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4.NO
Numbers and Operations
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4.1
Understand numbers, ways of representing numbers, relationships among numbers, and number systems
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4
Numbers and Number Systems
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4.1.1
Identify place value from ten-thousandths to millions
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4.1.2
Identify and list factors, multiples, prime numbers, and composite numbers
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4.1.3
Identify equivalent forms of commonly used fractions and decimals
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4.2
Understand the meaning of operations and how they relate to each other
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4
Operations
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4.2.1
Describe situations involving addition and subtraction of fractions and decimals
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4
Operation Properties
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4.2.2
Use associative, commutative, and distributive properties as they apply to operations involving whole numbers
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4.2.3
Apply the properties of zero and one as they relate to addition, subtraction, multiplication, and division
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4.3
Use computational tools and strategies fluently and, when appropriate, use estimation
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4
Computational Fluency
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4.3.1
Recall all multiplication facts and the corresponding division facts up to 12 x 12
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4.3.2
Select and use appropriate strategies and/or tools (e.g., mental math, calculators, paper/pencil, standard algorithms) for computing whole numbers
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Addition: Add numbers up to millions (Fourth grade - B.1)
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Addition: Add numbers up to millions: word problems (Fourth grade - B.2)
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Addition: Fill in the missing digits (Fourth grade - B.3)
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Addition: Add 3 or more numbers up to millions (Fourth grade - B.5)
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Addition: Addition patterns over increasing place values (Fourth grade - B.6)
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Addition: Choose numbers with a particular sum (Fourth grade - B.7)
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Subtraction: Subtract numbers up to millions (Fourth grade - C.1)
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Subtraction: Subtract numbers up to millions: word problems (Fourth grade - C.2)
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Subtraction: Fill in the missing digits (Fourth grade - C.3)
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Subtraction: Subtraction patterns over increasing place values (Fourth grade - C.4)
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Subtraction: Choose numbers with a particular difference (Fourth grade - C.5)
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Multiplication: Multiply 1-digit numbers by larger numbers (Fourth grade - D.3)
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Multiplication: Multiplication patterns over increasing place values (Fourth grade - D.4)
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Multiplication: Multiply a 2-digit number by a 2-digit number: complete the missing steps (Fourth grade - D.8)
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Multiplication: Multiply a 2-digit number by a 2-digit number (Fourth grade - D.9)
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Multiplication: Multiply a 2-digit number by a 2-digit number: word problems (Fourth grade - D.10)
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Multiplication: Multiply a 2-digit number by a larger number: complete the missing steps (Fourth grade - D.12)
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Multiplication: Multiply a 2-digit number by a larger number (Fourth grade - D.13)
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Multiplication: Multiply a 2-digit number by a larger number: word problems (Fourth grade - D.14)
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Multiplication: Multiply numbers ending in zeroes (Fourth grade - D.15)
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Multiplication: Multiply numbers ending in zeroes: word problems (Fourth grade - D.16)
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Multiplication: Multiply 3 numbers up to 2 digits each (Fourth grade - D.17)
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Multiplication: Inequalities with multiplication (Fourth grade - D.18)
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Division: Properties of division (Fourth grade - E.3)
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Division: Divide larger numbers, one-digit divisors (Fourth grade - E.4)
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Division: Divide larger numbers, one-digit divisors: word problems (Fourth grade - E.5)
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Division: Divide by 1-digit numbers: complete the table (Fourth grade - E.6)
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Division: Divide by 1-digit numbers: interpret remainders (Fourth grade - E.7)
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Division: Divide numbers ending in zeroes, one-digit divisors (Fourth grade - E.9)
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Division: Divisibility rules (Fourth grade - E.11)
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Division: Division patterns over increasing place values (Fourth grade - E.12)
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Division: Divide numbers ending in zeroes, multi-digit divisors (Fourth grade - E.13)
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Division: Divide numbers ending in zeroes, multi-digit divisors: word problems (Fourth grade - E.14)
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Division: Divide 2-digit numbers by multiples of 10 (Fourth grade - E.15)
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Division: Divide by 2-digit numbers (Fourth grade - E.16)
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Division: Divide by 2-digit numbers: word problems (Fourth grade - E.17)
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Division: Divide larger numbers by 2-digit numbers (Fourth grade - E.18)
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Division: Divide larger numbers by 2-digit numbers: word problems (Fourth grade - E.19)
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Division: Inequalities with division (Fourth grade - E.20)
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Mixed operations: Multi-step word problems (Fourth grade - F.1)
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Mixed operations: Word problems with extra or missing information (Fourth grade - F.3)
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Mixed operations: Solve word problems using guess-and-check (Fourth grade - F.4)
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Mixed operations: Choose numbers with a particular sum, difference, product, or quotient (Fourth grade - F.5)
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Mixed operations: Mentally add and subtract numbers ending in zeroes (Fourth grade - F.6)
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Mixed operations: Inequalities involving addition, subtraction, multiplication, and division (Fourth grade - F.7)
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4.3.3
Use a variety of strategies to add and subtract fractions with like and unlike denominators
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4.3.4
Add and subtract decimals to 3 places
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4
Estimation
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4.3.5
Determine the reasonableness of numerical solutions
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4.MEA
Measurement
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4.4
Understand attributes, units, and systems of units in measurement; and develop and use techniques, tools, and formulas for measuring
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4
Measurement Attributes and Units
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4.4.1
Explain the need to use standard units for measuring
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4.4.2
Select and apply appropriate customary and metric units and tools to measure length, perimeter, and area for the degree of accuracy needed
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4.4.3
Classify right angles, acute angles, obtuse angles, and straight angles
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4
Measurement Tools and Techniques
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4.4.4
Estimate and measure surface area and volume using U.S. customary units and metric units
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4
Measurement Formulas
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4.4.5
Use known measurements to calculate desired measurements of squares and rectangles (e.g., use the length of the square to calculate its area and perimeter)
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4.GEO
Geometry and Spatial Sense
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4.5
Analyze properties of objects and relationships among the properties
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4
Geometric Shapes and Their Properties and Relationships
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4.5.1
Classify different types of triangles and quadrilaterals according to their properties and identify the properties that define the classifications
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4.5.2
Describe lines in the plane (i.e., parallel, perpendicular, intersecting)
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4.5.3
Compare points, lines, line segments, and rays
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4.5.4
Predict and confirm the results of putting together and taking apart two- and three-dimensional shapes
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4.6
Use transformations and symmetry to analyze mathematical situations
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4
Transformation
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4.6.1
Use flips, slides, and turns to determine if two figures are congruent
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4
Symmetry
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4.6.2
Locate the plane of symmetry in three-dimensional objects
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4.7
Use visualization and spatial reasoning to solve problems both within and outside of mathematics
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4
Visualization and Spatial Reasoning
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4.7.1
Predict the three-dimensional object that will result from folding a two-dimensional net of the object and justify the prediction
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4.8
Select and use different representational systems, including coordinate geometry
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4
Coordinate Geometry
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4.8.1
Use ordered pairs to plot points on a coordinate grid
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4.PFA
Patterns, Functions, and Algebra
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4.9
Understand various types of patterns and functional relationships
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4
Patterns
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4.9.1
Extend, create, and generalize growing and shrinking numeric and geometric patterns (including multiplication patterns)
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4
Function
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4.9.2
Represent the relationship between quantities in a variety of forms (e.g., manipulatives, tables, pictures, symbols)
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4.1
Use symbolic forms to represent, model, and analyze mathematical situations
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4
Numeric and Algebraic Representations
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4.10.1
Use symbols to represent unknown quantities in open sentences and determine the unknown quantities
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4.10.2
Represent the commutative, associative, and distributive properties symbolically
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4
Rates of Change
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4.10.3
Describe the rate of change numerically and verbally based on data recorded in a table or graph
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4.DASP
Data Analysis, Statistics, and Probability
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4.11
Pose questions and collect, organize, and represent data to answer those questions
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4
Data Collection and Representation
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4.11.1
Pose questions, collect data using observations and experiments, and organize the data into tables or graphs
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4.11.2
Label the parts of a graph (e.g., axes, scale, legend, title)
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4.12
Interpret data using methods of exploratory data analysis
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4
Data Interpretation
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4.12.1
Compare related data sets (e.g., height of 4th grade boys vs. height of 4th grade girls) with an emphasis on how the data are distributed
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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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Data, charts, and graphs: Circle graphs (Fourth grade - J.6)
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4.12.2
Analyze important features in the shape of the graph of a data set
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4.13
Develop and evaluate inferences, predictions, and arguments that are based on data
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4
Predictions and Inferences
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4.13.1
Propose and justify conclusions/predictions based on data
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4.14
Understand and apply basic notions of chance and probability
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4
Probability
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4.14.1
Predict the probability of outcomes of simple experiments (e.g., coin toss, 4-colored spinner) and test the predictions
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