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4.NO
Number and Operations
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4.NO.1
Students shall understand numbers, ways of representing numbers, relationships among numbers and number systems.
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4
Whole Numbers
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4.NO.1.4.1
Recognize equivalent representations for the same whole number and generate them by composing and decomposing numbers
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4.NO.1.4.2
Use the place-value structure of the base-ten number system and be able to represent and compare whole numbers to millions (using models, illustrations, symbols, expanded notation and problem solving)
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4
Rational Numbers
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4.NO.1.4.3
Use mathematical language and symbols to compare and order any whole numbers with and without appropriate technology (<, >, =)
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4.NO.1.4.4
Write a fraction to name part of a whole, part of a set, a location on a number line, and the division of whole numbers, using models up to 12/12
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4.NO.1.4.5
Utilize models, benchmarks, and equivalent forms to recognize that the size of the whole determines the size of the fraction
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4.NO.1.4.6
Use the place-value structure of the baseten number system and be able to represent and compare decimals to hundredths (using models, illustrations, symbols, expanded notation and problem solving)
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4.NO.1.4.7
Write an equivalent decimal for a given fraction relating to money
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4.NO.1.4.8
Write a fraction that is equivalent to a given fraction with the use of models
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4.NO.2
Students shall understand meanings of operations and how they relate to one another.
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4
Number Theory
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4.NO.2.4.1
Develop an understanding of the associative and zero properties of multiplication using objects
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4.NO.2.4.2
Apply number theory
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4.NO.2.4.2.a
determine if any number is even or odd
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4.NO.2.4.2.b
use the terms multiple, factor, and divisible by in an appropriate context
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4.NO.2.4.2.c
generate and use divisibility rules for 2, 5, and 10
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4.NO.2.4.2.d
demonstrate various multiplication and division relationships
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4
Whole Number Operations
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4.NO.2.4.3
Use conventional mathematical symbols to write equations for contextual problems involving multiplication See Appendix for examples
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4.NO.2.4.4
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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4.NO.3
Students shall compute fluently and make reasonable estimates.
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4
Computational Fluency-Addition and Subtraction
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4.NO.3.4.1
Demonstrate, with and without appropriate technology, computational fluency in multi-digit addition and subtraction in contextual problems
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4
Computational Fluency-Multiplication and Division
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4.NO.3.4.2
Demonstrate fluency with combinations for multiplication and division facts (12 x 12) and use these combinations to mentally compute related problems (30 x 50)
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4.NO.3.4.3
Attain, with and without appropriate technology, computational fluency in multiplication and division using contextual problems using
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4.NO.3.4.3.a
two-digit by two-digit multiplication (larger numbers with technology),
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4.NO.3.4.3.b
up to three-digit by two digit division (larger numbers with technology),
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4.NO.3.4.3.c
strategies for multiplication and dividing numbers,
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4.NO.3.4.3.d
performance of operations in more than one way,
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4.NO.3.4.3.e
Estimation of products and quotients in appropriate situations, and
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4.NO.3.4.3.f
relationships between operations
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4
Application of Computation
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4.NO.3.4.4
Solve simple problems using operations involving addition, subtraction, and multiplication 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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4
Estimation
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4.NO.3.4.5
Use Estimation strategies to solve problems and judge the reasonableness of the answer
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4.A
Algebra
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4.A.4
Students shall recognize, describe and develop patterns, relations and functions.
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4
Recognize, describe and develop patterns
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4.A.4.4.1
Identify a number that is more or less than any whole number using multiples of 10, 100 and/or 1000
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4.A.4.4.2
Use repeating and growing numeric and geometric patterns to make predictions and solve problems
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4
Patterns, Relations and Functions
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4.A.4.4.3
Determine the relationship between sets of numbers by selecting the rule (2 step rule in words)
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4.A.5
Students shall represent and analyze mathematical situations and structures using algebraic symbols.
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4
Expressions, Equations and Inequalities
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4.A.5.4.1
Select and/or write number sentences (equations) to find the unknown in problem-solving contexts involving two-digit by one-digit division using appropriate labels
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4.A.5.4.2
Express mathematical relationships using simple equations and inequalities (>, <, =, "not equal to")
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4.A.5.4.3
Use a variable to represent an unknown quantity in a number sentence involving contextual situations and find the value
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4.A.6
Students shall develop and apply mathematical models to represent and understand quantitative relationships.
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4
Algebraic Models and Relationships
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4.A.6.4.1
Create a chart or table to organize given information and to understand relationships and explain the results
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4.A.7
Students shall analyze change in various contexts.
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4
Analyze Change
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4.A.7.4.1
Identify, describe and generalize relationships in which quantities change proportionally
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4.G
Geometry
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4.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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4
Characteristics and Properties - Three Dimensional
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4.G.8.4.1
Identify, describe and classify 3-D solids by properties including the number of vertices, edges, and shapes of faces using models
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4
Characteristics and Properties - Two Dimensional
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4.G.8.4.2
Identify regular and irregular polygons including octagon See the Polygons page in the Appendix
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4
Characteristics and Properties - One Dimensional
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4.G.8.4.3
Identify, draw, and describe a line, line segment, a ray, an angle, intersecting, perpendicular, and parallel lines
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4
Geometric Relationships
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4.G.8.4.4
Identify and describe intersecting, perpendicular and parallel lines in problem solving context
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4.G.8.4.5
Classify angles relative to 90° as more than, less than or equal to
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4.G.9
Students shall apply transformations and the use of symmetry to analyze mathematical situations.
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4
Symmetry and Transformations
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4.G.9.4.1
Determine the result of a transformation of a two-dimensional figure as a slide (translation), flip (reflection) or turn (rotation) and justify the answer
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4.G.10
Students shall specify locations and describe spatial relationships using coordinate geometry and other representational systems.
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4
Coordinate Geometry
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4.G.10.4.1
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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4.G.11
Students shall use visualization, spatial reasoning and geometric modeling.
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4
Spatial Visualization and Models
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4.G.11.4.1
Construct a threedimensional model composed of cubes when given an illustration
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4.G.11.4.2
Create new figures by combining and subdividing models of existing figures in multiple ways and record results in a table
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4.M
Measurement
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4.M.12
Students shall use attributes of measurement to describe and compare mathematical and real-world objects.
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4
Time: Clock
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4.M.12.4.1
Recognize that 60 seconds equals1 minute
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4
Temperature
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4.M.12.4.2
Distinguish the temperature in contextual problems using the Fahrenheit scale on a thermometer
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4
Tools and Attributes
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4.M.12.4.3
Use the relationship among units of measurement
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4.M.12.4.3.a
Length: 12 in = 1 ft; 3 ft = 1 yd; 36 in = 1 yd; 100 cm = 1 m
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4.M.12.4.3.b
Capacity: 2 cups = 1 pint; 2 pints = 1 quart; 4 quarts = 1 gallon
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4.M.12.4.3.c
Weight: 16 ounces = 1 lb
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4.M.12.4.4
Create and complete a conversion table to show relationships between units of measurement in the same system
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4.M.13
Students shall identify and use units, systems and processes of measurement.
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4
Calendar
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4.M.13.4.1
Using a calendar to determine elapsed time from month to month
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4
Clock
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4.M.13.4.2
Solve problems involving conversions between minutes and hours
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4.M.13.4.3
Restate the time in multiple ways given an analog clock to the nearest 1-minute
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4
Elapsed Time
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4.M.13.4.4
Determine elapsed time in contextual situations to five-minute intervals with beginning time unknown
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4
Money
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4.M.13.4.5
Apply money concepts in contextual situations
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4
Temperature
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4.M.13.4.6
Read temperatures on Fahrenheit and Celsius scales
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4
Applications
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4.M.13.4.7
Use appropriate customary and metric measurement tools for length, capacity and mass
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4.M.13.4.8
Estimate and measure length, capacity/volume and mass using appropriate customary and metric units
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4.M.13.4.8.a
Length: 1/2 inch, 1 cm
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4.M.13.4.8.b
Perimeter: inches, feet, centimeters, meters
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4.M.13.4.8.c
Area: square inches, square feet, square centimeters, square meters
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4.M.13.4.8.d
Weight: pounds/ounces
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4.M.13.4.8.e
Mass: kilograms/grams
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4.M.13.4.8.f
Capacity: cups, pints, quarts, gallons
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4.M.13.4.8.g
Volume: liters
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4
Perimeter
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4.M.13.4.9
Use strategies for finding the perimeter of a rectangle
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4
Area
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4.M.13.4.10
Use strategies for finding the area of a rectangle
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Volume
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4.M.13.4.11
Use strategies to find the volume (cubic units) of rectangular prisms and cubes
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4.DAP
Data Analysis and Probability
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4.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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4
Collect, Organize and display data
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4.DAP.14.4.1
Create a data collection plan after being given a topic and collect, organize, display, describe and interpret simple data using frequency tables or line plots, pictographs and bar graphs
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4.DAP.15
Students shall select and use appropriate statistical methods to analyze data.
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4
Data Analysis
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4.DAP.15.4.1
Represent and interpret data using pictographs, bar graphs and line graphs in which symbols or intervals are greater than one
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4.DAP.15.4.2
Match a set of data with a graphical representation of the data
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4.DAP.16
Students shall develop and evaluate inferences and predictions that are based on data.
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4
Inferences and Predictions
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4.DAP.16.4.1
Make predictions for a given set of data
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4.DAP.17
Students shall understand and apply basic concepts of probability.
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4
Probability
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4.DAP.17.4.1
Use fractions to predict probability of an event
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4.DAP.17.4.2
Conduct simple probability experiments, record the data and draw conclusions about the likelihood of possible outcome (roll number cubes, pull tiles from a bag, spin spinner, or determine the fairness of the game)
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4.DAP.17.4.3
Find all possible combinations of 2 or 3 sets of objects
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