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5.1
Numeric Reasoning: Students will develop Numeric Reasoning and an understanding of Number and Operations by solving problems in which there is a need to represent and model real numbers verbally, physically, and symbolically; to explain the relationship between numbers; to determine the relative magnitude of real numbers; to use operations with understanding; and to select appropriate methods of calculations from among mental math, paper-and-pencil, calculators, or computers.
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5.1.1
Number sense
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5.1.1.1
Describe whole numbers up to 100,000 using place value structure
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5.1.1.2
Develop understanding of fractions as parts of unit wholes, as part of a collection, as locations on number lines, and as division of whole numbers
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5.1.1.3
Describe numbers according to characteristics such as evens, odds, factors, multiples, and squares
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5.1.1.4
Find 1/10 or 10 times a number using mental math
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5.1.1.5
Generate and connect equivalent forms of benchmark fractions, decimals and percents
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5.1.1.6
Use multiple models and methods to compare decimals
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5.1.1.7
Use decimal form to represent benchmark fractions (1/3s, 1/4s, 1/5s, 1/10s)
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5.1.1.8
Use multiple methods and models to convert decimals to fractions and fractions to decimals
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5.1.1.9
Develop the meaning of percent as a ratio of a number out of 100
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5.1.1.10
Use a variety of familiar applications to represent positive and negative numbers as opposites
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5.1.2
Operations
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5.1.2.1
Apply more than one operation to solve a word problem
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5.1.2.2
Multiply and divide by large numbers (e.g., two digits by two digits) and show why the operation works
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5.1.2.3
Use multiplication clusters to build mental math strategies (e.g., 5x2, 5x20, 50x2, 50x20)
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5.1.2.4
Use partial products to prove how multiplication algorithms work
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5.1.2.5
Use and apply various meanings of multiplication and division (e.g., fair share, repeated addition/ subtraction, compare, rate)
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5.1.2.6
Develop and use strategies to estimate the results of operations on whole numbers
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5.1.2.7
Add and subtract benchmark fractions and fractions with common denominators using physical models
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5.1.2.8
Multiply fractions by whole numbers using models such as: clock fractions, number/ratio tables, number lines, fractions strips, skip counting or array models
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5.1.2.9
Multiply numbers by 10, 1/10th, 100 and 1/100th using mental math
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5.1.2.10
Connect multiplication by 1/3, 1/4, 1/5 to division by its inverse (3, 4, 5) (e.g., 12 x 1/4 = 12 divided by 4)
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5.1.2.11
Find benchmark percents of numbers using physical models
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5.1.2.12
Add and subtract decimals using models
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5.1.2.13
Add and subtract integers using familiar applications such as sea level, elevators, etc.
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5.1.2.14
Select and use appropriate methods and tools for computing (e.g., mental computation, estimation, calculators, paper and pencil) depending on the context and nature of the computation
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5.2
Algebraic Reasoning: Students will develop Algebraic Reasoning and an understanding of Patterns and Functions by solving problems in which there is a need to recognize and extend a variety of patterns; to progress from the concrete to the abstract using physical models, equations, and graphs; to describe, represent, and analyze relationships among variable quantities; and to analyze, represent, model, and describe real-world functional relationships.
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5.2.1
Patterns and change
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5.2.1.1
Find a given term in an arithmetic sequence
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5.2.1.2
Translate visual patterns into rules
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5.2.1.3
Describe trends in patterns and graphs
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5.2.2
Representations
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5.2.2.1
Model problem situations with objects and use representations such as graphs, tables or equations to draw conclusion
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5.2.3
Symbols
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5.2.3.1
Use equations to express mathematical relationships
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5.2.3.2
Develop an understanding of the Distributive Properties of whole number operations as a tool to solve problems (e.g., is 24 x 32 ever the same as 20 x 30 + 4 x 2?)
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5.3
Geometric Reasoning: Students will develop Geometric Reasoning and an understanding of Geometry and Measurement by solving problems in which there is a need to recognize, construct, transform, analyze properties of, and discover relationships among geometric figures; and to measure to a required degree pf accuracy by selecting appropriate tools and units.
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5.3.1
Classification
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5.3.1.1
Analyze and classify two-dimensional shapes according to their properties and develop definitions for classes of shapes (e.g., a square is a rectangle is a parallelogram is a quadrilateral)
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5.3.1.2
Draw the results of subdividing and combining shapes
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5.3.1.3
Identify and classify angles as acute, right, obtuse, or straight
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5.3.2
Location and transformation
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5.3.2.1
Predict and describe the results of a slide, flip, or turn of two-dimensional shapes
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5.3.2.2
Use the coordinate system to specify locations and to describe paths between locations
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5.3.3
Measurement
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5.3.3.1
Measure and compare objects using standard measures to the nearest 1/2, 1/4 or 1/8th unit
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5.3.3.2
Measure and compare objects using metric units to the nearest 1/10th
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5.3.3.3
Use measuring tools to find the size of turn angles in degrees
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5.3.3.4
Draw benchmark turn angles (30, 45, 60, 90, 180 degrees)
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5.3.3.5
Find the distance around a geometric figure to the nearest 1/2, 1/4 or 1/10th of a unit (perimeter)
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5.3.3.6
Find the number of square units it takes to cover a geometric figure (area)
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5.3.3.7
Find the volume of an object.
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5.3.3.8
Find the mass of an object to the nearest 1/2, 1/4, or 1/10 of a unit
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5.3.3.9
Convert a measurement from feet to inches, or from meters to centimeters
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5.3.3.10
Find elapsed time
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5.4
Quantitative Reasoning: Students will develop Quantitative Reasoning and an understanding of Data Analysis and Probability by solving problems in which there is a need to collect, appropriately represent, and interpret data; to make inferences or predictions and to present convincing arguments; and to model mathematical situations to determine the probability.
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5.4.1
Collect
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5.4.1.1
Pose questions that can be answered with data; systematically collect and organize categorical and numerical/ measurement data
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5.4.2
Represent
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5.4.2.1
Construct and use data displays (e.g., tables, scaled pictographs, line plots, bar graphs) in order to answer a question
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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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5.4.3
Analyze
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5.4.3.1
Compare related data sets noting similarities and differences in the distributions
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5.4.3.2
Find and use measures of center (mean, median, mode) and spread (range) to summarize and interpret data
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5.4.3.3
Identify the typical or average value in a data set as well as any atypical values
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5.4.4
Probability
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5.4.4.1
Conduct a probability experiment, represent the result as a number (fraction, decimal, percent) between 0 and 1, and draw conclusions from the results
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5.4.4.2
List all possible outcomes (i.e. the sample space) for a probability experiment involving a simple event
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