_04 Writes a fraction that represents a subset of a set of objects.

M12_05 Identifies the largest of a set of unit fractions.

M13_08 Solves a word problem involving measures and proportional
reasoning.

M14_04 Adds 2 two-place decimals.

M14_05 Follows a rule to complete a table.

Geometric Shapes and Measures

M02_07 Determines the perimeter of a rectangle given its
dimensions.

M02_08A Uses two specified geometric tiles to make a four-sided
figure.

M02_08B Uses two specified geometric tiles to make a six-sided
figure.

M02_08C Uses two specified geometric tiles to make a different sixsided
figure from one made previously.

M03_07 Determines the number of nonstandard units of area
needed to cover a figure.

M03_08B On a map drawn to scale, positions a building within a
range of distance from a specified point.

M03_09 Given a figure and the line of symmetry on a grid, draws
the reflection.

M04_09A States a property that two shapes have in common.

M04_09B States a property that two shapes do not have in common.

M06_07 Given a set of angles, identifies the right angle.

M06_09 Determines the number of cubes in a stack with some
hidden.

M06_10 Given the line of reflection, draws the reflection of a given
figure.

M06_11 Identifies the distance around a square given the length of
one side.

M08_10 Identifies a net of a cube.

M08_11 Identifies the area of a right triangle drawn on a grid.

M11_09 Draws an angle greater than 90°

M11_11 Identifies the figure in which a line of symmetry is shown.

M12_07 Identifies a pair of shapes which are not mirror images of
each other.

M14_07 Identifies the number of edges of a solid shown in a picture.

M14_08 Determines the perimeter of a figure made of squares.

Data Display

M02_10 Completes the scale so that a bar graph shows information
given in a table.

M02_11 Completes a bar graph to show a specified comparison.

M04_12 Reads a part symbol on a pictograph when the symbol
represents more than one.

M05_04B Reads and interprets data from two tables to answer a
question.

M05_04C Draws conclusions from data in two tables.

M08_13 Completes a bar graph from information given in a tally
chart.

M11_12 Interprets data from a bar graph to solve a problem.

M12_12 Recognizes the bar graph labeled appropriately to show
given information.

M12_13A Finds totals and decides which one is the least .

Items at Advanced International Benchmark (625)
Number

M01_03 Selects the appropriate information and uses it to solve a
multistep word problem involving whole numbers.

M01_04 Writes two-step rule for a linear relationship between pairs
of numbers.

M02_04 Identifies the fraction that is equivalent to the shaded
fraction of a rectangle.

M02_06 Solves a two-step word problem involving two-place
decimals.

M03_01 Solves a multistep word problem involving divisibility.

M03_02 Solves a problem involving proportional reasoning.

M03_03 Solves a multistep measurement problem involving
multiplication and subtraction.

M03_04 Writes a rule for a multiplicative relationship between
the first and second numbers in a set of ordered pairs of
numbers.

M03_05 Identifies the two-step rule used to describe the relationship
between adjacent terms in a sequence of numbers.

M04_02 Given a unit fraction, shows that fraction of a given set of
objects.

M04_03 Identifies a fraction equal to a given fraction.

M06_02 Solves a word problem involving division and rounding upthe remainder.

M06_06 Adds two familiar unit fractions to solve a word problem.

M07_08 Solves a multistep problem involving conversion between
hours and minutes.

M08_03 Identifies the smallest number from a set of one- and twoplace
decimals.

M08_04A Identifies the circular representation of a nonunit fraction.

M08_04B Explains why a chosen circular representation shows a given
nonunit fraction.

M08_05 Identifies the missing first number in a number sentence
involving subtraction.

M08_06 Identifies the two-step rule that relates the numbers in two
columns of a table.

M09_02 Identifies all the numbers in a given interval ending in a
given string of digits.

M09_03 Halves the amounts in a recipe involving whole numbers
and fractions.

M10_03 Finds all the factors of a multifactor number less than 20.

M11_01 Given a unit fraction, identifies a larger fraction with a
different denominator.

M11_05 Identifies the number that satisfies a number sentence
involving addition of two terms on each side.

M11_06C Generalizes from the first several terms of a numeric
sequence to find the tenth term.

M12_03 Estimates the quotient of a four-digit number divided by a
two-digit number.

M12_06 Solves a word problem involving proportional reasoning.

M13_01B Selects appropriate information and uses it to solve a
proportion problem.

M13_01C Selects appropriate information and uses it to solve a
multistep problem involving proportions.

M13_02 Selects appropriate information and uses it to solve a
proportion problem.

Geometric Shapes and Measures

M02_08D Uses three specified geometric tiles to make a seven-sided
figure.

M02_09 Identifies a shape rotated by a 90° turn.

M03_08A On a map drawn to scale, positions a park at a given
distance from a specified point.

M03_08C On a map drawn to scale, positions a building halfway
between two specified points.

M04_08 Calculates the area of a rectangle.

M05_06 Recognizes that the area does not change when a figure is
cut into parts and rearranged.

M05_08 Uses properties of rectangles and triangles to solve a
problem.

M07_11 Recognizes the net of a triangular prism.

M08_08 Uses knowledge about properties of rectangles to classify
statements as true or false.

M08_09 Solves a multistep word problem involving perimeter.

M09_08 Determines the area of a figure made up of squares and half
squares on a grid.

M10_09 Uses knowledge of two common solids to classify statements
about them as true or false.

M10_10 Matches a solid to its net.

M12_08 Determines the number of cubes in a given rectangular box.

M12_09 Identifies the area of an isosceles triangle drawn on a grid.

M12_10 Draws a line through a given point perpendicular to a given
line.

M13_07 Identifies the position of a shape after a half-turn rotation.

M14_09 Estimates the length of a curved line in nonstandard units.

Data Display

M01_10 Organizes data and completes a tally chart to represent it.

M04_13 Uses data from two different graph types to solve a problem.

M12_13B Draws and justifies a conclusion from data given in a table.

Items Above the Advanced International Benchmark (625)
Number

M05_03 Identifies the number that satisfies a number sentence
involving division of two terms on each side.

M05_05 Solves amultistep problem to find one of the two unknown
values.

M07_02 Subtracts a one-place decimal from a two-place decimal
presented horizontally.

M13_03 Selects the appropriate information and uses it to solve a
multistep problem involving two proportions.

Geometric Shapes and Measures

M04_10 Estimates a height using a nonstandard unit.

M06_12 Classifies polygons according to two given properties they
either have or do not have.

M11_07 Estimates the length of a curved line next to the middle of a
ruler.

M14_10 Draws all four lines of symmetry in a nonstandard shape.