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5.N
Number and Operations
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5
Students will understand numerical concepts and mathematical operations.
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5.N.1
Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
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5.N.1.1
Compare and order using concrete or illustrated models:
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5.N.1.1.a
whole numbers (to millions)
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5.N.1.1.b
common fractions (halves, thirds, fourths, eighths)
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5.N.1.1.c
decimals (thousandths)
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5.N.1.2
Demonstrate understanding of the magnitude of the value of numbers from thousandths to millions, including common fractions.
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5.N.1.3
Represent place value using concrete or illustrated models up to one billion (1,000,000,000).
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5.N.1.4
Interpret percents as part of a hundred (i.e., find decimal and percent equivalents for common fractions, explain how they represent the same value, and compute a given percent of a whole number).
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Ratios, proportions, and percents: What percentage is illustrated? (Fifth grade - U.8)
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Ratios, proportions, and percents: Convert between percents, fractions, and decimals (Fifth grade - U.9)
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Ratios, proportions, and percents: Percent of a number (Fifth grade - U.10)
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Ratios, proportions, and percents: Percent of a number: word problems (Fifth grade - U.11)
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Ratios, proportions, and percents: Compare percentages (Fifth grade - U.12)
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5.N.1.5
Identify and represent on a number line decimals, fractions, and mixed numbers.
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5.N.1.6
Identify prime and composite numbers to 50.
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5.N.2
Understand the meaning of operations and how they relate to one another.
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5.N.2.1
Explain and perform whole number division and express remainders as a whole number or a fractional part as appropriate to the context of real-life problems.
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5.N.2.2
Add and subtract decimals.
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5.N.2.3
Add and subtract fractions and mixed numbers without regrouping and express answers in simplest form.
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5.N.2.4
Find the factors and multiples of whole numbers.
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5.N.2.5
Use arithmetic operations and inverse relationships to represent and solve real-world problems.
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5.N.2.6
Identify and represent on a number line decimals, fractions, and mixed numbers.
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5.N.2.7
Demonstrate proficiency with division, including one- and two-digit divisors.
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5.N.2.8
Solve simple problems involving the addition and subtraction of fractions and mixed numbers.
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5.N.2.9
Represent and use fractions and decimals in equivalent forms.
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5.N.3
Compute fluently and make reasonable estimates.
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5.N.3.1
Add, subtract, multiply, and divide whole numbers.
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5.N.3.2
Add and subtract decimals.
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5.N.3.3
Use estimation strategies to verify the reasonableness of calculated results.
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5.N.3.4
Explain how the estimation strategy impacts the result.
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5.N.3.5
Relate the basic arithmetic operations to one another (e.g., multiplication and division are inverse operations).
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5.N.3.6
Simplify numerical expressions using order of operations.
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5.N.3.7
Recognize and explain the differences between exact and approximate values.
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5.A
Algebra
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5
Students will understand algebraic concepts and applications.
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5.A.1
Understand patterns, relations, and functions.
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5.A.1.1
Identify and graph ordered pairs in the first quadrant of the coordinate plane.
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5.A.1.2
Describe, represent, and analyze patterns and relationships.
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5.A.1.3
Identify, describe, and continue patterns presented in a variety of formats (e.g., numeric, visual, oral, written, kinesthetic, pictorial).
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5.A.1.4
Generate a pattern using a written description.
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5.A.2
Represent and analyze mathematical situations and structures using algebraic symbols.
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5.A.2.1
Compute the value of the expression for specific numerical values of the variable.
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5.A.2.2
Use a letter to represent an unknown number.
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5.A.2.3
Understand the differences between the symbols for 'less than', 'less than or equal to', 'greater than', and 'greater than or equal to'.
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5.A.3
Use mathematical models to represent and understand quantitative relationships.
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5.A.3.1
Use mathematical models to represent and explain mathematical concepts and procedures.
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5.A.3.2
Understand and use mathematical models such as:
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5.A.3.2.a
the number line to model the relationship between rational numbers and rational number operations
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5.A.3.2.b
pictorial representation of addition and subtraction of rational numbers with regrouping
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5.A.3.2.c
manipulatives or pictures to model computational procedures
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5.A.3.2.d
graphs, tables, and charts to describe data
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Data, charts, and graphs: Read a table (Fifth grade - R.1)
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Data, charts, and graphs: Line graphs (Fifth grade - R.2)
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Data, charts, and graphs: Bar graphs (Fifth grade - R.3)
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Data, charts, and graphs: Pictographs (Fifth grade - R.4)
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Data, charts, and graphs: Frequency charts (Fifth grade - R.5)
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Data, charts, and graphs: Stem-and-leaf plots (Fifth grade - R.6)
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Data, charts, and graphs: Circle graphs (Fifth grade - R.7)
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Data, charts, and graphs: Histograms (Fifth grade - R.8)
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Data, charts, and graphs: Choose the best type of graph (Fifth grade - R.9)
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5.A.3.2.e
diagrams or pictures to model problem situations
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5.A.3.3
Demonstrate how a situation can be represented in more than one way.
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5.A.4
Analyze changes in various contexts.
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5.A.4.1
Recognize and create patterns of change from everyday life using numerical or pictorial representations.
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5.A.4.2
Generalize patterns of change and recognize the same general patterns presented in different representations.
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5.G
Geometry
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5
Students will understand geometric concepts and applications.
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5.G.1
Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematics arguments about geometric relationships.
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5.G.1.1
Identify, describe, and classify two-dimensional shapes and three-dimensional figures by their properties.
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5.G.1.2
Recognize and describe properties of regular polygons having up to ten sides.
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5.G.1.3
Identify faces, edges, and bases on three-dimensional objects.
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5.G.2
Specify locations and describe spatial relationships using coordinate geometry and other representational systems.
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5.G.2.1
Recognize perpendicular and parallel lines.
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5.G.3
Apply transformations and use symmetry to analyze mathematical situations.
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5.G.3.1
Identify line of symmetry in simple geometric figures.
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5.G.4
Use visualization, spatial reasoning, and geometric modeling to solve problems.
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5.G.4.1
Understand and compute the perimeter of regular polygons.
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5.G.4.2
Identify and explain circumference, radius, and diameter.
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5.M
Measurement
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5
Students will understand measurement systems and applications.
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5.M.1
Understand measurable attributes of objects and the units, systems, and processes of measurement.
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5.M.1.1
Understand properties (e.g., length, area, weight, volume) and select the appropriate type of unit for measuring each using both U.S. customary and metric systems.
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5.M.1.2
Select and use appropriate units and tools to measure according to the degree of accuracy required in a particular problem-solving situation.
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5.M.1.3
Solve problems involving linear measurement, weight, and capacity (e.g., measuring to the nearest sixteenth of an inch or nearest millimeter; using ounces, milliliters, or pounds and kilograms) to the appropriate degree of accuracy.
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5.M.1.4
Perform one-step conversions within a system of measurement (e.g., inches to feet, centimeters to meters).
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5.M.2
Apply appropriate techniques, tools, and formulas to determine measurements.
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5.M.2.1
Solve measurement problems using appropriate tools involving length, perimeter, weight, capacity, time, and temperature.
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5.M.2.2
Select and use strategies to estimate measurements including length, distance, capacity, and time.
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5.M.2.3
Apply strategies and use tools for estimating and measuring the perimeter of regular and irregular shapes.
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5.D
Data Analysis and Probability
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5
Students will understand how to formulate questions, analyze data, and determine probabilities.
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5.D.1
Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.
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5.D.1.1
Construct, read, analyze, and interpret tables, charts, graphs, and data plots.
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5.D.1.2
Construct, interpret, and analyze data from graphical representations and draw simple conclusions using bar graphs, line graphs, circle graphs, frequency tables, and Venn diagrams.
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Data, charts, and graphs: Line graphs (Fifth grade - R.2)
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Data, charts, and graphs: Bar graphs (Fifth grade - R.3)
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Data, charts, and graphs: Pictographs (Fifth grade - R.4)
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Data, charts, and graphs: Frequency charts (Fifth grade - R.5)
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Data, charts, and graphs: Stem-and-leaf plots (Fifth grade - R.6)
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Data, charts, and graphs: Circle graphs (Fifth grade - R.7)
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Data, charts, and graphs: Histograms (Fifth grade - R.8)
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5.D.1.3
Display, analyze, compare, and interpret different data sets, including data sets of different sizes.
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5.D.1.4
Organize and display single-variable data in appropriate graphs and representations.
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5.D.1.5
Organize, read, and display numerical (quantitative) and non-numerical (qualitative) data in a clear, organized, and accurate manner including correct titles, labels, and intervals or categories including:
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5.D.1.5.a
frequency tables
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5.D.1.5.b
stem and leaf plots
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5.D.1.5.c
bar, line, and circle graphs
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5.D.1.5.d
Venn diagrams
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5.D.1.5.e
pictorial displays
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5.D.1.5.f
charts and tables
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5.D.1.6
Formulate questions and identify data to be collected to correctly answer a question.
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5.D.2
Select and use appropriate statistical methods to analyze data.
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5.D.2.1
Organize and display single-variable data in appropriate graphs and representations and determine which types of graphs are appropriate for various data sets.
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5.D.2.2
Use fractions and percentages to compare data sets of different sizes.
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5.D.2.3
Correctly rank the values of a numerical data set containing simple fractions and decimals, identify maximum and minimum data values, and calculate the range for a data set.
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5.D.3
Develop and evaluate inferences and predictions that are based on data.
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5.D.3.1
Make and justify valid inferences, predictions, and arguments based on statistical analysis.
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5.D.3.2
Compare a given prediction with the results of an investigation.
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5.D.3.3
Use counting strategies to determine all the possible outcomes of a particular familiar event.
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5.D.3.4
Find all possible outcome sets involving four or more sets of objects.
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5.D.3.5
Evaluate the reasonableness of inferences that are based on data in the context of the original solution.
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5.D.3.6
Identify the method used to make an inference and/or a prediction on a given data set and solve similar problems.
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5.D.3.7
Determine the accuracy of a prediction or an inference based on the accuracy of the data in a given data set.
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5.D.3.8
List all possible outcomes of simple events.
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5.D.4
Understand and apply basic concepts of probability.
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5.D.4.1
Determine probabilities through experiments and/or simulations and compare the results with mathematical expressions.
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5.D.4.2
Make predictions from the results of student-generated experiments of single events.
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5.D.4.3
Identify simple experiments where the probabilities of all outcomes are equal.
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5.D.4.4
Describe and predict the results of a probability experiment.
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5.D.4.5
Use fractions to describe the results of an experiment.
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5.D.4.6
Use probability to generalize from a simple pattern or set of examples and justify why the generalization is reasonable.
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