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4.1
Number and Operations
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4.1.1
Understand numbers, ways of representing numbers, relationships among numbers, and number systems
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4.1.1.A
Read, write and compare numbers
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4.1.1.A.1
read, write and compare decimals to the hundredths place and whole numbers up to 6 digits
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4.1.1.B
Represent and use rational numbers
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4.1.1.B.1
use models, benchmarks (0, 1/2 and 1) and equivalent forms to judge the size of fractions
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4.1.1.C
Compose and decompose numbers
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4.1.1.C.1
recognize equivalent representations for the same number and generate them by decomposing and composing numbers
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4.1.1.D
Classify and describe numeric relationships
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4.1.1.D.1
classify and describe numbers by their characteristics, including odd, even and multiples
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4.1.2
Understand meanings of operations and how they relate to one another
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4.1.2.A
Represent operations
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4.1.2.A.1
represent and recognize multiplication using various models, including sets and arrays
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4.1.2.C
Apply properties of operations
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4.1.2.C.1
apply commutative and identity properties of multiplication to whole numbers
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4.1.3
Compute fluently and make reasonable estimates
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4.1.3.A
Describe or represent mental strategies
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4.1.3.A.1
represent a mental strategy used to compute a given multiplication problem (up to 2-digit by 2-digit multiple of)
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4.1.3.B
Develop and demonstrate fluency
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4.1.3.B.1
demonstrate fluency with basic number relationships (12 X 12) of multiplication and division
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4.1.3.C
Compute problems
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4.1.3.C.1
apply and describe the strategy used to compute a given
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4.1.3.C.1.a
multiplication problem up to a 2-digit by 2-digit
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4.1.3.C.1.b
division problem up to a 3-digit by 1-digit
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4.1.3.D
Estimate and justify solutions
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4.1.3.D.1
estimate and justify the results of multiplication of whole numbers
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4.2
Algebraic Relationships
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4.2.1
Understand patterns, relations, and functions
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4.2.1.A
Recognize and extend patterns
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4.2.1.A.1
describe geometric and numeric patterns
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4.2.1.B
Create and analyze patterns
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4.2.1.B.1
analyze patterns using words, tables and graphs
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4.2.2
Represent and analyze mathematical situations and structures using algebraic symbols
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4.2.2.A
Represent mathematical situations
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4.2.2.A.1
represent a mathematical situation as an expression or number sentence
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4.2.2.B
Describe and use mathematical manipulation
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4.2.2.B.1
apply the commutative property of multiplication to whole numbers
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4.2.3
Use mathematical models to represent and understand quantitative relationships
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4.2.3.A
Use mathematical models
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4.2.3.A.1
model problem situations, using representations such as graphs, tables or number sentences
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4.2.4
Analyze change in various contexts
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4.2.4.A
Analyze change
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4.2.4.A.1
describe mathematical relationships in terms of constant rates of change
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4.3
Geometric and Spatial Relationships
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4.3.1
Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships
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4.3.1.A
Describe and use geometric relationships
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4.3.1.A.1
identify and describe the attributes of 2- and 3- dimensional shapes (prisms, cones, parallelism, perpendicularity)
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Geometry: Identify planar and solid figures (Fourth grade - P.1)
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Geometry: Types of triangles (Fourth grade - P.2)
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Geometry: Open and closed shapes and qualities of polygons (Fourth grade - P.3)
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Geometry: Which 2-dimensional shape is being described? (Fourth grade - P.4)
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Geometry: Which 3-dimensional figure is being described? (Fourth grade - P.5)
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Geometry: Number of sides in polygons (Fourth grade - P.6)
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Geometry: Count and compare sides, edges, faces, and vertices (Fourth grade - P.7)
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Geometry: Similar and congruent (Fourth grade - P.8)
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Geometry: Acute, right, obtuse, and straight angles (Fourth grade - P.10)
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Geometry: Angles of 90, 180, 270, and 360 degrees (Fourth grade - P.11)
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Geometry: Measure angles with a protractor (Fourth grade - P.12)
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Geometry: Parts of a circle (Fourth grade - P.13)
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Geometry: Parallel, perpendicular, intersecting (Fourth grade - P.21)
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4.3.1.C
Compose and decompose shapes
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4.3.1.C.1
describe the results of subdividing, combining and transforming shapes
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4.3.2
Specify locations and describe spatial relationships using coordinate geometry and other representational systems
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4.3.2.A
Use coordinate systems
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4.3.2.A.1
describe movement using common language and geometric vocabulary (forward, back, left, right, north, south, east, west)
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4.3.3
Apply transformations and use symmetry to analyze mathematical situations
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4.3.3.A
Use transformations on objects
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4.3.3.A.1
predict the results of sliding/translating, flipping/reflecting or turning/rotating around the center point of a polygon
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4.3.3.C
Use symmetry
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4.3.3.C.1
construct a figure with multiple lines of symmetry and identify the lines of symmetry
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4.3.4
Use visualization, spatial reasoning and geometric modeling to solve problems
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4.3.4.A
Recognize and draw three-dimensional representations
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4.3.4.A.1
given the picture of a prism, identify the shapes of the faces
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4.4
Measurement
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4.4.1
Understand measurable attributes of objects and the units, systems and processes of measurement
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4.4.1.A
Determine unit of measurement
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4.4.1.A.1
identify and justify the unit of linear measure including perimeter and (customary metric)
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4.4.1.B
Identify equivalent measures
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4.4.1.B.1
identify equivalent linear measures within a system of measurement
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4.4.1.C
Tell and use units of time
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4.4.1.C.1
tell time to the nearest minute
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4.4.1.D
Count and compute money
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4.4.1.D.1
determine change from $10.00 and add and subtract money values to $10.00
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4.4.2
Apply appropriate techniques, tools and formulas to determine measurements
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4.4.2.A
Use standard or non-standard measurement
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4.4.2.A.1
select and use benchmarks to estimate measurements (linear, capacity, weight)
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4.4.2.B
Use angle measurement
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4.4.2.B.1
select and use benchmarks to estimate measurements of 0-, 45-, 90- degree angles
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4.4.2.C
Apply geometric measurements
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4.4.2.C.1
determine the area of a polygon on a rectangular grid
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4.5
Data and Probability
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4.5.1
Formulate questions that can be addressed with data and collect, organize and display relevant data to answer them
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4.5.1.A
Formulate questions
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4.5.1.A.1
collect data using observations, surveys and experiments
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4.5.1.C
Represent and interpret data
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4.5.1.C.1
create tables or graphs to represent categorical and numerical data (including line plots)
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4.5.2
Select and use appropriate statistical methods to analyze data
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4.5.2.A
Describe and analyze data
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4.5.2.A.1
describe important features of the data set
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4.5.3
Develop and evaluate inferences and predictions that are based on data
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4.5.3.A
Develop and evaluate inferences
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4.5.3.A.1
given a set of data, propose and justify conclusions that are based on the data
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Data, charts, and graphs: Read a table (Fourth grade - J.1)
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Data, charts, and graphs: Line graphs (Fourth grade - J.2)
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Data, charts, and graphs: Bar graphs (Fourth grade - J.3)
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Data, charts, and graphs: Frequency charts (Fourth grade - J.4)
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Data, charts, and graphs: Stem-and-leaf plots (Fourth grade - J.5)
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Probability and statistics: Calculate probability (Fourth grade - U.1)
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Probability and statistics: Make predictions (Fourth grade - U.2)
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Probability and statistics: Combinations (Fourth grade - U.5)
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4.5.4
Understand and apply basic concepts of probability
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