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4.1
Number and Operations
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4.1.1
Understand and apply numbers, ways of representing numbers, and the relationships among numbers and different number systems.
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4.1.1.PO 1
Express whole numbers, fractions, decimals, and percents using and connecting multiple representations.
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4.1.1.PO 2
Compose and decompose whole numbers using factors and multiples.
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4.1.1.PO 3
Express fractions as fair sharing, parts of a whole, parts of a set, and locations on a real number line.
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4.1.1.PO 4
Compare and order decimals to hundredths.
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4.1.1.PO 5
Use simple ratios to describe problems in context.
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4.1.2
Understand and apply numerical operations and their relationship to one another.
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4.1.2.PO 1
Add and subtract decimals through hundredths including money to $1000.00 and fractions with like denominators.
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4.1.2.PO 2
Use multiple strategies to multiply whole numbers
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4.1.2.PO 2.a
two-digit by two-digit and
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4.1.2.PO 2.b
multi-digit by one-digit.
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4.1.2.PO 3
Demonstrate fluency of multiplication and division facts through 12.
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4.1.2.PO 4
Use multiple strategies to divide whole numbers.
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4.1.2.PO 5
Apply associative and distributive properties to solve multiplication and division problems.
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4.1.2.PO 6
Apply order of operations with whole numbers.
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4.1.3
Use estimation strategies reasonably and fluently while integrating content from each of the other strands.
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4.1.3.PO 1
Use benchmarks as meaningful points of comparison for whole numbers, decimals, and fractions.
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4.1.3.PO 2
Make estimates appropriate to a given situation or computation with whole numbers and fractions.
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4.2
Data Analysis, Probability, and Discrete Mathematics This
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4.2.1
Understand and apply data collection, organization, and representation to analyze and sort data.
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4.2.1.PO 1
Collect, record, organize, and display data using double bar graphs, single line graphs, or circle graphs.
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4.2.1.PO 2
Formulate and answer questions by interpreting and analyzing displays of data, including double bar graphs, single line graphs, or circle graphs.
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4.2.1.PO 3
Use median, mode, and range to describe the distribution of a given data set.
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4.2.1.PO 4
Compare two sets of related data.
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4.2.2
Understand and apply the basic concepts of probability.
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4.2.2.PO 1
Describe elements of theoretical probability by listing or drawing all possible outcomes of a given event and predicting the outcome using word and number benchmarks.
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4.2.3
Understand and demonstrate the systematic listing and counting of possible outcomes.
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4.2.3.PO 1
Construct tree diagrams to solve problems in context by
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4.2.3.PO 1.a
representing all possibilities for a variety of counting problems,
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4.2.3.PO 1.b
explaining how its properties relate to the problem,
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4.2.3.PO 1.c
representing the same counting problem in multiple ways, and
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4.2.3.PO 1.d
drawing conclusions.
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4.2.3.PO 2
Justify that all possibilities have been enumerated without duplication.
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4.2.4
Understand and apply vertex-edge graphs.
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4.2.4.PO 1
Demonstrate the connection between map coloring and vertex coloring.
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4.2.4.PO 2
Construct vertex-edge graphs to represent concrete situations and identify paths and circuits.
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4.2.4.PO 3
Solve conflict problems by constructing and coloring vertex-edge graphs.
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4.3
Patterns, Algebra, and Functions
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4.3.1
Identify patterns and apply pattern recognition to reason mathematically while integrating content from each of the other strands.
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4.3.1.PO 1
Recognize, describe, create, extend, and find missing terms in a numerical sequence involving whole numbers using all four basic operations.
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4.3.1.PO 2
Explain the rule for a given numerical sequence, verify that the rule works, and use the rule to make predictions.
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4.3.2
Describe and model functions and their relationships.
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4.3.3
Represent and analyze mathematical situations and structures using algebraic representations.
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4.3.3.PO 1
Use a symbol to represent an unknown quantity in a simple algebraic expression involving all operations.
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4.3.3.PO 2
Create and solve one-step equations that can be solved using addition, subtraction, multiplication, and division of whole numbers.
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4.3.4
Analyze how changing the values of one quantity corresponds to change in the values of another quantity.
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4.3.4.PO 1
Identify the change in a quantity over time and make simple predictions.
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4.4
Geometry and Measurement
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4.4.1
Analyze the attributes and properties of 2- and 3- dimensional figures and develop mathematical arguments about their relationships.
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4.4.1.PO 1
Draw and describe the relationships between points, lines, line segments, rays, and angles including parallelism and perpendicularity.
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4.4.1.PO 2
Justify which objects in a collection match a given geometric description.
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4.4.1.PO 3
Describe and classify triangles by angles and sides.
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4.4.1.PO 4
Recognize which attributes (such as shape or area) change and which do not change when 2-dimensional figures are cut up or rearranged.
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4.4.1.PO 5
Recognize and draw congruent figures, and match them in a given collection.
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4.4.1.PO 6
Draw right, acute, obtuse, and straight angles and identify these angles in other geometric figures.
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4.4.1.PO 7
Recognize the relationship between a 3-dimensional figure and its corresponding net(s).
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4.4.3
Specify and describe spatial relationships using rectangular and other coordinate systems while integrating content from each of the other strands.
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4.4.3.PO 1
Name, locate, and graph points in the first quadrant of the coordinate plane using ordered pairs.
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4.4.3.PO 2
Plot line segments in the first quadrant of the coordinate plane using a set of ordered pairs in a table.
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4.4.3.PO 3
Construct geometric figures with vertices at points on the coordinate plane.
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4.4.4
Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements.
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4.4.4.PO 1
Compute elapsed time to the minute.
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4.4.4.PO 2
Apply measurement skills to measure length, mass, and capacity using metric units.
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4.4.4.PO 3
Solve problems involving conversions within the same measurement system.
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4.4.4.PO 4
Solve problems involving perimeter of 2-dimensional figures and area of rectangles.
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4.4.4.PO 5
Describe the change in perimeter or area when one attribute (length or width) of a rectangle changes.
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4.5
Structure and Logic
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4.5.1
Use reasoning to solve mathematical problems. In Grade 4, students use symbols, pictures, or mathematical language to explain the reasoning behind their decisions and solutions.
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4.5.1.PO 1
Analyze common algorithms for computing (adding, subtracting, multiplying, and dividing) with whole numbers using the associative, commutative, and distributive properties.
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4.5.2
Evaluate situations, select problem-solving strategies, draw logical conclusions, develop and describe solutions, and recognize their applications.
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4.5.2.PO 1
Analyze a problem situation to determine the question(s) to be answered.
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4.5.2.PO 2
Identify relevant, missing, and extraneous information related to the solution to a problem.
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4.5.2.PO 3
Select and use one or more strategies to efficiently solve the problem and justify the selection.
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4.5.2.PO 4
Determine whether a problem to be solved is similar to previously solved problems, and identify possible strategies for solving the problem.
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4.5.2.PO 5
Represent a problem situation using any combination of words, numbers, pictures, physical objects, or symbols.
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4.5.2.PO 6
Summarize mathematical information, explain reasoning, and draw conclusions.
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4.5.2.PO 7
Analyze and evaluate whether a solution is reasonable, is mathematically correct, and answers the question.
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4.5.2.PO 8
Make and test conjectures based on data (or information) collected from explorations and experiments.
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