Problem Solving Strand

Students will build new mathematical knowledge through problem solving.

6.PS.1 Know the difference between relevant and irrelevant information when solving problems
6.PS.2 Understand that some ways of representing a problem are more efficient than others
6.PS.3 Interpret information correctly, identify the problem, and generate possible strategies and solutions

Students will solve problems that arise in mathematics and in other contexts.

6.PS.4 Act out or model with manipulatives activities involving mathematical content from literature
6.PS.5 Formulate problems and solutions from everyday situations
6.PS.6 Translate from a picture/diagram to a numeric expression
6.PS.7 Represent problem situations verbally, numerically, algebraically, and/or graphically
6.PS.8 Select an appropriate representation of a problem
6.PS.9 Understand the basic language of logic in mathematical situations (and, or, and not)

Students will apply and adapt a variety of appropriate strategies to solve problems.

6.PS.10 Work in collaboration with others to solve problems
6.PS.11 Translate from a picture/diagram to a number or symbolic expression
6.PS.12 Use trial and error and the process of elimination to solve problems
6.PS.13 Model problems with pictures/diagrams or physical objects
6.PS.14 Analyze problems by observing patterns
6.PS.15 Make organized lists or charts to solve numerical problems

Students will monitor and reflect on the process of mathematical problem solving.

6.PS.16 Discuss with peers to understand a problem situation
6.PS.17 Determine what information is needed to solve problem
6.PS.18 Determine the efficiency of different representations of a problem
6.PS.19 Differentiate between valid and invalid approaches
6.PS.20 Understand valid counterexamples
6.PS.21 Explain the methods and reasoning behind the problem solving strategies used
6.PS.22 Discuss whether a solution is reasonable in the context of the original problem
6.PS.23 Verify results of a problem

Reasoning and Proof Strand

Students will recognize reasoning and proof as fundamental aspects of mathematics.

6.RP.1 Recognize that mathematical ideas can be supported using a variety of strategies
6.RP.2 Understand that mathematical statements can be supported, using models, facts, and relationships to explain their thinking

Students will make and investigate mathematical conjectures.

6.RP.3 Investigate conjectures, using arguments and appropriate mathematical terms
6.RP.4 Make and evaluate conjectures, using a variety of strategies

Students will develop and evaluate mathematical arguments and proofs.

6.RP.5 Justify general claims or conjectures, using manipulatives, models, expressions, and mathematical relationships
6.RP.6 Develop and explain an argument verbally, numerically, algebraically, and/or graphically
6.RP.7 Verify claims other students make, using examples and counterexamples when appropriate

Students will select and use various types of reasoning and methods of proof.

6.RP.8 Support an argument through examples/counterexamples and special cases
6.RP.9 Devise ways to verify results

Communication Strand

Students will organize and consolidate their mathematical thinking through communication.

6.CM.1 Provide an organized thought process that is correct, complete, coherent, and clear
6.CM.2 Explain a rationale for strategy selection
6.CM.3 Organize and accurately label work

Students will communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

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
6.CM.5 Answer clarifying questions from others

Students will analyze and evaluate the mathematical thinking and strategies of others.

6.CM.6 Understand mathematical solutions shared by other students
6.CM.7 Raise questions that elicit, extend, or challenge others’ thinking
6.CM.8 Consider strategies used and solutions found by others in relation to their own work

Students will use the language of mathematics to express mathematical ideas precisely.

6.CM.9 Increase their use of mathematical vocabulary and language when communicating with others
6.CM.10 Use appropriate vocabulary when describing objects, relationships, mathematical solutions, and rationale
6.CM.11 Decode and comprehend mathematical visuals and symbols to construct meaning

Connections Strand

Students will recognize and use connections among mathematical ideas.

6.CN.1 Understand and make connections and conjectures in their everyday experiences to mathematical ideas
6.CN.2 Explore and explain the relationship between mathematical ideas
6.CN.3 Connect and apply mathematical information to solve problems

Students will understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

6.CN.4 Understand multiple representations and how they are related
6.CN.5 Model situations with objects and representations and be able to draw conclusions

Students will recognize and apply mathematics in contexts outside of mathematics.

6.CN.6 Recognize and provide examples of the presence of mathematics in their daily lives
6.CN.7 Apply mathematics to problem situations that develop outside of mathematics
6.CN.8 Investigate the presence of mathematics in careers and areas of interest
6.CN.9 Recognize and apply mathematics to other disciplines and areas of interest

Representation Strand

Students will create and use representations to organize, record, and communicate mathematical ideas.

6.R.1 Use physical objects, drawings, charts, tables, graphs, symbols, equations, or objects created using technology as representations
6.R.2 Explain, describe, and defend mathematical ideas using representations
6.R.3 Read, interpret, and extend external models
6.R.4 Use standard and nonstandard representations with accuracy and detail

Students will select, apply, and translate among mathematical representations to solve problems.

6.R.5 Use representations to explore problem situations
6.R.6 Investigate relationships between different representations and their impact on a given problem

Students will use representations to model and interpret physical, social, and mathematical phenomena.

6.R.7 Use mathematics to show and understand physical phenomena (e.g., determine the perimeter of a bulletin board)
6.R.8 Use mathematics to show and understand social phenomena (e.g., construct tables to organize data showing book sales)
6.R.9 Use mathematics to show and understand mathematical phenomena (e.g., Find the missing value: (3 + 4) + 5 = 3 + (4 + ___ )

Number Sense and Operations Strand

Number Systems

6.N.1 Read and write whole numbers to trillions
6.N.2 Define and identify the commutative and associative properties of addition and multiplication
6.N.3 Define and identify the distributive property of multiplication over addition
6.N.4 Define and identify the identity and inverse properties of addition and multiplication
6.N.5 Define and identify the zero property of multiplication
6.N.6 Understand the concept of rate
6.N.7 Express equivalent ratios as a proportion
6.N.8 Distinguish the difference between rate and ratio
6.N.9 Solve proportions using equivalent fractions
6.N.10 Verify the proportionality using the product of the means equals the product of the extremes
6.N.11 Read, write, and identify percents of a whole (0% to 100%)
6.N.12 Solve percent problems involving percent, rate, and base
6.N.13 Define absolute value and determine the absolute value of rational numbers (including positive and negative )
6.N.14 Locate rational numbers on a number line (including positive and negative)
6.N.15 Order rational numbers (including positive and negative)
6.N.16 Add and subtract fractions with unlike denominators
6.N.17 Multiply and divide fractions with unlike denominators
6.N.18 Add, subtract, multiply and divide mixed numbers with unlike denominators
6.N.19 Identify the multiplicative inverse (reciprocal) of a number
6.N.20 Represent fractions as terminating or repeating decimals
6.N.21 Find multiple representations of rational numbers (fractions, decimals , and percents 0 to 100)
6.N.22 Evaluate numerical expressions using order of operations (may include exponents of two and three)
6.N.23 Represent repeated multiplication in exponential form
6.N.24 Represent exponential form as repeated multiplication
6.N.25 Evaluate expressions having exponents where the power is an exponent of one, two, or three

Estimation

6.N.26 Estimate a percent of quantity (0% to 100%)
6.N.27 Justify the reasonableness of answers using estimation (including rounding)

Algebra Strand

Variables and Expressions

5.A.2 Translate simple verbal expressions into algebraic expressions.
5.A.3 Substitute assigned values into variable expressions and evaluate using order of operations.
6.A.1 Translate two -step verbal expressions into algebraic expressions

Equations and Inequalities

5.A.4 Solve simple one-step equations using basic whole-number facts.
5.A.5 Solve and explain simple one-step equations using inverse operations involving whole numbers.
6.A.6 Evaluate formulas for given input values (circumference, area, volume, distance, temperature, interest, etc.)

Geometry Strand

Shapes

6.G.1 Calculate the length of corresponding sides of similar triangles, using proportional reasoning
6.G.2 Determine the area of triangles and quadrilaterals (squares, rectangles, rhombi, and trapezoids) and develop formulas
6.G.3 Use a variety of strategies to find the area of regular and irregular polygons
6.G.4 Determine the volume of rectangular prisms by counting cubes and develop the formula
6.G.5 Identify radius, diameter, chords and central angles of a circle
6.G.6 Understand the relationship between the diameter and radius of a circle
6.G.7 Determine the area and circumference of a circle, using the appropriate formula
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
6.G.9 Understand the relationship between the circumference and the diameter of a circle

Coordinate Geometry

5.G.12 Identify and plot points in the first quadrant
5.G.13 Plot points to form basic geometric shapes (identify and classify)
5.G.14 Calculate perimeter of basic geometric shapes drawn on a coordinate plane (rectangles and shapes composed of rectangles having sides with integer lengths and parallel to the axes)

Measurement Strand

Units of Measurement

6.M.1 Measure capacity and calculate volume of a rectangular prism
6.M.2 Identify customary units of capacity (cups, pints, quarts, and gallons)
6.M.3 Identify equivalent customary units of capacity (cups to pints, pints to quarts, and quarts to gallons)
6.M.4 Identify metric units of capacity (liter and milliliter)
6.M.5 Identify equivalent metric units of capacity (milliliter to liter and liter to milliliter)

Tools and Methods

6.M.6 Determine the tool and technique to measure with an appropriate level of precision: capacity

Estimation

6.M.7 Estimate volume, area, and circumference (see figures identified in geometry strand)
6.M.8 Justify the reasonableness of estimates
6.M.9 Determine personal references for capacity

Statistics and Probability Strand

Analysis of Data

6.S.5 Determine the mean, mode and median for a given set of data
6.S.6 Determine the range for a given set of data
6.S.7 Read and interpret graphs

Predictions from Data

6.S.8 Justify predictions made from data

Probability

5.S.5 List the possible outcomes for a single-event experiment
5.S.6 Record experiment results using fractions/ratios
5.S.7 Create a sample space and determine the probability of a single event, given a simple experiment (e.g., rolling a number cube)

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