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5.1
Number, Number Sense and Operations
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5.1.A
Represent and compare numbers less than 0 through familiar applications and extending the number line.
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5
Meaning of Operations
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5.1.A.6
Represent and compare numbers less than 0 by extending the number line and using familiar applications; e.g., temperature, owing money.
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5.1.B
Compare, order and convert among fractions, decimals and percents.
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5
Number and Number Systems
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5.1.B.1
Use models and visual representation to develop the concept of ratio as part-to-part and part-to-whole, and the concept of percent as part-to-whole.
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5.1.B.2
Use various forms of "one" to demonstrate the equivalence of fractions; e.g., 8/24 = 9/12 x 2/2 = 3/4 x 6/6.
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5.1.B.3
Identify and generate equivalent forms of fractions, decimals and percents.
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5.1.C
Develop meaning for percents, including percents greater than 100 and less than 1.
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5.1.D
Use models and pictures to relate concepts of ratio, proportion and percent.
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5
Number and Number Systems
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5.1.D.1
Use models and visual representation to develop the concept of ratio as part-to-part and part-to-whole, and the concept of percent as part-to-whole.
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5.1.E
Use order of operations, including use of parenthesis and exponents to solve multi-step problems, and verify and interpret the results.
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5
Meaning of Operations
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5.1.E.9
Use order of operations, including use of parentheses, to simplify numerical expressions.
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5.1.F
Apply number system properties when performing computations.
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5
Meaning of Operations
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5.1.F.7
Use commutative, associative, distributive, identity and inverse properties to simplify and perform computations.
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5.1.F.8
Identify and use relationships between operations to solve problems.
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5.1.G
Apply and explain the use of prime factorizations, common factors, and common multiples in problem situations.
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5
Number and Number Systems
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5.1.G.5
Recognize and identify perfect squares and their roots.
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5.1.H
Use and analyze the steps in standard and non-standard algorithms for computing with fractions, decimals and integers.
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5
Meaning of Operations
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5.1.H.10
Justify why fractions need common denominators to be added or subtracted.
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5.1.H.11
Explain how place value is related to addition and subtraction of decimals; e.g., 0.2 + 0.14; the two tenths is added to the one tenth because they are both tenths.
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5.1.I
Use a variety of strategies, including proportional reasoning, to estimate, compute, solve and explain solutions to problems involving integers, fractions, decimals and percents.
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5
Number and Number Systems
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5.1.I.4
Round decimals to a given place value and round fractions (including mixed numbers) to the nearest half.
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5
Computation and Estimation
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5.1.I.12
Use physical models, points of reference, and equivalent forms to add and subtract commonly used fractions with like and unlike denominators and decimals.
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5.1.I.13
Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies.
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5.2
Measurement
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5.2.A
Select appropriate units to measure angles, circumference, surface area, mass and volume, using:
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5
Measurement Units
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5.2.A.1
Identify and select appropriate units to measure angles; i.e., degrees.
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5.2.B
Convert units of length, area, volume, mass and time within the same measurement system.
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5
Use Measurement Techniques and Tools
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5.2.B.5
Make conversions within the same measurement system while performing computations.
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5.2.C
Identify appropriate tools and apply appropriate techniques for measuring angles, perimeter or circumference and area of triangles, quadrilaterals, circles and composite shapes, and surface area and volume of prisms and cylinders.
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5
Use Measurement Techniques and Tools
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5.2.C.6
Use strategies to develop formulas for determining perimeter and area of triangles, rectangles and parallelograms, and volume of rectangular prisms.
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5.2.C.7
Use benchmark angles (e.g.; 45°, 90°, 120°) to estimate the measure of angles, and use a tool to measure and draw angles.
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5.2.D
Select a tool and measure accurately to a specified level of precision.
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5.2.E
Use problem solving techniques and technology as needed to solve problems involving length, weight, perimeter, area, volume, time and temperature.
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5
Measurement Units
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5.2.E.2
Identify paths between points on a grid or coordinate plane and compare the lengths of the paths; e.g., shortest path, paths of equal length.
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5.2.F
Analyze and explain what happens to area and perimeter or surface area and volume when the dimensions of an object are changed.
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5
Measurement Units
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5.2.F.3
Demonstrate and describe the differences between covering the faces (surface area) and filling the interior (volume) of three-dimensional objects.
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5.2.F.4
Demonstrate understanding of the differences among linear units, square units and cubic units.
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5.2.G
Understand and demonstrate the independence of perimeter and area for two-dimensional shapes and of surface area and volume for three-dimensional shapes.
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5
Measurement Units
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5.2.G.3
Demonstrate and describe the differences between covering the faces (surface area) and filling the interior (volume) of three-dimensional objects.
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5.2.G.4
Demonstrate understanding of the differences among linear units, square units and cubic units.
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5.3
Geometry and Spatial Sense
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5.3.A
Identify and label angle parts and the regions defined within the plane where the angle resides.
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5
Characteristics and Properties
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5.3.A.2
Use standard language to describe line, segment, ray, angle, skew, parallel and perpendicular.
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5.3.A.3
Label vertex, rays, interior and exterior for an angle.
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5.3.B
Draw circles, and identify and determine the relationships among the radius, diameter, center and circumference.
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5
Characteristics and Properties
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5.3.B.1
Draw circles, and identify and determine relationships among the radius, diameter, center and circumference; e.g., radius is half the diameter, the ratio of the circumference of a circle to its diameter is an approximation of pi.
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5.3.C
Specify locations and plot ordered pairs on a coordinate plane.
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5
Spatial Relationships
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5.3.C.6
Extend understanding of coordinate system to include points whose x or y values may be negative numbers.
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5.3.D
Identify, describe and classify types of line pairs, angles, two-dimensional figures and three-dimensional objects using their properties.
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5
Characteristics and Properties
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5.3.D.2
Use standard language to describe line, segment, ray, angle, skew, parallel and perpendicular.
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5.3.D.5
Use physical models to determine the sum of the interior angles of triangles and quadrilaterals.
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5
Visualization and Geometric Models
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5.3.D.7
Understand that the measure of an angle is determined by the degree of rotation of an angle side rather than the length of either side.
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5.3.E
Use proportions to express relationships among corresponding parts of similar figures.
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5.3.F
Describe and use the concepts of congruence, similarity and symmetry to solve problems.
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5
Characteristics and Properties
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5.3.F.4
Describe and use properties of congruent figures to solve problems.
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5.3.G
Describe and use properties of triangles to solve problems involving angle measures and side lengths of right triangles.
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5
Characteristics and Properties
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5.3.G.5
Use physical models to determine the sum of the interior angles of triangles and quadrilaterals.
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5.3.H
Predict and describe results (size, position, orientation) of transformations of two-dimensional figures.
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5.3.I
Identify and draw three-dimensional objects from different views (top, side, front and perspective).
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5
Visualization and Geometric Models
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5.3.I.8
Predict what three-dimensional object will result from folding a two-dimensional net, then confirm the prediction by folding the net.
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5.3.J
Apply properties of equality and proportionality to solve problems involving congruent or similar figures; e.g., create a scale drawing.
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5
Characteristics and Properties
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5.3.J.4
Describe and use properties of congruent figures to solve problems.
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5.4
Patterns, Functions and Algebra
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5.4.A
Describe, extend and determine the rule for patterns and relationships occurring in numeric patterns, computation, geometry, graphs and other applications.
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5
Use Patterns, Relations and Functions
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5.4.A.1
Justify a general rule for a pattern or a function by using physical materials, visual representations, words, tables or graphs.
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5.4.A.2
Use calculators or computers to develop patterns, and generalize them using tables and graphs.
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5.4.B
Represent, analyze and generalize a variety of patterns and functions with tables, graphs, words and symbolic rules.
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5
Use Algebraic Representation
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5.4.B.3
Use variables as unknown quantities in general rules when describing patterns and other relationships.
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5.4.C
Use variables to create and solve equations and inequalities representing problem situations.
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5
Use Algebraic Representation
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5.4.C.4
Create and interpret the meaning of equations and inequalities representing problem situations.
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5.4.D
Use symbolic algebra to represent and explain mathematical relationships.
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5.4.E
Use rules and variables to describe patterns, functions and other relationships.
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5
Use Algebraic Representation
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5.4.E.3
Use variables as unknown quantities in general rules when describing patterns and other relationships.
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5.4.F
Use representations, such as tables, graphs and equations, to model situations and to solve problems, especially those that involve linear relationships.
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5
Use Algebraic Representation
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5.4.F.5
Model problems with physical materials and visual representations, and use models, graphs and tables to draw conclusions and make predictions.
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5.4.G
Write, simplify and evaluate algebraic expressions.
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5
Use Algebraic Representation
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5.4.G.3
Use variables as unknown quantities in general rules when describing patterns and other relationships.
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5.4.H
Solve linear equations and inequalities symbolically, graphically and numerically.
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5.4.I
Explain how inverse operations are used to solve linear equations.
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5.4.J
Use formulas in problem-solving situations.
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5.4.K
Graph linear equations and inequalities.
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5
Use Algebraic Representation
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5.4.K.5
Model problems with physical materials and visual representations, and use models, graphs and tables to draw conclusions and make predictions.
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5.4.L
Analyze functional relationships, and explain how a change in one quantity results in a change in the other.
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5
Analyze Change
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5.4.L.6
Describe how the quantitative change in a variable affects the value of a related variable; e.g., describe how the rate of growth varies over time, based upon data in a table or graph.
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5.4.M
Approximate and interpret rates of change from graphical and numerical data.
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5.5
Data Analysis and Probability
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5.5.A
Read, create and use line graphs, histograms, circle graphs, box-and-whisker plots, stem-and-leaf plots, and other representations when appropriate.
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5
Data Collection
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5.5.A.1
Read, construct and interpret frequency tables, circle graphs and line graphs.
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5.5.B
Interpret data by looking for patterns and relationships, draw and justify conclusions, and answer related questions.
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5.5.C
Evaluate interpretations and conclusions as additional data are collected, modify conclusions and predictions, and justify new findings.
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5
Data Collection
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5.5.C.5
Modify initial conclusions, propose and justify new interpretations and predictions as additional data are collected.
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5.5.D
Compare increasingly complex displays of data, such as multiple sets of data on the same graph.
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5
Data Collection
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5.5.D.3
Read and interpret increasingly complex displays of data, such as double bar graphs.
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5.5.E
Collect, organize, display and interpret data for a specific purpose or need.
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5
Data Collection
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5.5.E.2
Select and use a graph that is appropriate for the type of data to be displayed; e.g., numerical vs. categorical data, discrete vs. continuous data.
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5.5.E.4
Determine appropriate data to be collected to answer questions posed by students or teacher, collect and display data, and clearly communicate findings.
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5.5.F
Determine and use the range, mean, median and mode to analyze and compare data, and explain what each indicates about the data.
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5
Statistical Methods
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5.5.F.6
Determine and use the range, mean, median and mode, and explain what each does and does not indicate about the set of data.
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5.5.G
Evaluate conjectures and predictions based upon data presented in tables and graphs, and identify misuses of statistical data and displays.
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5.5.H
Find all possible outcomes of simple experiments or problem situations, using methods such as lists, arrays and tree diagrams.
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5
Probability
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5.5.H.7
List and explain all possible outcomes in a given situation.
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5.5.I
Describe the probability of an event using ratios, including fractional notation.
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5
Probability
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5.5.I.8
Identify the probability of events within a simple experiment, such as three chances out of eight.
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5.5.I.9
Use 0,1 and ratios between 0 and 1 to represent the probability of outcomes for an event, and associate the ratio with the likelihood of the outcome.
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5.5.J
Compare experimental and theoretical results for a variety of simple experiments.
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5
Probability
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5.5.J.10
Compare what should happen (theoretical/expected results) with what did happen (experimental/actual results) in a simple experiment.
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5.5.K
Make and justify predictions based on experimental and theoretical probabilities.
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5
Probability
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5.5.K.11
Make predictions based on experimental and theoretical probabilities.
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5.6
Mathematical Processes
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5.6.A
Clarify problem-solving situation and identify potential solution processes; e.g., consider different strategies and approaches to a problem, restate problem from various perspectives.
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5.6.B
Apply and adapt problem-solving strategies to solve a variety of problems, including unfamiliar and non-routine problem situations.
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5.6.C
Use more than one strategy to solve a problem, and recognize there are advantages associated with various methods.
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5.6.D
Recognize whether an estimate or an exact solution is appropriate for a given problem situation.
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5.6.E
Use deductive thinking to construct informal arguments to support reasoning and to justify solutions to problems.
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5.6.F
Use inductive thinking to generalize a pattern of observations for particular cases, make conjectures, and provide supporting arguments for conjectures.
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5.6.G
Relate mathematical ideas to one another and to other content areas; e.g., use area models for adding fractions, interpret graphs in reading, science and social studies.
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5.6.H
Use representations to organize and communicate mathematical thinking and problem solutions.
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5.6.I
Select, apply, and translate among mathematical representations to solve problems; e.g., representing a number as a fraction, decimal or percent as appropriate for a problem.
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5.6.J
Communicate mathematical thinking to others and analyze the mathematical thinking and strategies of others.
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5.6.K
Recognize and use mathematical language and symbols when reading, writing and conversing with others.
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