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6.PS
Problem Solving
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Students will build new mathematical knowledge through problem solving.
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6.PS.1
Know the difference between relevant and irrelevant information when solving problems
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6.PS.2
Understand that some ways of representing a problem are more efficient than others
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6.PS.3
Interpret information correctly, identify the problem, and generate possible strategies and solutions
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Students will solve problems that arise in mathematics and in other contexts.
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6.PS.4
Act out or model with manipulatives activities involving mathematical content from literature
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6.PS.5
Formulate problems and solutions from everyday situations
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6.PS.6
Translate from a picture/diagram to a numeric expression
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6.PS.7
Represent problem situations verbally, numerically, algebraically, and/or graphically
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6.PS.8
Select an appropriate representation of a problem
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6.PS.9
Understand the basic language of logic in mathematical situations (and, or, and not)
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Students will apply and adapt a variety of appropriate strategies to solve problems.
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6.PS.10
Work in collaboration with others to solve problems
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6.PS.11
Translate from a picture/diagram to a number or symbolic expression
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6.PS.12
Use trial and error and the process of elimination to solve problems
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6.PS.13
Model problems with pictures/diagrams or physical objects
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6.PS.14
Analyze problems by observing patterns
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6.PS.15
Make organized lists or charts to solve numerical problems
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Students will monitor and reflect on the process of mathematical problem solving.
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6.PS.16
Discuss with peers to understand a problem situation
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6.PS.17
Determine what information is needed to solve problem
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6.PS.18
Determine the efficiency of different representations of a problem
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6.PS.19
Differentiate between valid and invalid approaches
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6.PS.20
Understand valid counterexamples
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6.PS.21
Explain the methods and reasoning behind the problem solving strategies used
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6.PS.22
Discuss whether a solution is reasonable in the context of the original problem
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6.PS.23
Verify results of a problem
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6.RP
Reasoning and Proof
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Students will recognize reasoning and proof as fundamental aspects of mathematics.
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6.RP.1
Recognize that mathematical ideas can be supported using a variety of strategies
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6.RP.2
Understand that mathematical statements can be supported, using models, facts, and relationships to explain their thinking
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Students will make and investigate mathematical conjectures.
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6.RP.3
Investigate conjectures, using arguments and appropriate mathematical terms
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6.RP.4
Make and evaluate conjectures, using a variety of strategies
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Students will develop and evaluate mathematical arguments and proofs.
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6.RP.5
Justify general claims or conjectures, using manipulatives, models, expressions, and mathematical relationships
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6.RP.6
Develop and explain an argument verbally, numerically, algebraically, and/or graphically
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6.RP.7
Verify claims other students make, using examples and counterexamples when appropriate
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Students will select and use various types of reasoning and methods of proof.
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6.RP.8
Support an argument through examples/counterexamples and special cases
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6.RP.9
Devise ways to verify results
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6.CM
Communication
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Students will organize and consolidate their mathematical thinking through communication.
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6.CM.1
Provide an organized thought process that is correct, complete, coherent, and clear
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6.CM.2
Explain a rationale for strategy selection
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6.CM.3
Organize and accurately label work
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Students will communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
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6.CM.4
Share organized mathematical ideas through the manipulation of objects, numerical tables, drawings, pictures, charts, graphs, tables, diagrams, models, and symbols in written and verbal form
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6.CM.5
Answer clarifying questions from others
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Students will analyze and evaluate the mathematical thinking and strategies of others.
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6.CM.6
Understand mathematical solutions shared by other students
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6.CM.7
Raise questions that elicit, extend, or challenge others' thinking
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6.CM.8
Consider strategies used and solutions found by others in relation to their own work
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Students will use the language of mathematics to express mathematical ideas precisely.
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6.CM.9
Increase their use of mathematical vocabulary and language when communicating with others
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6.CM.10
Use appropriate vocabulary when describing objects, relationships, mathematical solutions, and rationale
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6.CM.11
Decode and comprehend mathematical visuals and symbols to construct meaning
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6.CN
Connections
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Students will recognize and use connections among mathematical ideas.
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6.CN.1
Understand and make connections and conjectures in their everyday experiences to mathematical ideas
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6.CN.2
Explore and explain the relationship between mathematical ideas
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6.CN.3
Connect and apply mathematical information to solve problems
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Students will understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
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6.CN.4
Understand multiple representations and how they are related
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6.CN.5
Model situations with objects and representations and be able to draw conclusions
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Students will recognize and apply mathematics in contexts outside of mathematics.
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6.CN.6
Recognize and provide examples of the presence of mathematics in their daily lives
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6.CN.7
Apply mathematics to problem situations that develop outside of mathematics
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6.CN.8
Investigate the presence of mathematics in careers and areas of interest
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6.CN.9
Recognize and apply mathematics to other disciplines and areas of interest
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6.R
Representation
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Students will create and use representations to organize, record, and communicate mathematical ideas.
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6.R.1
Use physical objects, drawings, charts, tables, graphs, symbols, equations, or objects created using technology as representations
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6.R.2
Explain, describe, and defend mathematical ideas using representations
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6.R.3
Read, interpret, and extend external models
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6.R.4
Use standard and nonstandard representations with accuracy and detail
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Students will select, apply, and translate among mathematical representations to solve problems.
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6.R.5
Use representations to explore problem situations
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6.R.6
Investigate relationships between different representations and their impact on a given problem
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Students will use representations to model and interpret physical, social, and mathematical phenomena.
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6.R.7
Use mathematics to show and understand physical phenomena (e.g., determine the perimeter of a bulletin board)
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6.R.8
Use mathematics to show and understand social phenomena (e.g., construct tables to organize data showing book sales)
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6.R.9
Use mathematics to show and understand mathematical phenomena (e.g., Find the missing value: (3 + 4) + 5 = 3 + (4 + ___)
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6.N
Number Sense and Operations
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Students will understand numbers, multiple ways of representing numbers, relationships among numbers, and number systems.
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Number Systems
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6.N.1
Read and write whole numbers to trillions
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6.N.2
Define and identify the commutative and associative properties of addition and multiplication
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6.N.3
Define and identify the distributive property of multiplication over addition
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6.N.4
Define and identify the identity and inverse properties of addition and multiplication
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6.N.5
Define and identify the zero property of multiplication
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6.N.6
Understand the concept of rate
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6.N.7
Express equivalent ratios as a proportion
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6.N.8
Distinguish the difference between rate and ratio
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6.N.9
Solve proportions using equivalent fractions
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6.N.10
Verify the proportionality using the product of the means equals the product of the extremes
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6.N.11
Read, write, and identify percents of a whole (0% to 100%)
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6.N.12
Solve percent problems involving percent, rate, and base
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6.N.13
Define absolute value and determine the absolute value of rational numbers (including positive and negative)
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6.N.14
Locate rational numbers on a number line (including positive and negative)
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6.N.15
Order rational numbers (including positive and negative)
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Students will understand meanings of operations and procedures, and how they relate to one another.
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Operations
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6.N.16
Add and subtract fractions with unlike denominators
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6.N.17
Multiply and divide fractions with unlike denominators
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6.N.18
Add, subtract, multiply, and divide mixed numbers with unlike denominators
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6.N.19
Identify the multiplicative inverse (reciprocal) of a number
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6.N.20
Represent fractions as terminating or repeating decimals
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6.N.21
Find multiple representations of rational numbers (fractions, decimals, and percents 0 to 100)
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6.N.22
Evaluate numerical expressions using order of operations (may include exponents of two and three)
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6.N.23
Represent repeated multiplication in exponential form
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6.N.24
Represent exponential form as repeated multiplication
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6.N.25
Evaluate expressions having exponents where the power is an exponent of one, two, or three
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Students will compute accurately and make reasonable estimates.
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Estimation
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6.N.26
Estimate a percent of quantity (0% to 100%)
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6.N.27
Justify the reasonableness of answers using estimation (including rounding)
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6.A
Algebra
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Students will represent and analyze algebraically a wide variety of problem solving situations.
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Variables and Expressions
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6.A.1
Translate two-step verbal expressions into algebraic expressions
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Students will perform algebraic procedures accurately.
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Variables and Expressions
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6.A.2
Use substitution to evaluate algebraic expressions (may include exponents of one, two and three)
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Equations and Inequalities
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6.A.3
Translate two-step verbal sentences into algebraic equations
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6.A.4
Solve and explain two-step equations involving whole numbers using inverse operations
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6.A.5
Solve simple proportions within context
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6.A.6
Evaluate formulas for given input values (circumference, area, volume, distance, temperature, interest, etc.)
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6.G
Geometry
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Students will use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes.
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Shapes
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6.G.1
Calculate the length of corresponding sides of similar triangles, using proportional reasoning
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6.G.2
Determine the area of triangles and quadrilaterals (squares, rectangles, rhombi, and trapezoids) and develop formulas
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6.G.3
Use a variety of strategies to find the area of regular and irregular polygons
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6.G.4
Determine the volume of rectangular prisms by counting cubes and develop the formula
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6.G.5
Identify radius, diameter, chords and central angles of a circle
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6.G.6
Understand the relationship between the diameter and radius of a circle
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6.G.7
Determine the area and circumference of a circle, using the appropriate formula
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6.G.8
Calculate the area of a sector of a circle, given the measure of a central angle and the radius of the circle
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6.G.9
Understand the relationship between the circumference and the diameter of a circle
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Students will apply coordinate geometry to analyze problem solving situations.
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Coordinate Geometry
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6.G.10
Identify and plot points in all four quadrants
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6.G.11
Calculate the area of basic polygons drawn on a coordinate plane (rectangles and shapes composed of rectangles having sides with integer lengths)
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6.M
Measurement
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Students will determine what can be measured and how, using appropriate methods and formulas.
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Units of Measurement
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6.M.1
Measure capacity and calculate volume of a rectangular prism
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6.M.2
Identify customary units of capacity (cups, pints, quarts, and gallons)
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6.M.3
Identify equivalent customary units of capacity (cups to pints, pints to quarts, and quarts to gallons)
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6.M.4
Identify metric units of capacity (liter and milliliter)
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6.M.5
Identify equivalent metric units of capacity (milliliter to liter and liter to milliliter)
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Tools and Methods
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6.M.6
Determine the tool and technique to measure with an appropriate level of precision: capacity
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Students will develop strategies for estimating measurements.
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Estimation
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6.M.7
Estimate volume, area, and circumference (see figures identified in geometry strand)
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6.M.8
Justify the reasonableness of estimates
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6.M.9
Determine personal references for capacity
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6.S
Statistics and Probability
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Students will collect, organize, display, and analyze data.
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Collection of Data
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6.S.1
Develop the concept of sampling when collecting data from a population and decide the best method to collect data for a particular question
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Organization and Display of Data
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6.S.2
Record data in a frequency table
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6.S.3
Construct Venn diagrams to sort data
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6.S.4
Determine and justify the most appropriate graph to display a given set of data (pictograph, bar graph, line graph, histogram, or circle graph)
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Analysis of Data
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6.S.5
Determine the mean, mode and median for a given set of data
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6.S.6
Determine the range for a given set of data
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6.S.7
Read and interpret graphs
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Students will make predictions that are based upon data analysis.
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Predictions from Data
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6.S.8
Justify predictions made from data
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Students will understand and apply concepts of probability.
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Probability
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6.S.9
List possible outcomes for compound events
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6.S.10
Determine the probability of dependent events
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6.S.11
Determine the number of possible outcomes for a compound event by using the fundamental counting principle and use this to determine the probabilities of events when the outcomes have equal probability
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