6.N: Number & Operations

6.N.1: Read, write, and represent integers and rational numbers expressed as fractions, decimals, percents, and ratios; write positive integers as products of factors; use these representations in real-world and mathematical situations.

6.N.1.1: Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.

Adding and Subtracting Integers
Adding on the Number Line
Fraction Garden (Comparing Fractions)
Integers, Opposites, and Absolute Values
Modeling Decimals (Area and Grid Models)
Modeling Fractions (Area Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Rational Numbers, Opposites, and Absolute Values
Simplifying Algebraic Expressions I

6.N.1.4: Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.

Estimating Population Size
Modeling Decimals (Area and Grid Models)
Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals
Rational Numbers, Opposites, and Absolute Values

6.N.1.5: Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents.

Chocomatic (Multiplication, Arrays, and Area)
Factor Trees (Factoring Numbers)
Finding Factors with Area Models
Operations with Radical Expressions

6.N.1.6: Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.

Adding Fractions (Fraction Tiles)

6.N.2: Add and subtract integers in order to solve real-world and mathematical problems.

6.N.2.2: Illustrate addition and subtraction of integers using a variety of representations.

Adding and Subtracting Integers
Adding on the Number Line

6.N.2.3: Add and subtract integers; use efficient and generalizable procedures including but not limited to standard algorithms.

Adding and Subtracting Integers
Adding on the Number Line
Addition of Polynomials

6.N.3: Understand the concept of ratio and its relationship to fractions and percents and to the multiplication and division of whole numbers. Use ratios to solve real-world and mathematical problems.

6.N.3.2: Determine the unit rate for ratios.

Beam to Moon (Ratios and Proportions)
Household Energy Usage
Road Trip (Problem Solving)

6.N.3.3: Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.

Part-to-part and Part-to-whole Ratios

6.N.4: Multiply and divide decimals, fractions, and mixed numbers; solve real-world and mathematical problems with rational numbers.

6.N.4.1: Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.

Estimating Sums and Differences
Multiplying Decimals (Area Model)
Multiplying with Decimals

6.N.4.2: Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.

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

6.N.4.3: Multiply and divide fractions and decimals using efficient and generalizable procedures.

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

6.N.4.4: Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.

Box-and-Whisker Plots
Estimating Population Size
Modeling Decimals (Area and Grid Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)

6.A: Algebraic Reasoning & Algebra

6.A.1: Recognize and represent relationships between varying quantities; translate from one representation to another; use patterns, tables, graphs and rules to solve real-world and mathematical problems.

6.A.1.1: Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs.

City Tour (Coordinates)
Elevator Operator (Line Graphs)
Points in the Coordinate Plane
Points, Lines, and Equations

6.A.1.2: Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Geometric Sequences
Introduction to Functions
Points, Lines, and Equations

6.A.1.3: Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.

Absolute Value Equations and Inequalities
Compound Interest
Linear Inequalities in Two Variables
Order of Operations
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations I
Solving Equations by Graphing Each Side
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable
Using Algebraic Equations

6.A.2: Use properties of arithmetic to generate equivalent numerical expressions and evaluate expressions involving positive rational numbers.

6.A.2.1: Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.

Order of Operations

6.A.3: Use equations and inequalities to represent real-world and mathematical problems and use the idea of maintaining equality to solve equations. Interpret solutions in the original context.

6.A.3.1: Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.

Simplifying Algebraic Expressions II
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable

6.GM: Geometry & Measurement

6.GM.1: Calculate area of squares, parallelograms, and triangles to solve real-world and mathematical problems.

6.GM.1.1: Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithm.

Area of Parallelograms
Area of Triangles
Chocomatic (Multiplication, Arrays, and Area)
Fido's Flower Bed (Perimeter and Area)
Perimeter and Area of Rectangles
Square Roots

6.GM.1.2: Develop and use formulas to determine the area of triangles.

Area of Triangles

6.GM.1.3: Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.

Area of Parallelograms
Area of Triangles
Fido's Flower Bed (Perimeter and Area)
Perimeter and Area of Rectangles
Pythagorean Theorem with a Geoboard

6.GM.2: Understand and use relationships between angles in geometric figures.

6.GM.2.1: Solve problems using the relationships between the angles (vertical, complementary, and supplementary) formed by intersecting lines.

Triangle Angle Sum

6.GM.2.2: Develop and use the fact that the sum of the interior angles of a triangle is 180° to determine missing angle measures in a triangle.

Polygon Angle Sum
Triangle Angle Sum

6.GM.3: Choose appropriate units of measurement and use ratios to convert within measurement systems to solve real-world and mathematical problems.

6.GM.3.2: Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.

Unit Conversions

6.GM.4: Use translations, reflections, and rotations to establish congruency and understand symmetries.

6.GM.4.1: Predict, describe, and apply translations (slides), reflections (flips), and rotations (turns) to a two-dimensional figure.

Rotations, Reflections, and Translations

6.GM.4.2: Recognize that translations, reflections, and rotations preserve congruency and use them to show that two figures are congruent.

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

6.GM.4.4: Identify and describe the line(s) of symmetry in two-dimensional shapes.

Holiday Snowflake Designer
Quilting Bee (Symmetry)

6.D: Data & Probability

6.D.1: Display and analyze data.

6.D.1.1: Calculate the mean, median, and mode for a set of real-world data.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Stem-and-Leaf Plots

6.D.1.2: Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

6.D.1.3: Create and analyze box and whisker plots observing how each segment contains one quarter of the data.

Box-and-Whisker Plots

6.D.2: Use probability to solve real-world and mathematical problems; represent probabilities using fractions and decimals.

6.D.2.1: Represent possible outcomes using a probability continuum from impossible to certain.

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

6.D.2.2: Determine the sample space for a given experiment and determine which members of the sample space are related to certain events. Sample space may be determined by the use of tree diagrams, tables or pictorial representations.

Geometric Probability
Independent and Dependent Events
Permutations and Combinations
Spin the Big Wheel! (Probability)