M.O.6.1: Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will demonstrate understanding of numbers, ways of representing numbers, and relationships among numbers and number systems, demonstrate meanings of operations and how they relate to one another, and compute fluently and make reasonable estimates.

M.O.6.1.2: determine the greatest common factor and least common multiple using multiple strategies to solve real-world problems; find prime factorization of a number.

Factor Trees (Factoring Numbers)
Finding Factors with Area Models

M.O.6.1.3: compare and order integers using multiple strategies (e.g., symbols, manipulatives, number line).

Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

M.O.6.1.4: analyze and solve real-world problems involving addition, subtraction , multiplication and division of whole numbers, fractions, mixed numbers, decimals, integers, and justify the reasonableness by estimation.

Adding on the Number Line
Cargo Captain (Multi-digit Subtraction)
Dividing Mixed Numbers
Estimating Population Size
Fractions with Unlike Denominators
Improper Fractions and Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

M.O.6.1.5: apply the distributive, commutative, associative and identity properties to numeric expressions and use to prove equivalency.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

M.O.6.1.6: convert between fractions/ratios, mixed numbers, decimals and percents in appropriate real-world problems.

Modeling Decimals (Area and Grid Models)
Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals

M.O.6.1.7: compute the percent of a number to solve application problems and justify the reasonableness by estimation.

Percent of Change
Percents and Proportions
Polling: Neighborhood

M.O.6.1.8: demonstrate an understanding of the effect of multiplying and dividing, whole numbers, fractions and decimals by numbers including 0, 1 and values between 0 and 1.

Dividing Fractions
Dividing Mixed Numbers
Multiplying Decimals (Area Model)
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Square Roots

M.O.6.1.9: develop and test hypotheses to derive the rules for addition, subtraction, multiplication and division of integers, justify by using real-world examples and use them to solve problems.

Adding on the Number Line

M.O.6.2: Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will demonstrate understanding of patterns, relations and functions, represent and analyze mathematical situations and structures using algebraic symbols, use mathematical models to represent and understand quantitative relationships, and analyze change in various contexts.

M.O.6.2.1: simplify numerical expressions and evaluate algebraic expressions using order of operations.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Order of Operations

M.O.6.2.3: create algebraic expressions that correspond to real-world situations; use the expressions to solve problems.

Linear Inequalities in Two Variables
Solving Equations on the Number Line
Using Algebraic Expressions

M.O.6.2.4: determine the rule, output or input; given an input/output model using one operation, write an algebraic expression for the rule and use to identify other input/output values.

Function Machines 1 (Functions and Tables)

M.O.6.2.5: solve real-world proportion problems involving rates, probability and measurements using multiple strategies, justify selection of strategies.

Estimating Population Size

M.O.6.2.6: write and solve one-step equations using number sense, properties of operations and the idea of maintaining equality to represent and solve real-world problems.

Cargo Captain (Multi-digit Subtraction)
Solving Equations on the Number Line

M.O.6.3: Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships, specify locations and describe spatial relationships using coordinate geometry and other representational systems, apply transformations and use symmetry to analyze mathematical situations, and solve problems using visualization, spatial reasoning, and geometric modeling.

M.O.6.3.1: analyze characteristics using defining properties of lines, angles, polygons, triangles, and compare these geometric figures.

Classifying Triangles

M.O.6.3.3: apply the concepts of parallel, perpendicular, intersecting, and skew lines to real-world situations (i.e. roads and routes).

Parallel, Intersecting, and Skew Lines
Solving Equations by Graphing Each Side

M.O.6.3.4: create designs using line and rotational symmetry.

Holiday Snowflake Designer
Quilting Bee (Symmetry)

M.O.6.3.5: predict, describe, and perform transformations on two-dimensional shapes

M.O.6.3.5.a: translations

Rock Art (Transformations)
Rotations, Reflections, and Translations

M.O.6.3.5.b: rotations

Rock Art (Transformations)
Rotations, Reflections, and Translations

M.O.6.3.5.c: reflections

Holiday Snowflake Designer
Rock Art (Transformations)
Rotations, Reflections, and Translations

M.O.6.4: Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will demonstrate understanding of measurable attributes of objects and the units, systems, and processes of measurement, and apply appropriate techniques, tools and formulas to determine measurements.

M.O.6.4.2: develop and test hypotheses to determine formulas for

M.O.6.4.2.a: perimeter of polygons, including composite figures

Perimeter and Area of Rectangles

M.O.6.4.2.b: area of parallelograms

Area of Triangles
Perimeter and Area of Rectangles

M.O.6.4.2.c: area of triangles

Area of Triangles

M.O.6.4.2.e: circumference of a circle

Circumference and Area of Circles

M.O.6.4.2.f: area of a circle

Circumference and Area of Circles

M.O.6.4.2.g: volume of a rectangular prism

Balancing Blocks (Volume)
Prisms and Cylinders

M.O.6.4.3: investigate, model and describe surface area of rectangular prisms and cylinders; develop strategies to determine the surface area of rectangular prisms

Surface and Lateral Areas of Prisms and Cylinders

M.O.6.5: Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them, select and use appropriate statistical methods to analyze data, develop and evaluate inferences and predictions that are based on models, and apply and demonstrate an understanding of basic concepts of probability.

M.O.6.5.1: collect, organize, display, read, interpret and analyze real-world data using appropriate graphs and tables (with and without technology).

Describing Data Using Statistics
Distance-Time Graphs
Graphing Skills
Mascot Election (Pictographs and Bar Graphs)
Reaction Time 2 (Graphs and Statistics)
Stem-and-Leaf Plots

M.O.6.5.3: perform simple probability events using manipulatives; predict the outcome given events using experimental and theoretical probability; express experimental and theoretical probability as a ratio, decimal or percent.

Independent and Dependent Events
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

M.O.6.5.4: determine combinations and permutations of given real-world situations by multiple strategies, including creating lists.

Permutations and Combinations