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5.1
Number and Operations
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5.1.1
Understand and apply numbers, ways of representing numbers, and the relationships among numbers and different number systems.
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5.1.1.PO 1
Determine equivalence by converting between benchmark fractions, decimals, and percents.
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5.1.1.PO 2
Differentiate between prime and composite numbers; differentiate between factors and multiples for whole numbers.
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5.1.1.PO 3
Locate integers on a number line.
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5.1.1.PO 4
Compare and order positive fractions, decimals, and percents.
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5.1.1.PO 5
Use ratios and unit rates to model, describe and extend problems in context.
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Ratios, proportions, and percents: Determine the ratio (Fifth grade - U.1)
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Ratios, proportions, and percents: Ratio tables (Fifth grade - U.2)
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Ratios, proportions, and percents: Ratios: word problems (Fifth grade - U.3)
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Ratios, proportions, and percents: Equivalent ratios (Fifth grade - U.4)
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Ratios, proportions, and percents: Proportions (Fifth grade - U.5)
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Ratios, proportions, and percents: Unit rates and equivalent rates (Fifth grade - U.6)
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5.1.1.PO 6
Express or interpret positive and negative numbers in context.
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5.1.2
Understand and apply numerical operations and their relationship to one another.
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5.1.2.PO 1
Add and subtract decimals through thousandths and fractions expressing solutions in simplest form.
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5.1.2.PO 2
Multiply multi-digit whole numbers
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5.1.2.PO 3
Divide multi-digit whole numbers by whole number divisors with and without remainders.
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5.1.2.PO 4
Apply the associative, commutative, and distributive properties to solve numerical problems.
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5.1.2.PO 5
Simplify numerical expressions (including fractions and decimals) using the order of operations with or without grouping symbols.
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5.1.3
Use estimation strategies reasonably and fluently while integrating content from each of the other strands.
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5.1.3.PO 1
Make estimates appropriate to a given situation or computation with whole numbers, fractions, and decimals.
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5.2
Data Analysis, Probability, and Discrete Mathematics
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5.2.1
Understand and apply data collection, organization, and representation to analyze and sort data.
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5.2.1.PO 1
Collect, record, organize, and display data using multi-bar graphs or double line graphs.
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5.2.1.PO 2
Formulate and answer questions by interpreting and analyzing displays of data, including multi-bar graphs or double line graphs.
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5.2.1.PO 3
Use mean, median, mode, and range to analyze and describe the distribution of a given data set.
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5.2.2
Understand and apply the basic concepts of probability.
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5.2.2.PO 1
Describe the theoretical probability of events and represent the probability as a fraction, decimal, or percent.
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5.2.2.PO 2
Explore probability when performing experiments by
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5.2.2.PO 2.a
predicting the outcome,
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5.2.2.PO 2.b
recording the data,
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5.2.2.PO 2.c
comparing outcomes of the experiment to predictions, and
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5.2.2.PO 2.d
comparing the results of multiple repetitions of the experiment.
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5.2.3
Understand and demonstrate the systematic listing and counting of possible outcomes.
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5.2.3.PO 1
Analyze relationships among representations and make connections to the multiplication principle of counting.
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5.2.3.PO 2
Solve a variety of counting problems and explain the multiplication principle of counting.
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5.2.4
Understand and apply vertex-edge graphs.
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5.2.4.PO 1
Investigate properties of vertex-edge graphs
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5.2.4.PO 1.a
Euler paths,
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5.2.4.PO 1.b
Euler circuits, and
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5.2.4.PO 1.c
degree of a vertex.
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5.2.4.PO 2
Solve problems related to Euler paths and circuits.
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5.3
Patterns, Algebra, and Functions
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5.3.1
Identify patterns and apply pattern recognition to reason mathematically while integrating content from each of the other strands.
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5.3.1.PO 1
Recognize, describe, create, and analyze a numerical sequence involving fractions and decimals using addition and subtraction.
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5.3.2
Describe and model functions and their relationships.
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5.3.3
Represent and analyze mathematical situations and structures using algebraic representations.
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5.3.3.PO 1
Create and solve two-step equations that can be solved using inverse operations with whole numbers.
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5.3.4
Analyze how changing the values of one quantity corresponds to change in the values of another quantity.
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5.3.4.PO 1
Describe patterns of change including constant rate and increasing or decreasing rate.
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5.4
Geometry and Measurement
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5.4.1
Analyze the attributes and properties of 2- and 3- dimensional figures and develop mathematical arguments about their relationships.
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5.4.1.PO 1
Draw and label 2-dimensional figures given specific attributes including angle measure and side length.
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5.4.1.PO 2
Solve problems by understanding and applying the property that the sum of the interior angles of a triangle is 180°.
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5.4.1.PO 3
Classify quadrilaterals by their properties.
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5.4.1.PO 4
Compare attributes of 2-dimensional figures with 3-dimensional figures by drawing and constructing nets and models.
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5.4.2
Apply spatial reasoning to create transformations and use symmetry to analyze mathematical situations.
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5.4.3
Specify and describe spatial relationships using rectangular and other coordinate systems while integrating content from each of the other strands.
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5.4.4
Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements.
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5.4.4.PO 1
Solve problems using elapsed time.
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5.4.4.PO 2
State an appropriate measure and degree of accuracy in a given context.
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5.4.4.PO 3
Measure angles between 0 and 360 degrees.
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5.4.4.PO 4
Solve problems involving the area of 2-dimensional figures by using the properties of parallelograms and triangles.
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5.4.4.PO 5
Solve problems involving area and perimeter of regular and irregular polygons using reallotment of square units.
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5.5
Structure and Logic
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5.5.1
Use reasoning to solve mathematical problems.
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5.5.1.PO 1
Analyze common algorithms for adding and subtracting fractions and decimals using the associative, commutative, and distributive properties.
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5.5.1.PO 2
Develop an algorithm or formula to calculate areas and perimeters of simple polygons.
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5.5.2
Evaluate situations, select problem-solving strategies, draw logical conclusions, develop and describe solutions, and recognize their applications.
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5.5.2.PO 1
Analyze a problem situation to determine the question(s) to be answered.
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5.5.2.PO 2
Identify relevant, missing, and extraneous information related to the solution to a problem.
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5.5.2.PO 3
Select and use one or more strategies to efficiently solve the problem and justify the selection.
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5.5.2.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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5.5.2.PO 5
Represent a problem situation using any combination of words, numbers, pictures, physical objects, or symbols.
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5.5.2.PO 6
Summarize mathematical information, explain reasoning, and draw conclusions.
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5.5.2.PO 7
Analyze and evaluate whether a solution is reasonable, is mathematically correct, and answers the question.
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5.5.2.PO 8
Make and test conjectures based on data or information collected from explorations and experiments.
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5.5.2.PO 9
Identify simple valid arguments using if...then statements based on graphic organizers.
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5.5.2.PO 10
Construct if... then statements to generalize rules for computation, geometric properties and algebraic functions.
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