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Mathematics

Grade Level Benchmarks

Fourth Grade Benchmarks

Number and Operations Standard
E	Develop understanding of decimal place value
E	Develop understanding of fractions as parts of unit wholes, parts of collections, as
	locations on number lines, and as divisions of whole numbers
E	Recognize and generate equivalent forms of commonly used fractions, decimals, and
	percents
E	Use relationships between operations to solve problems (e.r. ?+28=54 can be solved
	using subtraction ?x23=253 can be solved using division)
T	Understand various meanings of multiplication and division of whole numbers
T	Understand the effects of multiplying and dividing whole numbers
T	Use a variety of methods to compute, including using objects, mental computation,
	estimation and paper and pencil
T	Develop and use strategies for whole-number multiplication and division
T	Use calculators appropriately to compute, check calculations, and aid in processing
	large amounts of data
T	Judge the reasonableness of numerical computations
T	Develop fluency with single-digit multiplication and division facts
R	Develop understanding of whole number place value
R	Compose and decompose numbers in flexible ways (33 can be thought of as 30+3 or
	20+13, or 3x11, depending on the situation)
R	Work informally with simple fractions (1/2. 1/4. Etc.)
Algebra Standard
E	Represent and analyze patterns and functions using words, tables, and graphs
E	Use  mathematical models to make predictions
E	Use tables, graphs, and equations to draw conclusions about real-world situations
E	Use commutative, associative and distributive properties to compute with whole numbers
E	Represent the idea of a variable as an unknown quantity using a letter or a symbol
T	Identify, describe, extend, and make generalizations about geometric and numeric
	patterns
T	Identify commutative and associative properties of addition and multiplication
R	Describe quantitative change, such as a student's growing two inches in one year
Geometry Standard
E	Develop definitions of types of shapes (triangles, rectangles, squares, etc.)
E	Identify and describe line and rotational symmetry in two- and three- dimensional shapes
T	Informally classify two- and three- dimensional shapes according to their properties
	(how is a rectangle different from a square, etc.)
T	Make and use a coordinate system to specify locations and to describe paths (grids)
T	Find the distance between points along horizontal and vertical lines of a coordinate
	system
T	Relate ideas in geometry to ideas in number and measurement
T	Build and draw geometric shapes
T	Predict and describe the results of sliding, flipping, and turning two-dimensional objects
R	Use  more formal language to describe attributes and parts of two- and three-
	dimensional shapes (area, perimeter, angles, sides, base, height, parallel,
	perpendicular, etc.)
R	Recognize and apply slides, flips, and turns to two-dimensional objects
Measurement Standard
E	Understand angle size and the units used to measure it
E	Use appropriate tools to measure angles
E	Develop strategies for estimating perimeters and areas of irregular shapes
T	Understand volume and the units used to measure it (customary and metric)
T	Understand weight and the units used to measure it (customary and metric)
T	Use appropriate tools to measure volume
T	Use appropriate tools to measure weight
T	Use appropriate tools to measure temperature
T	Develop, understand, and use formulas to find the areas and perimeters of rectangles
	and squares
R	Select appropriate tools for the attribute being measured
R	Understand length and the units used to measure it (customary and metric)
R	Understand area and the units used to measure it (customary and metric)
R	Measure area with multiple copies of units of the same size
R	Use appropriate tools to measure length
R	Use appropriate tools to measure time
Data Analysis and Probability Standard
E	Predict the probability of outcomes of simple experiments and test the predictions
E	Understand that the measure of likelihood of an event can be represented by a number
	from 0 to 1
T	Collect data using observations, surveys, and experiments
T	Represent data using tables and graphs such as line plots, bar graphs and line graphs
T	Describe events as likely or unlikely and discuss the degree of likelihood using such
	words as certain, equally likely, and impossible
R	Describe parts of the data and the set of data as a whole to determine what the data
	show
R	Describe the shape and important features of a set of data

Fifth Grade Benchmarks

Number and Operations Standard
E	Use visual models, benchmarks, and equivalent forms to add and subtract commonly
	used fractions and decimals
E	Judge the size of fractions using models, benchmarks, and equivalent forms
E	Work flexibly with fractions, decimals, and percents to solve problems
E	Use exponents and scientific notation
E	Use factors, multiples, and prime factorization to solve problems
T	Use relationships between operations to solve problems (i.e. ? + 28=54 can be solved
	using subtraction, ? X 23 = 253 can be solved using division)
T	Use a variety of methods to compute, including using objects, mental computation,
	estimation, and paper and pencil
T	Use calculators appropriately to compute, check calculations, and aid in processing
	large amounts of data
T	Develop understanding of decimal place value
T	Develop understanding of fractions as parts of unit wholes, parts of collections, as
	locations on number lines, and as divisions of whole numbers
T	Recognize and generate equivalent forms of commonly used fractions, decimals, and
	percents
T	Judge the reasonableness of numerical computations