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3.NO
Number and Operations
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3.NO.1
Students shall understand numbers, ways of representing numbers, relationships among numbers and number systems.
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3
Whole Numbers
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3.NO.1.3.1
Recognize equivalent representations for the same whole number and generate them by composing and decomposing numbers
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3.NO.1.3.2
Use the place-value structure of the base-ten number system and be able to represent and compare whole numbers including thousands (using models, illustrations, symbols, expanded notation and problem solving)
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3.NO.1.3.3
Use mathematical language and symbols to compare and order 4 digit numbers with and without appropriate technology (<, >, =)
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3
Rational Numbers
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3.NO.1.3.4
Represent fractions (halves, thirds, fourths, sixths and eighths) using words, numerals and physical models
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3.NO.1.3.5
Utilize models to recognize that the size of the whole determines the size of the fraction depending on the original quantity
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3.NO.1.3.6
Use the place-value structure of the baseten number system and be able to represent and compare decimals to hundredths in money (using models, illustrations, symbols, expanded notation and problem solving)
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3.NO.1.3.7
Write a fraction that is equivalent to a given fraction with the use of models
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3.NO.2
Students shall understand meanings of operations and how they relate to one another.
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3
Number Theory
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3.NO.2.3.1
Develop an understanding of the commutative and identity properties of multiplication using objects
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3.NO.2.3.2
Apply number theory
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3.NO.2.3.2.a
determine if a 3-digit number is even or odd
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3.NO.2.3.2.b
use the terms multiple, factor, product and quotient in an appropriate context (e.g., Since 3x4=12, 3 and 4 are factors; 12 is the product , 3,6,9,12 are multiples of 3; 4, 8,12,16 are multiples of 4; 12 รท 4 = 3, the quotient)
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3
Whole Number Operations
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3.NO.2.3.3
Use conventional mathematical symbols to write equations for contextual problems involving multiplication See Appendix for examples
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3.NO.2.3.4
Model, represent and explain division as measurement and partitive division including equal groups, related rates, price, rectangular arrays (area model), combinations and multiplicative comparison See Appendix for more details
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3.NO.3
Students shall compute fluently and make reasonable estimates.
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3
Computational Fluency-Addition and Subtraction
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3.NO.3.3.1
Develop, with and without appropriate technology, computational fluency, in multi-digit addition and subtraction through 999 using contextual problems
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3.NO.3.3.1.a
strategies for adding and subtracting numbers
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3.NO.3.3.1.b
Estimation of sums and differences in appropriate situations
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3.NO.3.3.1.c
relationships between operations
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3
Computational Fluency-Multiplication and Division
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3.NO.3.3.2
Develop, with and without appropriate technology, fluency with basic number combinations for multiplication and division facts (10 x 10)
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3.NO.3.3.3
Develop, with and without appropriate technology, computational fluency in multiplication and division up to two-digit by one-digit numbers using two-digit by onedigit number contextual problems using
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3.NO.3.3.3.a
strategies for multiplying and dividing numbers,
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3.NO.3.3.3.b
performance of operations in more than one way,
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3.NO.3.3.3.c
Estimation of products and quotients in appropriate situations, and
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3.NO.3.3.3.d
relationships between operations
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3
Application of Computation
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3.NO.3.3.4
Solve simple problems using one operation involving addition and subtraction using a variety of methods and tools (e.g., objects, mental computation, paper and pencil and with and without appropriate technology)
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3
Estimation
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3.NO.3.3.5
Use Estimation strategies to solve problems and judge the reasonableness of the answer
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3.A
Algebra
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3.A.4
Students shall recognize, describe and develop patterns, relations and functions.
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3
Recognize, describe and develop patterns
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3.A.4.3.1
Count forward and backward when given a number less than or equal to 1000, ____, 399, ___, ____
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3.A.4.3.2
Relate skip-counting patterns to multiplication
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3.A.4.3.3
Identify a number that is more or less than any whole number up to 1000 using multiples of ten and/or 100
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3.A.4.3.4
Use repeating and growing numeric or geometric patterns to solve problems
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3
Patterns, Relations and Functions
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3.A.4.3.5
Determine the relationship between sets of numbers by selecting the rule (1 step rule in words)
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3.A.5
Students shall represent and analyze mathematical situations and structures using algebraic symbols.
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3
Expressions, Equations and Inequalities
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3.A.5.3.1
Select and/or write number sentences (equations) to find the unknown in problem-solving contexts involving two-digit times one-digit multiplication using appropriate labels
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3.A.5.3.2
Express mathematical relationships using equalities and inequalities (>, <, =, "not equal to")
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3.A.5.3.3
Use a symbol to represent an unknown quantity in a number sentence involving contextual situations and find the value
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3.A.6
Students shall develop and apply mathematical models to represent and understand quantitative relationships.
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3
Algebraic Models and Relationships
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3.A.6.3.1
Complete a chart or table to organize given information and to understand relationships and explain the results
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3.A.7
Students shall analyze change in various contexts.
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3
Analyze Change
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3.A.7.3.1
Identify the change over time
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3.G
Geometry
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3.G.8
Students shall analyze characteristics and properties of 2 and 3 dimensional geometric shapes and develop mathematical arguments about geometric relationships.
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3
Characteristics and Properties - Three Dimensional
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3.G.8.3.1
Compare, contrast and build 3-D solids by investigating the number of faces, edges, and vertices on models
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3
Characteristics and Properties - Two Dimensional
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3.G.8.3.2
Identify regular polygons with at least 4 sides (square, pentagon, hexagon and octagon)
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3
Characteristics and Properties - One Dimensional
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3.G.8.3.3
Identify and draw line, line segment and ray using appropriate labels
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3
Geometric Relationships
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3.G.8.3.4
Identify and draw intersecting and parallel lines
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3.G.9
Students shall apply transformations and the use of symmetry to analyze mathematical situations.
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3
Symmetry and Transformations
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3.G.9.3.1
Draw one or more lines of symmetry in a polygon
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3.G.9.3.2
Describe the motion (transformation) of a two-dimensional figure as a flip (reflection), slide (translation) or turn (rotation)
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3.G.10
Students shall specify locations and describe spatial relationships using coordinate geometry and other representational systems.
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3
Coordinate Geometry
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3.G.10.3.1
Locate and identify points on a coordinate grid and name the ordered pair (quadrant one only) using common language and geometric vocabulary (horizontal and vertical)
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3.G.11
Students shall use visualization, spatial reasoning and geometric modeling.
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3
Spatial Visualization and Models
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3.G.11.3.1
Replicate a threedimensional model composed of cubes when given a physical model
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3.G.11.3.2
Determine which new figure will be formed by combining and subdividing models of existing figures
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3.M
Measurement
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3.M.12
Students shall use attributes of measurement to describe and compare mathematical and real-world objects.
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3
Time: Calendar
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3.M.12.3.1
Determine the number of days in a month, days in a year and identify the number of weeks in a year
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3
Time: Clock
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3.M.12.3.2
Recognize that 60 minutes equals 1 hour and that a day is divided into A.M. and P.M.
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3
Temperature
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3.M.12.3.3
Distinguish the temperature in contextual problems using the Fahrenheit scale on a thermometer
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3
Tools and Attributes
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3.M.12.3.4
Demonstrate the relationship among different standard units
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3.M.12.3.4.a
Length: 12 in = 1 ft, 3 ft = 1 yd, 36 in = 1 yd
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3.M.12.3.4.b
Capacity: 2 cups = 1 pint, 2 pints = 1 quart 4 quarts = 1gallon
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3.M.12.3.4.c
Weight: 16 ounces = 1 lb
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3.M.12.3.5
Create and complete a conversion table (from larger unit to smaller unit) to show relationships between units of measurement in the same system
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3.M.13
Students shall identify and use units, systems and processes of measurement.
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3
Calendar
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3.M.13.3.1
Use a calendar to determine elapsed time from month to month
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3
Clock
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3.M.13.3.2
Tell time to the nearest 1-minute intervals
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3.M.13.3.3
Express time to the half hour and quarter hour using the terms halfpast, quarter after, quarter -until
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3
Elapsed Time
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3.M.13.3.4
Determine elapsed time in contextual situations to five-minute intervals
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3.M.13.3.4.a
End time unknown
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3.M.13.3.4.b
Elapsed hours unknown
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3
Money
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3.M.13.3.5
Determine the value of money up to $10
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3.M.13.3.6
Apply money concepts in contextual situations up to $10.00
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3
Temperature
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3.M.13.3.7
Read temperatures on Fahrenheit and Celsius scales in intervals of two and five
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3
Applications
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3.M.13.3.8
Use appropriate customary measurement tools for length, capacity and mass
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3.M.13.3.9
Estimate and measure length, capacity/volume and mass using appropriate customary units
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3.M.13.3.9.a
Length: 1 inch
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3.M.13.3.9.b
Perimeter: inches, feet, etc
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3.M.13.3.9.c
Area: square inches (use models)
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3.M.13.3.9.d
Weight: pounds/ounces
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3.M.13.3.9.e
Capacity: cups, pints, quarts, gallons
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3
Perimeter
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3.M.13.3.10
Find the perimeter of a figure by measuring the length of the sides
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3
Area
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3.M.13.3.11
Find the area of any region counting squares and half-squares
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3
Volume
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3.M.13.3.12
Develop strategies for finding the volume (cubic units) of rectangular prisms and cubes using models
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3.DAP
Data Analysis and Probability
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3.DAP.14
Students shall formulate questions that can be addressed with data and collect, organize and display relevant data to answer them.
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3
Collect, Organize and display data
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3.DAP.14.3.1
Design a survey question after being given a topic and collect, organize, display and describe simple data using frequency tables or line plots, pictographs, and bar graphs
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3.DAP.15
Students shall select and use appropriate statistical methods to analyze data.
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3
Data Analysis
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3.DAP.15.3.1
Read and interpret pictographs and bar graphs in which symbols or intervals are greater than one
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3.DAP.15.3.2
Match a set of data with a graphical representation of the data
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3.DAP.16
Students shall develop and evaluate inferences and predictions that are based on data.
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3
Inferences and Predictions
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3.DAP.16.3.1
Make predictions for a given set of data
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3.DAP.17
Students shall understand and apply basic concepts of probability.
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3
Probability
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3.DAP.17.3.1
Use fractions to predict probability of an event
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3.DAP.17.3.2
Conduct simple probability experiments, record the data and draw conclusions about the likelihood of possible outcomes (roll number cubes, pull tiles from a bag, spin a spinner, or determine the fairness of games)
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3.DAP.17.3.3
Use physical models, pictures, and organized lists to find combinations of two sets of objects
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