**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 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)