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3.1
Number, Number Sense and Operations
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3.1.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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3
Number and Number Systems
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3.1.A.2
Use place value concepts to represent whole numbers and decimals using numerals, words, expanded notation and physical models. For example:
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3.1.A.2.a
Recognize 100 means "10 tens" as well as a single entity (1 hundred) through physical models and trading games.
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3.1.A.2.b
Describe the multiplicative nature of the number system; e.g., the structure of 3205 as 3 x 1000 plus 2 x 100 plus 5 x 1.
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3.1.A.2.c
Model the size of 1000 in multiple ways; e.g., packaging 1000 objects into 10 boxes of 100, modeling a meter with centimeter and decimeter strips, or gathering 1000 pop-can tabs.
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3.1.A.2.d
Explain the concept of tenths and hundredths using physical models, such as metric pieces, base ten blocks, decimal squares or money.
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3.1.A.3
Use mathematical language and symbols to compare and order; e.g., less than, greater than, at most, at least, <, >, =, "lesser than or equal", "greater than or equal".
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3.1.B
Recognize and generate equivalent representations for whole numbers, fractions and decimals.
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3
Number and Number Systems
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3.1.B.1
Identify and generate equivalent forms of whole numbers; e.g., 36, 30 + 6, 9 x 4, 46 - 10, number of inches in a yard.
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3.1.B.7
Recognize and use decimal and fraction concepts and notations as related ways of representing parts of a whole or a set; e.g., 3 of 10 marbles are red can also be described as 3/10 and 3 tenths are red.
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3.1.C
Represent commonly used fractions and mixed numbers using words and physical models.
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3
Number and Number Systems
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3.1.C.5
Represent fractions and mixed numbers using words, numerals and physical models.
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3.1.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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3
Number and Number Systems
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3.1.D.3
Use mathematical language and symbols to compare and order; e.g., less than, greater than, at most, at least, <, >, =, "less than or equal", "greater than or equal".
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3.1.D.6
Compare and order commonly used fractions and mixed numbers using number lines, models (such as fraction circles or bars), points of reference (such as more or less than ½), and equivalent forms using physical or visual models.
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3.1.E
Recognize and classify numbers as prime or composite and list factors.
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3.1.F
Count money and make change using both coins and paper bills.
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3
Number and Number Systems
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3.1.F.4
Count money and make change using coins and paper bills to ten dollars.
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3.1.G
Model and use commutative and associative properties for addition and multiplication.
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3
Meaning of Operations
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3.1.G.11
Model and use the commutative and associative properties for addition and multiplication.
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3.1.H
Use relationships between operations, such as subtraction as the inverse of addition and division as the inverse of multiplication.
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3
Meaning of Operations
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3.1.H.10
Explain and use relationships between operations, such as:
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3.1.H.10.a
relate addition and subtraction as inverse operations;
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3.1.H.10.b
relate multiplication and division as inverse operations;
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3.1.H.10.c
relate addition to multiplication (repeated addition);
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3.1.H.10.d
relate subtraction to division (repeated subtraction).
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3.1.I
Demonstrate fluency in multiplication facts with factors through 10 and corresponding divisions.
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3
Computation and Estimation
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3.1.I.13
Demonstrate fluency in multiplication facts through 10 and corresponding division facts.
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3.1.J
Estimate the results of whole number computations using a variety of strategies, and judge the reasonableness.
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3
Computation and Estimation
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3.1.J.15
Evaluate the reasonableness of computations based upon operations and the numbers involved; e.g., considering relative size, place value and estimates.
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3.1.K
Analyze and solve multi-step problems involving addition, subtraction, multiplication and division of whole numbers.
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3
Computation and Estimation
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3.1.K.12
Add and subtract whole numbers with and without regrouping.
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3.1.K.14
Multiply and divide 2- and 3-digit numbers by a single-digit number, without remainders for division.
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3.1.L
Use a variety of methods and appropriate tools (mental math, paper and pencil, calculators) for computing with whole numbers.
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3
Meaning of Operations
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3.1.L.8
Model, represent and explain multiplication; e.g., repeated addition, skip counting, rectangular arrays and area model. For example:
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3.1.L.8.a
Use conventional mathematical symbols to write equations for word problems involving multiplication.
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3.1.L.8.b
Understand that, unlike addition and subtraction, the factors in multiplication and division may have different units; e.g., 3 boxes of 5 cookies each.
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3.1.L.9
Model, represent and explain division; e.g., sharing equally, repeated subtraction, rectangular arrays and area model. For example:
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3.1.L.9.a
Translate contextual situations involving division into conventional mathematical symbols.
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3.1.L.9.b
Explain how a remainder may impact an answer in a real-world situation; e.g., 14 cookies being shared by 4 children.
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3.1.M
Add and subtract commonly used fractions with like denominators and decimals, using models and paper and pencil.
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3.2
Measurement
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3.2.A
Select appropriate units for perimeter, area, weight, volume (capacity), time and temperature, using:
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3
Measurement Units
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3.2.A.1
Identify and select appropriate units for measuring:
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3.2.A.1.a
length - miles, kilometers and other units of measure as appropriate.
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3.2.A.1.b
volume (capacity) - gallons;
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3.2.A.1.c
weight - ounces, pounds, grams, or kilograms;
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3.2.A.1.d
temperature - degrees (Fahrenheit or Celsius).
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3.2.A.4
Read thermometers in both Fahrenheit and Celsius scales.
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3.2.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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3.2.C
Develop common referents for units of measure for length, weight, volume (capacity) and time to make comparisons and estimates.
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3
Measurement Units
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3.2.C.2
Establish personal or common referents to include additional units; e.g., a gallon container of milk; a postage stamp is about a square inch.
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3
Use Measurement Techniques and Tools
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3.2.C.5
Estimate and measure length, weight and volume (capacity), using metric and U.S. customary units, accurate to the nearest ½ or ¼ unit as appropriate.
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3.2.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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3
Use Measurement Techniques and Tools
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3.2.D.4
Read thermometers in both Fahrenheit and Celsius scales.
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3.2.D.6
Use appropriate measurement tools and techniques to construct a figure or approximate an amount of specified length, weight or volume (capacity); e.g., construct a rectangle with length 2½ inches and width 3 inches, fill a measuring cup to the ¾ cup mark.
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3.2.D.7
Make estimates for perimeter, area and volume using links, tiles, cubes and other models.
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3.2.E
Tell time to the nearest minute.
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3.2.E.3
Tell time to the nearest minute and find elapsed time using a calendar or a clock.
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3.3
Geometry and Spatial Sense
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3.3.A
Provide rationale for groupings and comparisons of two-dimensional figures and three-dimensional objects.
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3
Characteristics and Properties
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3.3.A.1
Analyze and describe properties of two-dimensional shapes and three-dimensional objects using terms such as vertex, edge, angle, side and face.
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3.3.B
Describe and identify points, lines and planes in the environment.
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3.3.C
Describe and identify intersecting, parallel and perpendicular lines or segments in the environment.
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3.3.D
Identify and draw right, obtuse, acute and straight angles.
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3.3.D.2
Identify and describe the relative size of angles with respect to right angles as follows:
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3.3.D.2.a
Use physical models, like straws, to make different sized angles by opening and closing the sides, not by changing the side lengths.
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3.3.D.2.b
Identify, classify and draw right, acute, obtuse and straight angles.
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3.3.E
Use attributes to describe, classify and sketch plane figures and build solid objects.
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3
Characteristics and Properties
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3.3.E.1
Analyze and describe properties of two-dimensional shapes and three-dimensional objects using terms such as vertex, edge, angle, side and face.
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3
Visualization and Geometric Models
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3.3.E.5
Build a three-dimensional model of an object composed of cubes; e.g., construct a model based on an illustration or actual object.
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3.3.F
Develop definitions of classes of shapes.
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3.3.G
Find and name locations in coordinate systems.
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3
Spatial Relationships
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3.3.G.3
Find and name locations on a labeled grid or coordinate system; e.g., a map or graph.
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3.3.H
Identify and describe line and rotational symmetry in two-dimensional shapes and designs.
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3
Transformations and Symmetry
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3.3.H.4
Draw lines of symmetry to verify symmetrical two-dimensional shapes.
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3.3.I
Describe, identify and model reflections, rotations and translations, using physical materials.
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3.3.J
Describe a motion or series of transformations that show two shapes are congruent.
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3.4
Patterns, Functions and Algebra
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3.4.A
Analyze and extend patterns, and describe the rule in words.
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3
Use Patterns, Relations and Functions
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3.4.A.1
Extend multiplicative and growing patterns, and describe the pattern or rule in words.
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3.4.A.2
Analyze and replicate arithmetic sequences with and without a calculator.
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3.4.B
Use patterns to make predictions, identify relationships, and solve problems.
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3
Use Patterns, Relations and Functions
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3.4.B.3
Use patterns to make predictions, identify relationships, and solve problems.
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3.4.C
Write and solve open sentences and explain strategies.
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3
Use Algebraic Representations
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3.4.C.5
Write, solve and explain simple mathematical statements, such as 7 + "square" > 8 or "triangle" + 8 = 10.
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3.4.C.6
Express mathematical relationships as equations and inequalities.
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3.4.D
Represent an unknown quantity as a variable using a symbol, including letters.
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3.4.E
Use variables to create and solve equations representing problem situations.
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3
Use Algebraic Representations
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3.4.E.4
Model problem situations using objects, pictures, tables, numbers, letters and other symbols.
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3.4.F
Construct and use a table of values to solve problems associated with mathematical relationships.
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3
Analyze Change
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3.4.F.7
Create tables to record, organize and analyze data to discover patterns and rules.
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3.4.G
Describe how a change in one variable affects the value of a related variable.
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3
Analyze Change
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3.4.G.8
Identify and describe quantitative changes, especially those involving addition and subtraction; e.g., the height of water in a glass becoming 1 centimeter lower each week due to evaporation.
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3.5
Data Analysis and Probability
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3.5.A
Gather and organize data from surveys and classroom experiments, including data collected over a period of time.
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3
Data Collection
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3.5.A.1
Collect and organize data from an experiment, such as recording and classifying observations or measurements, in response to a question posed.
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3.5.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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3
Data Collection
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3.5.B.4
Support a conclusion or prediction orally and in writing, using information in a table or graph.
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3.5.B.5
Match a set of data with a graphical representation of the data.
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3.5.B.7
Analyze and interpret information represented on a timeline.
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3.5.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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3
Data Collection
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3.5.C.6
Translate information freely among charts, tables, line plots, picture graphs and bar graphs; e.g., create a bar graph from the information in a chart.
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3.5.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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3
Data Collection
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3.5.D.2
Draw and interpret picture graphs in which a symbol or picture represents more than one object.
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3.5.D.3
Read, interpret and construct bar graphs with intervals greater than one.
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3.5.E
Describe data using mode, median and range.
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3
Statistical Methods
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3.5.E.8
Identify the mode of a data set and describe the information it gives about a data set.
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Probability and statistics: Median, mode, and range (Second grade - V.3)
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Probability and statistics: Interpret graphs to find median, mode, and range (Second grade - V.4)
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Probability and statistics: Mean, median, mode, and range (Third grade - S.2)
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Probability and statistics: Interpret charts to find mean, median, mode, and range (Third grade - S.3)
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3.5.F
Conduct a simple probability experiment and draw conclusions about the likelihood of possible outcomes.
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3
Probability
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3.5.F.9
Conduct a simple experiment or simulation of a simple event, record the results in a chart, table or graph, and use the results to draw conclusions about the likelihood of possible outcomes.
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3.5.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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3
Probability
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3.5.G.10
Use physical models, pictures, diagrams and lists to solve problems involving possible arrangements or combinations of two to four objects.
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3.5.H
Use the set of possible outcomes to describe and predict events.
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3.6
Mathematical Processes
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3.6.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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3.6.B
Use an organized approach and appropriate strategies to solve multi-step problems.
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3.6.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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3.6.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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3.6.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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3.6.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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3.6.G
Use reasoning skills to determine and explain the reasonableness of a solution with respect to the problem situation.
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3.6.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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3.6.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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3.6.J
Read, interpret, discuss and write about mathematical ideas and concepts using both everyday and mathematical language.
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3.6.K
Use mathematical language to explain and justify mathematical ideas, strategies and solutions.
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