Board Approved - April 24, 2003 For best printing results, click here (pdf).
MATHEMATICS K-10 – Grade Level Expectations
Grade 3	Grade 4	Grade 5
NUMBER SENSE	NUMBER SENSE	NUMBER SENSE
Understand and use numbers (0–999) through varied and multiple experiences, including:	Understand and use numbers (0–10,000) through varied and multiple experiences, including:	Understand and use numbers (0.01 to 1,000,000) through varied and multiple experiences, including:
number and numeration	number and numeration	number and numeration
§ use physical models, pictures, and symbols to demonstrate the relationship between ones, tens 100s, and 1000s § recognize and represent whole numbers in standard, expanded and word forms § use physical models and equations (symbols) to demonstrate the commutative property related to place value, for example , 100+4+60=100+60+4 § use physical models, pictures and symbols to order fractions with like denominators § explore decimals and fractional parts § represent parts of a whole and/or parts of a set using symbols § compare amounts using the symbols for “greater than,” “less than” and “equal to” § classify numbers as odd or even	§ identify, compare, and order numbers to 1,000,000 using standard form, expanded form and word form § identify, compare and order fractions § use objects, pictures or symbols to illustrate the meaning of commutative, associative and identify properties of addition and multiplication § demonstrate understanding of fractions with denominators of 2, 4, 8, 3, or 6	§ use objects, pictures or symbols to describe the meaning of fractions, decimals, and percents and the relationship between decimals and fractional parts § identify, compare, and order non-negative whole numbers § order fractions with fractions and decimals with decimals, e.g. which is bigger 3/8 or 2/3? § identify equivalent fractions and simplify fractions to lowest terms § use visual and physical models to describe prime and composite numbers, factors and multiples, and determine divisibility by 2, 5, and 10 § use objects, pictures, and symbols to illustrate equivalent ratios, e.g. 1:2 is equivalent to 4:8 § make comparisons between two part:part relationships, e.g. which makes a lighter paint – 2 white:3 blue or 4 white:5 blue?
computation	computation	computation
§ compute using addition and subtraction facts 1–20 § compute using multiplication facts using 1's, 2's, 5's, 10's and explore division § use mental math to multiply one-digit numbers by 10s and 100s § use place value materials to solve addition and subtraction problems containing multi-digit whole numbers through hundreds § compute to solve problems in realistic situations containing multi-digit numbers using the addition or subtraction strategy most appropriate to the situation (mental math strategies, paper and pencil, calculator) § use models, diagrams, and symbols to demonstrate the relationship between multiplication and division § create and use strategies to solve multiplication and division basic facts	§ compute using multiplication and division facts to 10 § estimate and solve realistic problems involving multiplication and division using an appropriate computation strategy § demonstrate meaning of multiplication and division using physical models to solve problems containing one- or two-digit factors § use physical models to solve problems involving a combination of any two whole number operations § write number sentences representing addition, subtraction, multiplication, and division situations § solve problems involving addition, subtraction, multiplication, and division of multi-digit whole numbers where the operations are not specified § divide by 10s and 100s	§ add, subtract, multiply and divide non-negative whole numbers up to 12 § add and subtract decimals, fractions, mixed numbers, and whole numbers 0 to 999 § use physical models to demonstrate and explain the meaning of multiplication of a fraction by a whole number and a fraction by a fraction § use mental math strategies, paper and pencil, calculator, or computer as appropriate for a given situation
estimation	estimation	estimation
§ describe and justify reasonableness of an estimate in a multiplication context § use estimation strategies (i.e. multiples of 10 and 100, rounding, front-end estimation, compatible numbers, clustering)	§ describe and justify reasonableness of an estimate in computation § use mental math strategies to approximate simple sums, differences, and products by using rounded numbers	§ determine and justify the reasonableness of answers by estimating prior to actual computation with whole numbers
MEASUREMENT	MEASUREMENT	MEASUREMENT
attributes and dimensions	attributes and dimensions	attributes and dimensions
§ use language and symbols to compare attributes of perimeter and area § determine area and perimeter of irregular 2-D figures § use physical models to determine volume or rectangular solids	§ select an appropriate type of unit for measuring area, perimeter and volume § use language and symbols to compare attributes of perimeter, area, and volume § solve problems involving measurement of area, perimeter, length, weight, time, and temperature when given diagrams or objects § compare objects using attributes of perimeter, area and volume	§ compare and contrast perimeter, area and volume for a variety of shapes § measure elapsed time and duration § explore and recognize the relationship between area and perimeter § measure objects directly and apply procedures for determining perimeter of polygons and area of rectangles
approximation and precision	approximation and precision	approximation and precision
§ understand the benefits of using standard units of measurement § estimate and measure using standard units § describe and justify reasonableness of an estimate involving length, weight, area, time, and temperature § use physical models to estimate volume of rectangular solids	§ determine and justify whether exact or approximate measures are needed when given a realistic situation § estimate to predict and determine when measurements are reasonable	§ use estimation to obtain reasonable approximations of linear measurements
systems and tools	systems and tools	systems and tools
§ measure to the nearest whole and common fractional parts of standard units when given a realistic situation § explore how to use measurement tools § select appropriate standard units of measurement for given objects or situations § tell time using analog and digital clock displays	§ know approximate size of basic standard units (U.S. and metric) and make reasonable estimates based on approximations § identify application uses for various measurements § use a ruler, tape measure, scale, and thermometer to measure accurately § use a clock to tell standard and international time to the minute	§ chose the appropriate standard unit and tool and measure objects directly § choose standard units of measure yielding the most appropriate measurement § explain the advantages of standard units of measure § make conversions within the U.S. Customary System and within the Metric System (length, mass/weight, volume)
GEOMETRIC SENSE	GEOMETRIC SENSE	GEOMETRIC SENSE
properties and relationships	properties and relationships	properties and relationships
§ identify and describe attributes of 2-D and 3-D geometrical figures using appropriate vocabulary § identify and describe regular polygons § classify real world objects as containing squares, rectangles, triangles, circles, cubes, rectangular solids, spheres, cylinders, or pyramids § construct models of 3-D shapes	§ identify and describe irregular polygons § identify and describe attributes of 2-D and 3-D geometric figures using appropriate adjectives such as parallel, symmetric, congruent, similar, and perpendicular § draw or create 2-D geometric figures using appropriate tools, for example, toothpicks to create 2-D shapes § identify geometric shapes in the surrounding environment	§ identify and describe properties of geometric figures (ray, angle, line segment, parallel, symmetric, perpendicular, similar, and congruent) and find examples in the physical world § identify and draw multiple lines of symmetry § build and record similar and congruent figures § construct geometric figures using a variety of tools
locations and transformations	locations and transformations	locations and transformations
§ identify, describe, and compare symmetrical congruent and similar figures § explore relative size, direction, and position in space § predict and verify transformations on a geometric figure (translations, reflections, and rotations) § describe the location of figures on a coordinate plane using ordered pairs	§ describe the relative position of figures located on a coordinate plane § identify, describe and compare symmetrical, congruent, and similar figures § predict and verify transformations on a geometric figure (translations, reflections, and rotations)	§ describe the location of points on coordinate grids in first quadrant § identify simple transformations using combinations of translations, reflections, or rotations
PROBABILITY AND STATISTICS	PROBABILITY AND STATISTICS	PROBABILITY AND STATISTICS
probability	probability	probability
§ places events in the order they would likely occur § list possible outcomes of a simple probability experiment § conduct experiments to determine the probability of events	§ place events in the order they would likely occur § use organized counting to determine the number of possible outcomes of an event § list all possible outcomes of a simple probability experiment § explain why some outcomes are more or less likely to happen than others	§ prepare and organize displays of all possible results for a given probability experiment § use and describe strategies for determining the probability of an event
statistics	statistics	statistics
§ collect data in an organized way § formulate questions § describe measures of central tendency using words like “middle” and “most often” § pose questions from data and choose and explain one type of graph over another § describe pictographs, bar graphs and line graphs and how they communicate solutions to problems	§ identify or describe an appropriate method for collecting data § describe measures of central tendency using mean, median, and mode § pose simple questions and hypotheses, collect data, and communicate results using graphs or tables supported by written or oral explanations	§ identify a random sample taken from a described population § differentiate between random and non-random samples § organize and display data using frequency tables § identify outliers in a set of data § describe mean, median, mode, and range for simple data
prediction and inference	prediction and inference	prediction and inference
§ use data to build an argument or point of view § predict and verify likelihood of occurrence using physical objects such as number cubes or coins § determine if games are fair or unfair	§ describe how data can be used to support an argument § make inferences based on experimental results using coins, spinners, number cubes, etc.	§ carry out experiments to determine probabilities and compare predictions to experimental results § ask questions and collect data from specific samples and infer data to the population § make inferences and note trends on data collected from bar graphs and line graphs
ALGEBRAIC SENSE	ALGEBRAIC SENSE	ALGEBRAIC SENSE
patterns	patterns	patterns
§ analyze, extend, and find a rule for numeric and geometric patterns when given manipulatives or pictorial displays § recognize patterns involved in a variety of estimation and computation strategies	§ create, analyze and extend number patterns using words, tables and graphs § investigate patterns using 100's chart to extend understanding of numbers § recognize and create sequential number patterns and generate rules for them	§ create and extend number patterns that may involve a combination of addition, subtraction, and multiplication using words, tables and graphs § describe patterns using rules, tables, graphs and charts § recognize number patterns and sequences § use variables to describe patterns and sequences
representations