Grade 3 Competency

· Accurately adds and subtracts whole numbers, up to and including four digits (1.3.7)

· Recognizes, describes, and illustrates the concepts of multiplication and division with whole numbers (repeating addition and subtraction, arrays and partitioning.) (1.3.4)

· Multiplies pairs of multiples of 10, and 100

· Knows the multiplication facts through the 10’s table

· Accurately adds and subtracts whole numbers, multiplies two-digit by one-digit numbers and divides by one-digit numbers (1.4.7)

· Multiplies, uses repeated addition, counts by multiples, combines things that come in groups, makes arrays, area models, computes simple rates

· Divides, puts things into groups, shares equally, calculates simple rates

· Uses simple concepts of negative numbers

· Recognizes order of operations with parenthesis (1.4.4)

· Accurately multiplies whole numbers 2 digit by three digit and divides wholes numbers by up to 2 digits (1.5.7)

· Recognizes and applies order of operations with and without parenthesis (1.5.9)

§ Demonstrates conceptual understanding of whole numbers through models, explanations, and different representations of the same number. (1.4.1)

§ Demonstrates a number sense, etc. i.e. writes number words and dictated 3,4,5 digit numbers

· Uses knowledge about ones, tens, hundreds, and thousands to figure out answers to addition, subtraction, and multiplication tasks

· Begins to analyze problem situations and contexts in order to figure out when to add, subtract, multiply and divide

· Uses strategies to analyze problem solving situations

· Recognizes and applies the commutative and associative properties with addition, and the inverse relationship between and subtraction with whole numbers (1.3.5)

· Demonstrates conceptual understanding of whole numbers through models, explanations, and different representations of the same number. (1.4.1)

· Counts 1, 10, 100, or 1,000 more than or less than a given number

· Analyzes problem situations and contexts in order to figure out when to add, subtract, multiply and divide

· Solves arithmetic problems by relating addition, subtraction, multiplication ,and division to one another

· Uses knowledge about ones, tens, hundreds, and thousands to figure out answers to addition, subtraction,  multiplication, and division tasks

· Recognizes and applies the commutative, associative, distributive, identity and inverse properties among the four operations with whole numbers (1.4.5)

§ Understands and uses properties of operations  such as commutative, associative, distributive, and identity with whole numbers (1.5.5)

· Uses the inverse operations to determine unknown quantities and equations with whole numbers (1.5.5)

· Understand various meanings of multiplication and division

·   Understand the effects  of multiplying and dividing whole numbers

·   Identifies and uses relationships between operations to solve problems

· Describe number relationships through counting, comparing, estimating, ordering and grouping and patterning whole numbers through 1,000 (1.4.2)

· Mentally adds and subtracts whole numbers through 100; rounds and estimates to evaluate the reasonableness of numbers of results for addition and subtraction with whole numbers (1.3.8)

· Demonstrates an understanding of the use of estimation in appropriate situations including approximation, rounding off, making reasonable landmarks numbers within the range of tens, hundreds, and thousands

· Describe number relationships through counting, comparing, estimating, ordering and grouping and patterning whole numbers through 1,000,000 (1.4.2)

· Mentally adds and subtracts whole numbers and multiplies two-digit by one-digit whole numbers, rounds and estimates to evaluate the reasonableness of numbers of results of the four operations with whole numbers (1.4.8)

· Describe number relationships through counting, comparing, estimating, ordering and grouping and patterning whole numbers, whole number powers of ten, integers, fractions and decimals to the thousandths place. (1.5.2)

· Recognize equivalent representation for the same number

·   Explore numbers less than zero by extending the number line and through familiar applications

·   Mentally adds and subtracts whole numbers and decimals to the hundredths place, multiplies with whole numbers, rounds and estimates to evaluate the reasonableness of numbers of results of the four operations with whole numbers (1.5.8)

· Demonstrates conceptual understanding of fractions through models, explanations, and different representations of the same number. (1.3.1)

· Develops an understanding of fractions as simple parts of wholes, fractional parts of a group/collection

· Develops an understanding of fractions in an linear situation

· Uses drawing diagrams or models to show what the numerator and denominator mean

· Describes number relationships through counting, comparing, estimating, ordering and grouping and patterning of fractions of  halves, fourths, thirds, sixths, eighths, and twelfths (1.3.2)

· Uses proportional reasoning with simple ratios

· Identifies the whole unit in relation to its fraction 

· Adds and subtracts fractions using concrete or pictorial representations (1.3.7)

· Demonstrates conceptual understanding of fractions (improper and mixed numbers) through models, explanations, and different representations of the same number. (1.4.1)

· Finds simples parts of wholes

· Uses drawings, diagrams, or models to show what the denominator and numerator means

· Uses proportional; reasoning and simples ratios

· Describes number relationships through counting, comparing, estimating, ordering and grouping and patterning of fractions of tenths, halves, thirds, fourths, sixths, eighths, and twelfths (1.4.2)

·  Recognizes the place of fractions on the number line

· Recognizes, describes, and illustrates the concepts of addition and subtraction of fractions with like denominators (1.4.4)

· Recognizes simple fractions as instructions to divide,

· Adds and subtracts fractions with like denominators and expresses the answer in simplest form (1.4.7)

§ Develops conceptual understanding 0f fractions through models, explanations, and different representations of the same number. (1.5.1)

§ Develop understanding of fractions  as locations on number lines and as division of whole numbers

· Use models benchmarks and equivalent forms to judge the size of fractions 

· Recognize and generate equivalent forms of commonly used fractions, decimals, and percent

·   recognize and use common fraction, decimal, and percent equivalents

·   Recognize, describe, and illustrate the concepts of addition and subtraction of fractions. (1.5.4)

·   use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions

·   Adds and subtracts fractions with unlike denominators (1.5.7)

· Develops the whole unit in relationship to its part in tenths, and hundredths

· Develops an awareness of relationships among simple fractions and decimal fractions, and percentages

· Describe number relationships through counting, comparing, estimating, ordering and grouping and patterning decimals in the context of money (1.3.2)

· Accurately adds and subtracts decimals in the context of money (1.3.7)

· Demonstrates conceptual understanding of decimals through models, explanations, and different representations of the same number. (1.4.1)

· Recognizes the whole in relationship to tenths, hundredths, and thousandths

· Describe number relationships through counting, comparing, estimating, ordering and grouping and patterning decimals to the hundredths place (1.4.2)

· Recognizes relationships among simple fractions, decimal fractions, and percents

· Accurately multiplies decimals to the hundredths place (1.4.7)

· Adds, subtracts, multiplies, and divides money amounts

§ Develops conceptual understanding of decimals and benchmark percents through models, explanations, and different representations of the same number. (1.5.1)

§ Develop understanding of decimals as locations on number lines and as division of whole numbers

· Use models benchmarks and equivalent forms to judge the size of decimals and percents

· Develop strategies for recognizing the value of fractions and decimals and for comparing them using a variety of models and of bench marks, such as 1/2 or .5

·   Recognize, describe, and illustrate the concepts of addition and subtraction of decimals (1.5.4)

·   Use visual models, benchmarks, and equivalent forms to add and subtract commonly used  decimals (1.5.1)

·   Accurately multiplies decimals to the hundredths place (1.5.7)

· Finds the total values of coin combinations

· Estimates and compares amounts

· Writes given numbers as fractions and decimals greater than one

· Reads and writes 1 and 2 place decimals greater than 1

· Extends decimals to one hundreths

· Compares up to 5 digits

· Connects ideas of quantities to the real world

· Recognizes, describes, and illustrates odd and even numbers (1.3.3)

· Finds, identifies and sorts numbers by their properties

· Uses inequality symbols (<,>)

· Finds, identifies, and sorts numbers by their properties

· Describes, illustrates and identifies factors and multiples (1.4.3)

· Uses inequality symbols (<,>)

· Recognizes and applies the concepts of prime and composite numbers, divisibility and remainders (1.5.3)

· Understands relationships among factors, multiples, divisors, and products

· Develops strategies for finding factors and multiples, least common multiples, and greatest common factors

· Becomes fluent with factor and multiple

relationships

· Classifies numbers according to their factors

· Recognizes and use the fact that every whole number can be written in exactly one way as a product of primes

· Connects ideas of quantities to the real world

  uses inequalities to compare greater and less

than equations

· Properties as in odd, even, multiples

· Properties as in odd, even, multiples, factors

· connects ideas of quantities to the real world

· Identifies attributes of three- dimensional shapes and develop vocabulary to describe attributes

· Trace faces of solids (cubes, rectangular prisms) to form two dimensional views

· Compares attributes of  3- dimensional shapes and develop vocabulary to describes the attributes

· Uses nets (two-dimensional pattern) to determine which solids can be created.

· Creates nets from a three-dimensional solid.

· Analyzes three dimensional shapes from two dimensional perspectives; draws two dimensional sketches of three dimensional object that preserve significant features

· Uses coordinate systems to specify and compare locations (2.3.3)

· Describes location and movement using common language and geometric vocabulary

· Uses coordinate systems, such as maps, to describe, name and interpret direction and relative positions in space. (2.4.3)

· Makes and uses coordinate system to specify locations and to describes paths

· Describes location and movement using common language and geometric vocabulary

· Plots positions on a coordinate system and describe the distance between the points horizontally and vertically (2.5.3)

· Makes and uses coordinate system to specify locations and to describes paths

· Describes location and movement using common language and geometric vocabulary

· Uses properties and attributes (number of sides, number of angles, length of sides) to identify, describe, and distinguish among triangles, squares, rectangles, rhombi, hexagons, and circles (2.3.1)

· Uses properties and attributes to identify, describe and create three-dimensional shapes ( cubes, rectangular prisms, triangular prisms) (2.3.2)

· Develop definitions of classes of shape and describe the attributes of polygons such as triangles, squares…

· Creates an awareness of symmetry and congruence with simple two-dimensional shapes

· Uses properties and attributes (number of sides, number of angles, length of sides, lines of symmetry, parallelism, and angles relative to 90 ) to identify, describe, and distinguish among polygons (2.4.1)

· Understands and uses vocabulary and notation for line segments, lines and rays

· Understands properties of angles, triangles, and polygons

· Classifies quadrilaterals

· Understands the concept of parallel, polygon, regular polygons, concave and convex

· Explores congruency and similarity

·  Uses properties and attributes to identify, describe and create three-dimensional shapes (cylinders, spheres, pyramids, and cones) (2.4.2)

· Identifies, compares, and analyzes attributes of 2- and 3- dimensional shapes and develops a vocabulary of their attributes

· Explores congruency and similarity

· Creates geometric constructions using appropriate tools

· Uses properties and attributes of angles (right, acute, obtuse) and sides (number of sides, number of angles, length of sides for regular and irregular polygons, lines of symmetry, parallelism) to identify, describe, classify and distinguish among the different types of triangles and quadrilaterals (2.5.1)

· Applies the property of symmetry to identify, classify, and distinguish among three dimensional shapes (rectangular prisms, cubes, triangular prisms)

· Properties by the number of faces, edges, points, angles,

· Uses symmetry sing concrete objects

· Polygons- triangles, quadrilaterals and quadrangles, parallelograms

· Constructs concentric circles, regular hexagons, equilateral triangles inscribed in a circles using a compass and straightedge

· Demonstrates and applies symmetry, congruency and similarity using transformations (flips, slides, and rotations) and the properties of size and shape of polygons (2.3.3)

· Predicts and describes the results of sliding, flipping, and turning two-dimensional shapes

· Forms angles by making turns 1/4, 1/2, or 3/4 turns

· Investigates the results of subdividing, combining, and transforming shapes

· Demonstrates and applies symmetry, congruency and similarity using transformations (flips, slides, and rotations) and the properties of size and shape of polygons (2.4.3)

· Identifies and builds a three dimensional object from two dimensional representations of that object

· Predicts and describes the results of sliding, flipping, and turning two-dimensional shapes

· Describes  line symmetry in two- and three- dimensional objects

· Builds a two- dimensional objects from a three-dimensional object

· Investigates the results of subdividing, combining, and transforming shapes

· Demonstrates and applies symmetry, congruency and similarity using the results of combining and subdividing shapes and transformations(flips, slides and rotations) (2.5.3)

· Identifies similar and congruent shapes and use transformations in the coordinate plane, i.e., translations, rotations, and reflections.

· Predicts and the results of sliding, flipping, and turning two- dimensional shapes

· Identifies and describes line and rotational symmetry in two- and three- dimensional shapes and designs

· Recognizes geometric patterns as tesselation and sequence of shapes

· Determine the perimeter of polygons, the area of rectangles and the volume of rectangular prism/cubes using a variety of models and manpulatives, and estimate the perimeter and area of shapes (2.3.4)

· Understands such attributes as length, weight and area

· Develops a sense of the unit (e.g. length, area) through estimation

· Makes comparisons and describes change qualitatively and quantitatively

· Determine the perimeter of polygons, the area of rectangles and the volume of rectangular prism/cubes and estimate the perimeter and area of shapes (2.4.4)

· Understands the attributes of length, capacity, weight, area

· Selects and uses  benchmarks to estimates measurements

· Creates and understanding of formulas to find the area of rectangles and related triangles and parallelograms

· Determine perimeter, area, surface area and volume of two-dimensional and three-dimensional geometric shapes using models and formulas. (2.5.4)

· Understands such attributes as length, area, weight, volume, and the size of angle and selects the appropriate type of unit for measuring each attribute

· Selects and uses  benchmarks to estimates measurements

· Uses formulas to find the area of rectangles and related triangles and parallelograms

· Creates an awareness of the concept of perimeter, and areas a rectangle and other irregular shapes

· Selects and uses units, formal and informal as appropriate for estimating and measuring quantities such as weight, length, area, volume and time

· Develops strategies for estimating the perimeter, and areas of rectangles and irregular shapes

· Explores what happens to measurements of a two-dimensional shape such as its perimeter and area when the shape is changed in some way

· Develops strategies for estimating the perimeter, areas, volumes of irregular shapes

· Develops strategies to determine the surface areas and volumes of rectangular shapes

· Selects and uses appropriate tools and uses (both customary and metric) to measure length, time, capacity, mass/weight and temperature (2.3.5)

· Identifies the attributes of length, capacity (volume) weight, area and time

· Uses the ruler correctly for inches and centimeters

· Selects and uses an appropriate unit of time

· Computes time in hours and minutes

· Selects and uses appropriate tools and uses (both customary and metric) to measure length, time, capacity, mass/weight and temperature (2.4.5)

· Selects and uses appropriate units and tools for the attributes being measured

· Uses repetition of a single unit to measure something larger that the unit

· Selects and uses an appropriate unit of time

· Computes time in hours and minutes

· Selects and uses appropriate tools and uses (both customary and metric) to measure length, time, capacity, mass/weight and temperature and degrees of angles (2.5.5)

· Understands the need for measuring with standard units and becomes familiar with standard units in customary and metric systems

· Selects and uses benchmarks to estimate measurements

· Uses repetition of a single unit to measure something larger than the unit

· Uses tools to measure

· Develops common referents for measures to make comparisons and estimates

Tells time to  5-minute intervals

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-Uses ruler, tape measure meter/yardstick correctly

· Makes simple conversions within systems (2.3.5)

· Carries out simple unit conversions such as inches to feet, centimeters to meters

· Makes simple conversions within systems (2.4.5)

·   Makes simple conversions within systems (2.5.5)

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· Analyzes, describes, extends, creates and finds missing parts of numeric and non-numeric patterns (4.3.1)

· Describes geometric and numeric patterns

· Identifies how both repeating and growing are generated

· Analyzes, describes, extends, creates and finds missing parts of linear numeric patterns, and geometric patterns, and determines a specific term in the sequence (4.4.1)

· Evaluates simple linear algebraic expressions using whole numbers (4.4.5)

·   Describes and extends generalizations about geometric and numeric patterns

·   Determines rules for a given or extended pattern

·   Identifies how both repeating and growing patterns are generated

· Analyzes , extends, creates,, and finds missing parts of numeric and geometric patterns and represents numeric patterns with models, tables, graphs, and rules, (4.5.1)

· Evaluates simple linear algebraic expressions using whole numbers and decimals (4.4.5)

· Describes, extends, and makes generalizations about geometric and numeric patterns

· Represents and analyzes patterns and functions, using words, tables, and graphs

§ Uses “Frames and Arrows” to determine addition and subtraction patterns

· Recognizes an awareness of non-linear patterns (growing patterns)

· Recognizes patterns  of successive square products

· Analyzes, describes, extends, creates and finds missing parts of non-linear numeric patterns, and geometric patterns, and determines a specific term in the sequence (4.4.1)

· Describes an awareness of non-linear patterns (growing patterns)

· Describes patterns  of successive square products

· Describes, extends, and makes generalizations about geometric and numeric patterns

· Represents and analyzes patterns and functions, using words, tables, and graphs

-Uses arrays to investigate square numbers

· Demonstrates the relationship between quantities by using the equal sign or the greater than/less than symbols (4.3.2)

· Investigates how a change in one variable relates to a change in a second variable

· Demonstrates with models that two simple linear expressions are equal (4.4.2)

· Investigates how a change in one variable relates to a change in a second in a second variable

· Investigates and describes a constant rate of change in set of data (4.4.3)

· Demonstrates that two linear expressions are equal for a given set of replacement values (4.5.2)

·  Investigates and describes how change in one variable relates to change in a second variable, including situations with constant or varying rats of change. (4.5.3)

·  Investigates how a change in one variable relates to a change in a second in a second variable

· Identifies and describes situations with constant or varying rates of change and compares them

§ Uses “What’s my rule “ to determine missing number in the additive structure

§ Translates a simple mathematical or real world relationship into algebraic expression using addition and subtraction (4.3.4)

§ Writes and solves one-step equations involving addition or subtraction (4.3.6)

· Represents the idea of a variable as an unknown quantity using a letter or a symbol

· Translates a simple mathematical or real world relationship into algebraic expression using whole numbers (4.4.4)

· Writes and solves one-step equations (using a letter as a variable) involving any one of the four operations (4.4.6)

· Represents the idea of a variable as an unknown quantity using a letter or a symbol

· Expresses mathematical relationships using equations

· Translates a simple mathematical or real world relationship into algebraic expression using whole numbers and decimals(4.5.3)

· Writes and solves one-step equations using whole numbers and decimals (4.5.6)

· Represents the idea of a variable as an own quantity using a letter or a symbol

· Expresses mathematical relationships using equations

· Collects and organizes numerical data using observations and surveys to draw conclusions, makes predictions and hypothesizes about a question (3.3.1)

· Collects data using observations, surveys, and experiments

·   Collects and organizes numerical  and categorical data using observations, surveys and experiments: analyzes the data to draw and justify conclusions, make predictions and hypothesizes about a question (3.4.1)

·   Collects data using observations, surveys, and experiments

·   Begins to address questions with investigations to consider how data collection methods affect the nature of the data set

· Collects and organizes numerical and categorical data using observations, surveys and experiments; analyzes the data and draw conclusions, makes predictions and hypothesizes about a question, and asks new questions (3.5.1)

· Collects data using observations, surveys, and experiments

· Designs investigations to address questions and considers how data collection methods affect the nature of the data set

· Recognizes the differences in representing categorical and numerical data

· Describes the shape and important features of a set of data and compares related data sets with an emphasis of how the data is distributed

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· Represents data by accurately constructing Venn diagrams, line plots, bar graphs, tables, histograms and tally charts (3.3.2)

· Represents categorical and numerical  data using tables and graphs such as line plots, bar graphs and line graphs

· Represents data by accurately constructing Venn diagrams, line plots, bar graphs, tables, histograms and line graphs (3.4.2)

· Represents categorical and numerical  data using tables and graphs such as line plots, bar graphs and line graphs

· Represents data by accurately constructing  line plots, bar graphs, tables, histograms and line graphs that represents continuous data and sketch circle graphs using simple fractions (3.5.2)

·  Represents categorical and numerical  data using tables and graphs such as line plots, bar graphs and line graphs

-Sunrise/sunset project: collect, record, and make a bar graphs from the data throughout the year

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· Describes the shape and important features of a set of data, such as most frequent, least frequent, largest and smallest (3.3.3)

· Compares data in order to make true statements

· Identifies true statements based on simple concept of average

(mean/median)

·   Uses data to propose and justify conclusions

· Describes the important features of a set of data using median, mode and range; compares and evaluates different representations of the same data (3.4.3)

· Compares data in order to make true statements

· Makes true statements based on simple concept of average  (mean/median)

·   Interprets data to determine the reasonableness of statements about the data

·   Uses data to propose and justify conclusions

· Describes the important features of sets of data by computing and using mean, median, mode and range, with emphasis on frequency distribution; compares and evaluates different representations of the same data (3.5.3)

·  Uses measures of center, focusing on the median and understand what each does and does not indicate about the data set

· Compares different representations of the same data and evaluate how well each representation shows important aspects of data

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· Begins to understand how sample sizes effect reliability of results

·   Begins to understand how sample sizes effect reliability of results

·   Designs investigations to address a question and considers how data-collection methods affect the nature of the data set

· Recognizes and describes the likelihood of the occurrence of an event (using “most likely”, “less likely”, or “equally likely”) (3.3.4)

· Describes events as likely or unlikely and discusses the degree of likelihood using such words as certain, equally likely, and impossible

·   Predicts the probability of outcomes of simple experiments

·   Recognizes, numerically describes and predicts the likelihood of the occurrence of an event based on a given sample space of equally likely outcomes using organized lists, tables, and tree diagrams (3.4.4)

·   Describes events as likely or unlikely and discusses the degree of likelihood using such words as certain, equally likely, and impossible

·   Predicts the probability of outcomes of simple experiments

·   Determines simple experimental and theoretical probabilities based on an event and expresses the result as a fraction between and including 0 and 1 (3.5.4)

·   Describes events as likely or unlikely and discusses the degree of likelihood using such words as certain, equally likely, and impossible

·   Understands that the measure of the likelihood of an event can be represented by a number from 0 to 1

· Predicts the probability of outcomes of simple experiments and tests predictions

· Determines the number of possibilities on a given set of data (3.3.4)

·   Finds combinations up to three different constraints

·   All possible combinations and arrangements with certain constraints involving a limited number of variables

·   Predicts results, analyzes data and finds out why some results are more likely, less likely, or equally likely