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MATHEMATICS K-10 – Grade Level Expectations
Kindergarten	Grade 1	Grade 2
NUMBER SENSE	NUMBER SENSE	NUMBER SENSE
Explore and use numbers (especially 0–10) through varied and multiple experiences, including:	Explore and use numbers (especially 0–20) through varied and multiple experiences, including:	Explore and use numbers (especially 0–100) through varied and multiple experiences, including:
number and numeration	number and numeration	number and numeration
§ establish a one-to-one correspondence in counting objects § determine the cardinal number of a set of objects less than 31 § when given three groups of objects (1–20), order them from smallest to largest § given two sets of objects, each less than five, determine how many in all § demonstrate an understanding of equal parts and fair sharing § recognize if amounts are the same or different	§ count forward and backward by ones to 100 § count sets of objects less than 100 using a variety of grouping strategies (twos, fives, tens) § read and write numerals to 100 § given three numerals between 1 and 100 order them from smallest to largest § identify the ordinal position of objects through tenth § create groupings that represent equal parts § recognize equal and unequal parts § use the equal symbol in an appropriate manner to represent two equivalent values	§ use physical models to demonstrate the relationship between ones, tens and 100s, and identify them appropriately as place values § count forward and backward by tens and hundreds to 1000 § read and write numerals to 1000 § use models to represent halves, thirds, and fourths of objects and sets of objects § compare amounts using the vocabulary “greater than,” “less than” and “equal to” § recognize and identify the relationships between parts and a whole (e.g., fourths means 4 equal parts) § use physical models and equations to demonstrate addition and subtraction
computation	computation	computation
§ use a variety of approaches, strategies, and manipulative materials to create and tell stories involving addition and subtraction as found in familiar settings § demonstrate the relationship between addition and subtraction situations when creating and telling stories § use mental math strategies to compose and decompose numbers through 10	§ explore addition and subtraction facts for numbers 0–10 § given two sets of objects, each less than twenty, determine sum or difference. § use physical models to demonstrate the relationship between addition and subtraction § create and use strategies for solving addition and subtraction basic facts (counting on, counting back, doubles, etc.) § use mental math strategies to compose and decompose numbers through 100	§ compute using addition and subtraction facts for numbers 0–10 and explore facts 0–20 § create and use strategies to solve basic addition and subtraction facts (doubles, doubles plus one, doubles plus two, and their reverses) § describe and compare strategies to solve addition and subtraction computation problems § add and subtract two-digit numbers § use physical models, diagrams, and/or acts out problems involving real life multiplication and division situations § use mental math strategies to compose and decompose numbers through 1000
estimation	estimation	estimation
§ estimate the number of objects in a set using comparative language (less than ten, more than ten, etc.) § use a known quantity to estimate an unknown quantity (sets of objects to 30) using a variety of strategies and approaches	§ estimate reasonable results when presented with an addition or subtraction situation § estimate using the language “about how many”	§ describe and justify reasonableness of an estimate to an addition or subtraction problem § use comparative language to determine the reasonableness of an answer
MEASUREMENT	MEASUREMENT	MEASUREMENT
attributes and dimensions	attributes and dimensions	attributes and dimensions
§ use comparative words to compare objects and events to determine which is heavier, longer, holds more, takes longer	§ identify tools for measuring (e.g. calendars, coins, clocks, rulers, etc.) § estimate and measure using non-standard units § order objects using length, capacity, weight § measure in meaningful situations in other disciplines with non-standard units	§ identify and use appropriate measurement tools § estimate and measure length, weight, capacity, time, and temperature using non-standard and standard units § measure to the nearest whole unit § make change from one dollar § explore area and perimeter of regular 2-D figures § recognize penny, nickel, dime, quarter and dollar and express value using cent notation
	approximation and precision	systems and tools
	§ recognize usefulness of estimation when presented with situations involving time and money § describe the passing of time including yesterday and tomorrow using days of the week and months of the year	§ select appropriate unit of measure for given objects or situations § use cents and dollar notation when relating values of coins, up to one dollar
GEOMETRIC SENSE	GEOMETRIC SENSE	GEOMETRIC SENSE
properties and relationships	properties and relationships	properties and relationships
§ identify shapes (squares, circles, rectangles, and triangles) in surroundings, combine shapes or objects to make larger shapes or objects § classify real world 3-D objects as a ball, box, or can shape § describe and compare figures using geometric and spatial vocabulary, such as corners, curves, inside, outside, right, left, below, and above	§ explore and classify 2-D and 3-D shapes and objects, investigate the results of combining and breaking down shapes § name and draw square, rectangle, circle, parallelogram § use informal geometric vocabulary to describe similarities and differences of physical objects and geometric figures presented in familiar settings	§ explore 2-D and 3-D shapes/objects (e.g. rectangles, prisms, spheres, cylinders and pyramids), investigate results of combining and breaking down shapes § sorts, classifies, and uses 2-D and 3-D geometric figures § recognize geometric shapes in the surrounding environment
		locations and transformations
		§ use manipulatives and drawings to describe geometric transformations (translations, reflections, and rotations) § identify and graph ordered pairs of whole numbers on a coordinate plane § recognize symmetrical and congruent figures and identify a line of symmetry § describe the location of letters or numbers on a coordinate grid in terms of horizontal and vertical positions
PROBABILITY AND STATISTICS	PROBABILITY AND STATISTICS	PROBABILITY AND STATISTICS
probability	statistics	probability
§ discriminate between impossible, probable, and certain events in a real world context § sort and classify data in order to draw conclusions in familiar situations	§ collect, organize, and interpret data using objects and bar graphs § discriminate between impossible, probable and certain events in a real world context	§ develop vocabulary using words like “most of ten,” “least of ten” § describe possible outcomes in a simple experiment where outcomes are not equally likely § recognize when data is being used to support a point of view
statistics	prediction and inference	statistics
§ use physical objects and/or pictures to build and discuss graphs in order to answer questions	§ collect, organize and interpret data using objects and pictographs	§ formulate questions for the purpose of gathering data § collect, organize, and interpret data using tables, bar graphs and pictographs § describe data using words like “most often” and “least often”
		prediction and inference
		§ perform and predict outcomes of simple experiments involving chance, record and discuss results § predict the likelihood of an event and perform simple experiments to record and discuss results § predict which event is more likely or less likely to occur in a real world context
ALGEBRAIC SENSE	ALGEBRAIC SENSE	ALGEBRAIC SENSE
patterns	patterns	patterns
§ recognize, copy and extend patterns using sounds, objects and symbols § recognize, analyze, make predictions with repetitive patterns § explore number patterns § sort and classify objects by common attributes	§ recognize, analyze, create and record repetitive patterns in order to solve problems and make predictions § introduce growth patterns § explore number patterns	§ recognize repetitive and growth patterns § explore number patterns § represent patterns symbolically § use symbols to describe equality
representations	operations	representations
§ use objects and numerals to show the meaning of equality and inequality § use manipulatives to solve equations involving addition and subtraction with sums through 10	§ use objects to solve a problem situation where addend is unknown § evaluate expressions with >, <, =, using a variety of strategies and physical models § use manipulatives to solve equations involving addition and subtraction with sums through 20	§ given pairs of numbers, orally describe the functional relationship § use pictures, symbols etc., to represent simple expressions
		operations
		§ complete number sentences using +, -, = § use manipulatives to solve equations involving multiplication and division
PROBLEM SOLVING	PROBLEM SOLVING	PROBLEM SOLVING
investigate situations	investigate situations	investigate situations
§ recognize and search for patterns in familiar situations, for example, find a simple A-B-A-B color pattern in a striped shirt	§ use a variety of strategies, such as act it out, draw a picture, or guess-check, to solve problems	§ use a variety of strategies and approaches, such as physical models, diagrams, act it out, to solve problems
formulate questions and define the problem	formulate questions and define the problem	formulate questions and define the problem
§ identify questions to be answered in familiar situations, for example, when shown a completed attendance graph, can ask questions like “How many boys are here today?”	§ define problems in familiar situations, for example, how many children can be on each of the three teams? § organize relevant information to solve a problem, for example, after surveying class about favorite ice cream flavors, can determine the most popular; identify irrelevant information	§ define problems in familiar situations, for example, how much time do we have before PE?
construct solutions	construct solutions	construct solutions
§ organize relevant information to solve a problem, for example, when asked how many more boys there are in class than girls, will arrange children in a way that helps answer the question § select appropriate tools for a given problem, such as cubes, calculator, pan balance	§ describe and justify strategies used to solve real life problems arising in the classroom § select appropriate tools to measure length, capacity, weight/mass, time, and temperature	§ organize relevant information to solve a problem, for example, make a Venn diagram to determine which of three recipes each classmate likes; identify missing information § select appropriate tools to measure length, mass, and capacity
REASONING	REASONING	REASONING
analyze information	analyze information	analyze information
§ identify likenesses and differences to sort and classify objects and events, focusing on one attribute § validate own thinking using models, for example, use a manipulative such as links to prove that one object is longer than another, and use appropriate models given choices	§ sort and classify objects and events according to one or more attributes § interpret and compare data in familiar settings to solve problems § validate own thinking using models and/or patterns, for example, use cubes to explain or justify method of solving a problem	§ sort and classify objects and events according to one or more attributes § interpret and compare information in familiar situations, for example, determine which day of the week was the hottest § validate own thinking using models and patterns, for example, use square tiles to illustrate the area of a rectangle; recognize relatedness of similar problems
predict results	predict results	predict results
§ predict results, for example, guess what color cube will most likely be drawn from a bag containing 2 red cubes and 1 blue cube	§ make and test conjectures based on collected data, for example, upon completing a survey about pets each classmate has, guess which pet is most popular and analyze the data to see if his/her guess was correct	§ make and test conjectures based on collected data, for example ,given a ba