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5.NO
Number and Operations
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5.NO.1
Students shall understand numbers, ways of representing numbers, relationships among numbers and number systems.
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5
Rational Numbers
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5.NO.1.5.1
Use models and visual representations to develop the concepts of the following:
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5.NO.1.5.1.a
Fractions:
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5.NO.1.5.1.a.1
parts of unit wholes
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5.NO.1.5.1.a.2
parts of a collection
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5.NO.1.5.1.a.3
locations on number lines
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5.NO.1.5.1.a.4
locations on ruler (benchmark fractions)
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5.NO.1.5.1.a.5
divisions of whole numbers
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5.NO.1.5.1.b
Ratios:
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5.NO.1.5.1.b.1
part-to-part (2 boys to 3 girls)
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5.NO.1.5.1.b.2
part-to-whole (2 boys to 5 people)
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5.NO.1.5.1.c
Percents:
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5.NO.1.5.1.c.1
part-to-100
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5.NO.1.5.2
Develop understanding of decimal place value using models
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5.NO.1.5.3
Identify decimal and percent equivalents for benchmark fractions
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5.NO.1.5.4
Round and compare decimals to a given place value (whole number, tenths, hundredths)
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5.NO.1.5.5
Use models of benchmark fractions and their equivalent forms:
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5.NO.1.5.5.a
to analyze the size of fractions
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5.NO.1.5.5.b
to determine that simplification does not change the value of the fraction
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5.NO.1.5.5.c
to convert between mixed numbers and improper fractions
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5.NO.1.5.6
Use models to differentiate between perfect squares up to 100 and other numbers
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5.NO.2
Students shall understand meanings of operations and how they relate to one another.
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5
Number Theory
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5.NO.2.5.1
Use divisibility rules to determine if a number is a factor of another number (2, 3, 5, 10)
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5.NO.2.5.2
Identify commutative and associative properties
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5.NO.2.5.3
Identify the distributive property by using physical models to solve computation and real world problems
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5.NO.2.5.4
Apply rules (conventions) for order of operations to whole numbers where the left to right computations are modified only by the use of parentheses
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5
Understand Operations
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5.NO.2.5.5
Model addition, subtraction, and multiplication of fractions with like and unlike denominators and decimals
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5.NO.3
Students shall compute fluently and make reasonable estimates.
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5
Computational Fluency
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5.NO.3.5.1
Develop and use a variety of algorithms with computational fluency to perform whole number operations using addition and subtraction (up to 5 digit numbers), multiplication (up to 3-digit x 2 digit), division (up to 2-digit divisor) interpreting remainders, including real world problems
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5.NO.3.5.2
Develop and use algorithms:
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5.NO.3.5.2.a
to add and subtract numbers containing decimals (up to thousandths place)
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5.NO.3.5.2.b
to multiply decimals (hundredths x tenths)
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5.NO.3.5.2.c
to divide decimals by whole number divisors
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5.NO.3.5.2.d
to add and subtract fractions with like denominators
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5.NO.3.5.3
Solve, with and without appropriate technology, two-step problems using a variety of methods and tools (i.e. objects, mental computation, paper and pencil)
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5
Estimation
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5.NO.3.5.4
Develop and use strategies to Estimate the results of whole number computations and to judge the reasonableness of such results
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5
Application of Computation
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5.NO.3.5.5
Use factors of numbers:
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5.NO.3.5.5.a
to introduce exponents (Ex: 36= 6 x 6 or 62)
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5.NO.3.5.5.b
to find common factors of two numbers
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5.NO.3.5.5.c
to simplify fractions to the lowest terms
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5.A
Algebra
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5.A.4
Students shall recognize, describe and develop patterns, relations and functions.
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5
Patterns, Relations and Functions
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5.A.4.5.1
Solve problems by finding the next term or missing term in a pattern or function table using real world situations
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5.A.4.5.2
Interpret and write a rule for a one-operation function table
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5.A.5
Students shall represent and analyze mathematical situations and structures using algebraic symbols.
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5
Expressions, Equations and Inequalities
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5.A.5.5.1
Model and solve simple equations by informal methods using manipulatives and appropriate technology
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5.A.5.5.2
Write expressions containing one variable (a letter representing an unknown quantity) using rules for addition and subtraction
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5.A.5.5.3
Select, write and evaluate algebraic expressions with one variable by substitution
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5.A.6
Students shall develop and apply mathematical models to represent and understand quantitative relationships.
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5
Algebraic Models and Relationships
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5.A.6.5.1
Draw conclusions and make predictions, with and without appropriate technology, from models, tables and line graphs
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5.A.7
Students shall analyze change in various contexts.
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5
Analyze Change
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5.A.7.5.1
Model and describe quantities that change using real world situations
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5.G
Geometry
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5.G.8
Students shall analyze characteristics and properties of 2 and 3 dimensional geometric shapes and develop mathematical arguments about geometric relationships.
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5
Characteristics of Geometric Shapes
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5.G.8.5.1
Identify and model regular and irregular polygons including decagon
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5.G.8.5.2
Identify and draw congruent, adjacent, obtuse, acute, right and straight angles (Label parts of an angle: vertex, rays, interior and exterior)
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5.G.8.5.3
Model and identify circle, radius, diameter, center, circumference and chord
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5.G.8.5.4
Model and identify the properties of congruent figures
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5.G.9
Students shall apply transformations and the use of symmetry to analyze mathematical situations.
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5
Symmetry and Transformations
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5.G.9.5.1
Predict and describe the results of translation (slide), reflection (flip), rotation (turn), showing that the transformed shape remains unchanged
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5.G.10
Students shall specify locations and describe spatial relationships using coordinate geometry and other representational systems.
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5
Coordinate Geometry
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5.G.10.5.1
Use geometric vocabulary (horizontal/x-axis, vertical/ y-axis, ordered pairs) to describe the location and plot points in Quadrant I
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5.G.11
Students shall use visualization, spatial reasoning and geometric modeling.
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5
Spatial Visualization and Models
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5.G.11.5.1
Using grid paper, draw and identify two-dimensional patterns (nets) for cubes
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5.M
Measurement
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5.M.12
Students shall use attributes of measurement to describe and compare mathematical and real-world objects.
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5
Attributes and Tools
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5.M.12.5.1
Identify and select appropriate units and tools to measure
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5.M.12.5.2
Make conversions within the customary measurement system in real world problems
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5.M.12.5.3
Establish through experience benchmark prefixes of mili-, centi-, and kilo-
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5.M.12.5.4
Understand when to use linear units to describe perimeter, square units to describe area or surface area, and cubic units to describe volume, in real world situations
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5.M.12.5.5
Model the differences between covering the faces (surface area/nets) and filling the interior (volume of cubes)
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5.M.13
Students shall identify and use units, systems and processes of measurement.
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5
Attributes and Tools
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5.M.13.5.1
Solve real world problems involving one elapsed time, counting forward (calendar and clock)
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5.M.13.5.2
Determine which unit of measure or measurement tool matches the context for a problem situation
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5.M.13.5.3
Draw and measure distance to the nearest cm and ΒΌ inch accurately
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5.M.13.5.4
Develop and use strategies to solve real world problems involving perimeter and area of rectangles
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5.M.13.5.5
Count the distance between two points on a horizontal or vertical line and compare the lengths of the paths on a grid
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5.M.13.5.6
Use benchmark angles to estimate the measure of angles
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5.DAP
Data Analysis and Probability
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5.DAP.14
Students shall formulate questions that can be addressed with data and collect, organize and display relevant data to answer them.
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5
Collect, organize and display data
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5.DAP.14.5.1
Develop appropriate questions for surveys
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5.DAP.14.5.2
Collect numerical and categorical data using surveys, observations and experiments that would result in bar graphs, line graphs, line plots and stem-and-leaf plots
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5.DAP.14.5.3
Construct and interpret frequency tables, charts, line plots, stem-and-leaf plots and bar graphs
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5.DAP.15
Students shall select and use appropriate statistical methods to analyze data.
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5
Data Analysis
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5.DAP.15.5.1
Interpret graphs such as line graphs, double bar graphs, and circle graphs
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5.DAP.15.5.2
Determine, with and without appropriate technology, the range, mean, median and mode (whole number data sets) and explain what each indicates about the set of data
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5.DAP.16
Students shall develop and evaluate inferences and predictions that are based on data.
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5
Data Analysis
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5.DAP.16.5.1
Make predictions and justify conclusions based on data
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5.DAP.17
Students shall understand and apply basic concepts of probability.
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5
Data Analysis
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5.DAP.17.5.1
Identify and predict the probability of events within a simple experiment
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5.DAP.17.5.2
List and explain all possible outcomes in a given situation
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