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4.1
Number, Number Sense and Operations
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4.1.A
Use place value structure of the base-ten number system to read, write, represent and compare whole numbers and decimals.
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4
Number and Number Systems
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4.1.A.2
Use place value structure of the base-ten number system to read, write, represent and compare whole numbers through millions and decimals through thousandths.
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4.1.A.3
Round whole numbers to a given place value.
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4.1.B
Recognize and generate equivalent representations for whole numbers, fractions and decimals.
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4
Number and Number Systems
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4.1.B.1
Identify and generate equivalent forms of fractions and decimals. For example:
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4.1.B.1.a
Connect physical, verbal and symbolic representations of fractions, decimals and whole numbers; e.g., 1/2, 5/10, "five tenths," 0.5, shaded rectangles with half, and five tenths.
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4.1.B.1.b
Understand and explain that ten tenths is the same as one whole in both fraction and decimal form.
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4.1.C
Represent commonly used fractions and mixed numbers using words and physical models.
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4.1.D
Use models, points of reference and equivalent forms of commonly used fractions to judge the size of fractions and to compare, describe and order them.
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4
Number and Number Systems
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4.1.D.5
Use models and points of reference to compare commonly used fractions.
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4.1.E
Recognize and classify numbers as prime or composite and list factors.
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4
Number and Number Systems
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4.1.E.4
Identify and represent factors and multiples of whole numbers through 100, and classify numbers as prime or composite.
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4.1.F
Count money and make change using both coins and paper bills.
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4
Computation and Estimation
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4.1.F.8
Solve problems involving counting money and making change, using both coins and paper bills.
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4.1.G
Model and use commutative and associative properties for addition and multiplication.
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4.1.H
Use relationships between operations, such as subtraction as the inverse of addition and division as the inverse of multiplication.
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4.1.I
Demonstrate fluency in multiplication facts with factors through 10 and corresponding divisions.
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4
Computation and Estimation
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4.1.I.14
Demonstrate fluency in adding and subtracting whole numbers and in multiplying and dividing whole numbers by 1- and 2-digit numbers and multiples of ten.
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4.1.J
Estimate the results of whole number computations using a variety of strategies, and judge the reasonableness.
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4
Computation and Estimation
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4.1.J.9
Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies.
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4.1.K
Analyze and solve multi-step problems involving addition, subtraction, multiplication and division of whole numbers.
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4
Meaning of Operations
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4.1.K.6
Use associative and distributive properties to simplify and perform computations; e.g., use left to right multiplication and the distributive property to find an exact answer without paper and pencil, such as 5 x 47 = 5 x 40 + 5 x 7 = 200 + 35 = 235.
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4.1.K.7
Recognize that division may be used to solve different types of problem situations and interpret the meaning of remainders; e.g., situations involving measurement, money.
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4
Computation and Estimation
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4.1.K.12
Analyze and solve multi-step problems involving addition, subtraction, multiplication and division using an organized approach, and verify and interpret results with respect to the original problem.
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4.1.L
Use a variety of methods and appropriate tools (mental math, paper and pencil, calculators) for computing with whole numbers.
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4
Computation and Estimation
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4.1.L.11
Develop and explain strategies for performing computations mentally.
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4.1.L.13
Use a variety of methods and appropriate tools for computing with whole numbers; e.g., mental math, paper and pencil, and calculator.
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4.1.L.14
Demonstrate fluency in adding and subtracting whole numbers and in multiplying and dividing whole numbers by 1- and 2-digit numbers and multiples of ten.
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4.1.M
Add and subtract commonly used fractions with like denominators and decimals, using models and paper and pencil.
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4
Computation and Estimation
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4.1.M.9
Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies.
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4.1.M.10
Use physical models, visual representations, and paper and pencil to add and subtract decimals and commonly used fractions with like denominators.
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4.2
Measurement
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4.2.A
Select appropriate units for perimeter, area, weight, volume (capacity), time and temperature, using:
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4
Measurement Units
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4.2.A.3
Identify and select appropriate units to measure:
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4.2.A.3.a
perimeter - string or links (inches or centimeters).
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4.2.A.3.b
area - tiles (square inches or square centimeters).
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4.2.A.3.c
volume - cubes (cubic inches or cubic centimeters).
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4.2.B
Know that the number of units is inversely related to the size of the unit for any item being measured.
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4
Measurement Units
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4.2.B.1
Relate the number of units to the size of the units used to measure an object; e.g., compare the number of cups to fill a pitcher to the number of quarts to fill the same pitcher.
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4
Use Measurement Techniques and Tools
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4.2.B.5
Make simple unit conversions within a measurement system; e.g., inches to feet, kilograms to grams, quarts to gallons.
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4.2.C
Develop common referents for units of measure for length, weight, volume (capacity) and time to make comparisons and estimates.
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4
Measurement Units
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4.2.C.2
Demonstrate and describe perimeter as surrounding and area as covering a two-dimensional shape, and volume as filling a three-dimensional object.
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4.2.D
Identify appropriate tools and apply counting techniques for measuring side lengths, perimeter and area of squares, rectangles, and simple irregular two-dimensional shapes, volume of rectangular prisms, and time and temperature.
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4
Use Measurement Techniques and Tools
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4.2.D.4
Develop and use strategies to find perimeter using string or links, area using tiles or a grid, and volume using cubes; e.g., count squares to find area of regular or irregular shapes on a grid, layer cubes in a box to find its volume.
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4.2.D.6
Write, solve and verify solutions to multi-step problems involving measurement.
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4.2.E
Tell time to the nearest minute.
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4
Measurement Units
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4.3
Geometry and Spatial Sense
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4.3.A
Provide rationale for groupings and comparisons of two-dimensional figures and three-dimensional objects.
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4
Characteristics and Properties
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4.3.A.3
Identify similarities and differences of quadrilaterals; e.g., squares, rectangles, parallelograms and trapezoids.
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4.3.A.4
Identify and define triangles based on angle measures (equiangular, right, acute and obtuse triangles) and side lengths (isosceles, equilateral and scalene triangles).
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4.3.B
Describe and identify points, lines and planes in the environment.
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4
Spatial Relationships
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4.3.B.5
Describe points, lines and planes, and identify models in the environment.
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4.3.C
Describe and identify intersecting, parallel and perpendicular lines or segments in the environment.
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4
Characteristics and Properties
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4.3.C.1
Identify, describe and model intersecting, parallel and perpendicular lines and line segments; e.g., use straws or other material to model lines.
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4.3.D
Identify and draw right, obtuse, acute and straight angles.
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4.3.E
Use attributes to describe, classify and sketch plane figures and build solid objects.
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4
Characteristics and Properties
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4.3.E.2
Describe, classify, compare and model two- and three-dimensional objects using their attributes.
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4
Visualization and Geometric Models
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4.3.E.8
Use geometric models to solve problems in other areas of mathematics, such as number (multiplication/division) and measurement (area, perimeter, border).
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4.3.F
Develop definitions of classes of shapes.
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4
Characteristics and Properties
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4.3.F.3
Identify similarities and differences of quadrilaterals; e.g., squares, rectangles, parallelograms and trapezoids.
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4.3.F.4
Identify and define triangles based on angle measures (equiangular, right, acute and obtuse triangles) and side lengths (isosceles, equilateral and scalene triangles).
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4.3.G
Find and name locations in coordinate systems.
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4
Spatial Relationships
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4.3.G.6
Specify locations and plot ordered pairs on a coordinate plane, using first quadrant points.
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4.3.H
Identify and describe line and rotational symmetry in two-dimensional shapes and designs.
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4.3.I
Describe, identify and model reflections, rotations and translations, using physical materials.
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4
Transformations and Symmetry
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4.3.I.7
Identify, describe and use reflections (flips), rotations (turns), and translations (slides) in solving geometric problems; e.g., use transformations to determine if 2 shapes are congruent.
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4.3.J
Describe a motion or series of transformations that show two shapes are congruent.
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4
Visualization and Geometric Models
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4.3.J.7
Identify, describe and use reflections (flips), rotations (turns), and translations (slides) in solving geometric problems; e.g., use transformations to determine if 2 shapes are congruent.
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4.4
Patterns, Functions and Algebra
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4.4.A
Analyze and extend patterns, and describe the rule in words.
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4
Use Patterns, Relations and Functions
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4.4.A.2
Represent and analyze patterns and functions using words, tables and graphs.
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4.4.B
Use patterns to make predictions, identify relationships, and solve problems.
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4
Use Patterns, Relations and Functions
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4.4.B.1
Use models and words to describe, extend and make generalizations of patterns and relationships occurring in computation, numerical patterns, geometry, graphs and other applications.
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4.4.C
Write and solve open sentences and explain strategies.
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4
Use Algebraic Representations
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4.4.C.5
Represent mathematical relationships with equations or inequalities.
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4.4.D
Represent an unknown quantity as a variable using a symbol, including letters.
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4
Use Patterns, Relations and Functions
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4.4.D.2
Represent and analyze patterns and functions using words, tables and graphs.
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4.4.E
Use variables to create and solve equations representing problem situations.
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4
Use Algebraic Representations
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4.4.E.4
Use rules and variables to describe patterns and other relationships.
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4.4.F
Construct and use a table of values to solve problems associated with mathematical relationships.
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4
Use Algebraic Representations
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4.4.F.3
Construct a table of values to solve problems associated with a mathematical relationship.
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4.4.G
Describe how a change in one variable affects the value of a related variable.
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4
Analyze Change
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4.4.G.6
Describe how a change in one variable affects the value of a related variable; e.g., as one increases the other increases or as one increases the other decreases.
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4.5
Data Analysis and Probability
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4.5.A
Gather and organize data from surveys and classroom experiments, including data collected over a period of time.
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4
Data Collection
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4.5.A.1
Create a plan for collecting data for a specific purpose.
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4.5.B
Read and interpret tables, charts, graphs (bar, picture, line, line plot), and timelines as sources of information, identify main idea, draw conclusions, and make predictions.
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4
Data Collection
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4.5.B.2
Represent and interpret data using tables, bar graphs, line plots and line graphs.
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4.5.B.5
Propose and explain interpretations and predictions based on data displayed in tables, charts and graphs.
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4.5.C
Construct charts, tables and graphs to represent data, including picture graphs, bar graphs, line graphs, line plots and Venn diagrams.
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4
Data Collection
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4.5.C.2
Represent and interpret data using tables, bar graphs, line plots and line graphs.
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4.5.C.3
Interpret and construct Venn diagrams to sort and describe data.
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4.5.C.4
Compare different representations of the same data to evaluate how well each representation shows important aspects of the data, and identify appropriate ways to display the data.
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4.5.D
Read, interpret and construct graphs in which icons represent more than a single unit or intervals greater than one; e.g., each "bicycle picture" = 10 bicycles or the intervals on an axis are multiples of 10.
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4.5.E
Describe data using mode, median and range.
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4
Statistical Methods
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4.5.E.6
Describe the characteristics of a set of data based on a graphical representation, such as range of the data, clumps of data, and holes in the data.
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4.5.E.7
Identify the median of a set of data and describe what it indicates about the data.
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4.5.E.8
Use range, median and mode to make comparisons among related sets of data.
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4.5.F
Conduct a simple probability experiment and draw conclusions about the likelihood of possible outcomes.
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4
Probability
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4.5.F.9
Conduct simple probability experiments and draw conclusions from the results; e.g., rolling number cubes or drawing marbles from a bag.
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4.5.F.10
Represent the likelihood of possible outcomes for chance situations; e.g., probability of selecting a red marble from a bag containing 3 red and 5 white marbles.
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4.5.F.11
Relate the concepts of impossible and certain-to-happen events to the numerical values of 0 (impossible) and 1 (certain).
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4.5.F.12
Place events in order of likelihood and use a diagram or appropriate language to compare the chance of each event occurring; e.g. impossible, unlikely, equal, likely, certain.
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4.5.G
Identify and represent possible outcomes, such as arrangements of a set of up to four members and possible combinations from several sets, each containing 2 or 3 members.
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4
Probability
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4.5.G.13
List and count all possible combinations using one member from each of several sets, each containing 2 or 3 members; e.g., the number of possible outfits from 3 shirts, 2 shorts and 2 pair of shoes.
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4.5.H
Use the set of possible outcomes to describe and predict events.
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4
Probability
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4.5.H.10
Represent the likelihood of possible outcomes for chance situations; e.g., probability of selecting a red marble from a bag containing 3 red and 5 white marbles.
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4.5.H.11
Relate the concepts of impossible and certain-to-happen events to the numerical values of 0 (impossible) and 1 (certain).
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4.6
Mathematical Processes
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4.6.A
Apply and justify the use of a variety of problem-solving strategies; e.g., make an organized list, guess and check.
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4.6.B
Use an organized approach and appropriate strategies to solve multi-step problems.
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4.6.C
Interpret results in the context of the problem being solved; e.g., the solution must be a whole number of buses when determining the number of buses necessary to transport students.
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4.6.D
Use mathematical strategies to solve problems that relate to other curriculum areas and the real world; e.g., use a timeline to sequence events; use symmetry in artwork.
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4.6.E
Link concepts to procedures and to symbolic notation; e.g., model 3 x 4 with a geometric array, represent one-third by dividing an object into three equal parts.
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4.6.F
Recognize relationships among different topics within mathematics; e.g., the length of an object can be represented by a number.
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4.6.G
Use reasoning skills to determine and explain the reasonableness of a solution with respect to the problem situation.
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4.6.H
Recognize basic valid and invalid arguments, and use examples and counter examples, models, number relationships, and logic to support or refute.
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4.6.I
Represent problem situations in a variety of forms (physical model, diagram, in words or symbols), and recognize when some ways of representing a problem may be more helpful than others.
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4.6.J
Read, interpret, discuss and write about mathematical ideas and concepts using both everyday and mathematical language.
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4.6.K
Use mathematical language to explain and justify mathematical ideas, strategies and solutions.
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