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5.1
Number and Operations
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5.1.1
Understand numbers, ways of representing numbers, relationships among numbers, and number systems
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5.1.1.A
Read, write and compare numbers
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5.1.1.A.1
read, write, compare and order unit fractions and decimals to thousandths
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5.1.1.B
Represent and use rational numbers
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5.1.1.B.1
recognize and generate equivalent forms of commonly used fractions, decimals and percents
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Decimals: What decimal number is illustrated? (Fifth grade - C.1)
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Decimals: Equivalent decimals (Fifth grade - C.4)
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Decimals: Convert fractions to decimals (Fifth grade - C.9)
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Decimals: Convert decimals to fractions (Fifth grade - C.10)
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Decimals: Repeating decimals (Fifth grade - C.12)
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Fractions and mixed numbers: Equivalent fractions (Fifth grade - L.2)
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Fractions and mixed numbers: Reduce fractions to simplest form (Fifth grade - L.3)
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Fractions and mixed numbers: Convert between improper fractions and mixed numbers (Fifth grade - L.4)
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Fractions and mixed numbers: Least common denominator (Fifth grade - L.5)
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Ratios, proportions, and percents: Proportions (Fifth grade - U.5)
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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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5.1.1.C
Compose and decompose numbers
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5.1.1.C.1
recognize equivalent representations for the same number and generate them by decomposing and composing numbers
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5.1.1.D
Classify and describe numeric relationships
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5.1.1.D.1
describe numbers according to their characteristics, including whole number factors, prime or composite, odd or even and square numbers
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5.1.2
Understand meanings of operations and how they relate to one another
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5.1.2.A
Represent operations
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5.1.2.A.1
represent and recognize division using various models, including quotative and partitive
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5.1.2.B
Describe effects of operations
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5.1.2.B.1
describe the effects of multiplying and dividing whole numbers as well as the relationship between the two operations
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5.1.2.C
Apply properties of operations
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5.1.2.C.1
apply the distributive and associative properties to whole numbers
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5.1.3
Compute fluently and make reasonable estimates
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5.1.3.A
Describe or represent mental strategies
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5.1.3.A.1
describe a mental strategy used to compute a given division problem, where the quotient is a multiple of 10 and the divisor is a 1-digit number (e.g., 350 /7)
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5.1.3.C
Compute problems
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5.1.3.C.1
apply and describe the strategy used to compute a given division problem up to a 3-digit by 2-digit
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5.1.3.D
Estimate and justify solutions
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5.1.3.D.1
estimate and justify the results of division of whole numbers
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5.2
Algebraic Relationships
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5.2.1
Understand patterns, relations, and functions
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5.2.1.A
Recognize and extend patterns
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5.2.1.A.1
make and describe generalizations about geometric and numeric patterns
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5.2.1.B
Create and analyze patterns
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5.2.1.B.1
represent and analyze patterns using words, tables and graphs
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5.2.2
Represent and analyze mathematical situations and structures using algebraic symbols
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5.2.2.A
Represent mathematical situations
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5.2.2.A.1
represent a mathematical situation as an expression or number sentence using a letter or symbol
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5.2.2.B
Describe and use mathematical manipulation
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5.2.2.B.1
apply the distributive and associative properties to whole numbers
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5.2.3
Use mathematical models to represent and understand quantitative relationships
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5.2.3.A
Use mathematical models
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5.2.3.A.1
model problem situations and draw conclusions, using representations such as graphs, tables or number sentence
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Problem solving: Use Venn diagrams to solve problems (Fifth grade - J.5)
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Multiply fractions: Multiply fractions by whole numbers: word problems (Fifth grade - N.3)
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Multiply fractions: Multiply fractions - with models (Fifth grade - N.5)
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Multiply fractions: Multiply two fractions: word problems (Fifth grade - N.7)
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Multiply fractions: Multiplication with mixed numbers: word problems (Fifth grade - N.15)
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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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Consumer math: Price lists (Fifth grade - T.1)
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5.2.4
Analyze change in various contexts
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5.2.4.A
Analyze change
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5.2.4.A.1
identify, model and describe situations with constant or varying rates of change
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5.3
Geometric and Spatial Relationships
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5.3.1
Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships
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5.3.1.A
Describe and use geometric relationships
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5.3.1.A.1
analyze 2- and 3-dimensional shapes by describing the attributes
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5.3.1.C
Compose and decompose shapes
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5.3.1.C.1
predict and justify the results of subdividing, combining and transforming shapes
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5.3.2
Specify locations and describe spatial relationships using coordinate geometry and other representational systems
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5.3.2.A
Use coordinate systems
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5.3.2.A.1
use coordinate systems to specify locations, describe paths and find the distance between points along horizontal and vertical lines
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5.3.3
Apply transformations and use symmetry to analyze mathematical situations
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5.3.3.A
Use transformations on objects
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5.3.3.A.1
predict, draw and describe the results of sliding/translating, flipping/reflecting and turning/rotating around a center point of a polygon
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5.3.3.C
Use symmetry
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5.3.3.C.1
identify polygons and designs with rotational symmetry
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5.3.4
Use visualization, spatial reasoning and geometric modeling to solve problems
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5.3.4.A
Recognize and draw three-dimensional representations
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5.3.4.A.1
given a net of a prism or cylinder, identify the 3-dimensional shape
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5.4
Measurement
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5.4.1
Understand measurable attributes of objects and the units, systems and processes of measurement
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5.4.1.A
Determine unit of measurement
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5.4.1.A.1
identify and justify the unit of measure for area (customary and metric)
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5.4.1.B
Identify equivalent measures
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5.4.1.B.1
identify the equivalent weights and equivalent capacities within a system of measurement
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5.4.1.C
Tell and use units of time
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5.4.1.C.1
solve problems involving elapsed time (hours)
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5.4.2
Apply appropriate techniques, tools and formulas to determine measurements
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5.4.2.C
Apply geometric measurements
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5.4.2.C.1
describe how to solve problems involving the area of polygons and nonpolygonal regions imposed on a rectangular grid
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5.4.2.E
Use relationships within a measurement system
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5.4.2.E.1
convert from one unit to another within a system of measurement (linear)
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5.5
Data and Probability
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5.5.1
Formulate questions that can be addressed with data and collect, organize and display relevant data to answer them
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5.5.1.A
Formulate questions
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5.5.1.A.1
evaluate data collection methods
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5.5.1.C
Represent and interpret data
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5.5.1.C.1
describe methods to collect, organize and represent categorical and numerical data
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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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Probability and statistics: Calculate mean, median, mode, and range (Fifth grade - X.1)
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Probability and statistics: Mean, median, mode, and range: find the missing number (Fifth grade - X.2)
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Probability and statistics: Interpret charts to find mean, median, mode, and range (Fifth grade - X.3)
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5.5.2
Select and use appropriate statistical methods to analyze data
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5.5.2.A
Describe and analyze data
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5.5.2.A.1
compare related data sets
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5.5.2.B
Compare data representations
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5.5.2.B.1
compare different representations of the same data and evaluate how well each representation shows important aspects of the data
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5.5.3
Develop and evaluate inferences and predictions that are based on data
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5.5.3.A
Develop and evaluate inferences
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5.5.3.A.1
given a set of data make and justify prediction(s)
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5.5.4
Understand and apply basic concepts of probability
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5.5.4.A
Apply basic concepts of probability
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5.5.4.A.1
describe the degree of likelihood of events using such words as certain, equally likely and impossible
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