6.N: Number Sense and Operations

6.N.2: Demonstrate an understanding of place value to billions and thousandths.

Cannonball Clowns (Number Line Estimation)
Number Systems
Rounding Whole Numbers (Number Line)
Target Sum Card Game (Multi-digit Addition)

6.N.3: Represent and compare very large (billions) and very small (thousandths) positive numbers in various forms such as expanded notation without exponents, e.g., 9724 = 9 x 1000 + 7 x 100 + 2 x 10 + 4.

Unit Conversions

6.N.4: Demonstrate an understanding of fractions as a ratio of whole numbers, as parts of unit wholes, as parts of a collection, and as locations on the number line.

Beam to Moon (Ratios and Proportions)
Equivalent Fractions (Fraction Tiles)
Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Fraction, Decimal, Percent (Area and Grid Models)
Fractions Greater than One (Fraction Tiles)
Modeling Fractions (Area Models)
Percents, Fractions, and Decimals
Rational Numbers, Opposites, and Absolute Values
Toy Factory (Set Models of Fractions)

6.N.5: Identify and determine common equivalent fractions, mixed numbers, decimals, and percents.

Dividing Mixed Numbers
Fraction, Decimal, Percent (Area and Grid Models)
Improper Fractions and Mixed Numbers
Modeling Decimals (Area and Grid Models)
Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals

6.N.6: Find and position integers, fractions, mixed numbers, and decimals (both positive and negative) on the number line.

Adding and Subtracting Integers
Adding on the Number Line
Fractions Greater than One (Fraction Tiles)
Integers, Opposites, and Absolute Values

6.N.7: Compare and order integers (including negative integers), and positive fractions, mixed numbers, decimals, and percents.

Adding Whole Numbers and Decimals (Base-10 Blocks)
Comparing and Ordering Decimals
Fraction, Decimal, Percent (Area and Grid Models)
Integers, Opposites, and Absolute Values
Modeling Decimals (Area and Grid Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Rational Numbers, Opposites, and Absolute Values
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Treasure Hunter (Decimals on the Number Line)

6.N.8: Apply number theory concepts-including prime and composite numbers, prime factorization, greatest common factor, least common multiple, and divisibility rules for 2, 3, 4, 5, 6, 9, and 10-to the solution of problems.

Chocomatic (Multiplication, Arrays, and Area)
Pattern Flip (Patterns)

6.N.9: Select and use appropriate operations to solve problems involving addition, subtraction, multiplication, division, and positive integer exponents with whole numbers, and with positive fractions, mixed numbers, decimals, and percents.

Adding Whole Numbers and Decimals (Base-10 Blocks)
Cargo Captain (Multi-digit Subtraction)
Number Line Frog Hop (Addition and Subtraction)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)

6.N.10: Use the number line to model addition and subtraction of integers, with the exception of subtracting negative integers.

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

6.N.11: Apply the Order of Operations for expressions involving addition, subtraction, multiplication, and division with grouping symbols (+, -, x, ÷).

Order of Operations

6.N.13: Accurately and efficiently add, subtract, multiply, and divide (with double-digit divisors) whole numbers and positive decimals.

Adding Whole Numbers and Decimals (Base-10 Blocks)
Cargo Captain (Multi-digit Subtraction)
Critter Count (Modeling Multiplication)
Multiplying Decimals (Area Model)
Multiplying with Decimals
No Alien Left Behind (Division with Remainders)
Number Line Frog Hop (Addition and Subtraction)
Square Roots
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Sums and Differences with Decimals
Target Sum Card Game (Multi-digit Addition)

6.N.14: Accurately and efficiently add, subtract, multiply, and divide positive fractions and mixed numbers. Simplify fractions.

Adding Fractions (Fraction Tiles)
Dividing Fractions
Dividing Mixed Numbers
Equivalent Fractions (Fraction Tiles)
Estimating Sums and Differences
Factor Trees (Factoring Numbers)
Fraction Artist 2 (Area Models of Fractions)
Fractions Greater than One (Fraction Tiles)
Fractions with Unlike Denominators
Improper Fractions and Mixed Numbers
Modeling Fractions (Area Models)
Multiplying Fractions
Multiplying Mixed Numbers
Toy Factory (Set Models of Fractions)

6.N.15: Add and subtract integers, with the exception of subtracting negative integers.

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

6.N.16: Estimate results of computations with whole numbers, and with positive fractions, mixed numbers, decimals, and percents. Describe reasonableness of estimates.

Cannonball Clowns (Number Line Estimation)
Multiplying Decimals (Area Model)

6.P: Patterns, Relations, and Algebra

6.P.1: Analyze and determine the rules for extending symbolic, arithmetic, and geometric patterns and progressions, e.g., ABBCCC; 1, 5, 9, 13 ...; 3, 9, 27, ....

Finding Patterns
Function Machines 1 (Functions and Tables)
Pattern Flip (Patterns)

6.P.2: Replace variables with given values and evaluate/simplify, e.g., 2(x) + 3 when x = 4.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II

6.P.3: Use the properties of equality to solve problems, e.g., if __ + 7 = 13, then = 13 - 7, therefore __ = 6; if 3 x __ = 15, then 1/3 x 3 x __ = 1/3 x 15, therefore __ = 5.

Solving Two-Step Equations
Using Algebraic Equations

6.P.4: Represent real situations and mathematical relationships with concrete models, tables, graphs, and rules in words and with symbols, e.g., input-output tables.

Improper Fractions and Mixed Numbers
Multiplying with Decimals
Using Algebraic Expressions

6.P.5: Solve linear equations using concrete models, tables, graphs, and paper-pencil methods.

Modeling One-Step Equations
Points, Lines, and Equations
Solving Equations by Graphing Each Side
Solving Equations on the Number Line
Solving Two-Step Equations

6.P.6: Produce and interpret graphs that represent the relationship between two variables in everyday situations.

Points in the Coordinate Plane
Slope-Intercept Form of a Line

6.G: Geometry

6.G.1: Identify polygons based on their properties, including types of interior angles, perpendicular or parallel sides, and congruence of sides, e.g., squares, rectangles, rhombuses, parallelograms, trapezoids, and isosceles, equilateral, and right triangles.

Classifying Quadrilaterals
Classifying Triangles
Perimeter and Area of Rectangles
Triangle Angle Sum

6.G.2: Identify three-dimensional shapes (e.g., cubes, prisms, spheres, cones, and pyramids) based on their properties, such as edges and faces.

Pyramids and Cones
Surface and Lateral Areas of Pyramids and Cones

6.G.3: Identify relationships among points, lines, and planes, e.g., intersecting, parallel, perpendicular.

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

6.G.4: Graph points and identify coordinates of points on the Cartesian coordinate plane (all four quadrants).

City Tour (Coordinates)
Points in the Coordinate Plane

6.G.6: Predict, describe, and perform transformations on two-dimensional shapes, e.g., translations, rotations, and reflections.

Absolute Value with Linear Functions
Circles
Holiday Snowflake Designer
Rock Art (Transformations)
Rotations, Reflections, and Translations

6.G.7: Identify types of symmetry, including line and rotational.

Holiday Snowflake Designer
Quilting Bee (Symmetry)

6.G.8: Determine if two shapes are congruent by measuring sides or a combination of sides and angles, as necessary; or by motions or series of motions, e.g., translations, rotations, and reflections.

Rock Art (Transformations)
Rotations, Reflections, and Translations

6.G.9: Match three-dimensional objects and their two-dimensional representations, e.g., nets, projections, and perspective drawings.

3D and Orthographic Views
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

6.M: Measurement

6.M.1: Apply the concepts of perimeter and area to the solution of problems. Apply formulas where appropriate.

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

6.M.2: Identify, measure, describe, classify, and construct various angles, triangles, and quadrilaterals.

Classifying Quadrilaterals
Classifying Triangles
Concurrent Lines, Medians, and Altitudes
Polygon Angle Sum
Similarity in Right Triangles
Triangle Angle Sum

6.M.3: Solve problems involving proportional relationships and units of measurement, e.g., same system unit conversions, scale models, maps, and speed.

Beam to Moon (Ratios and Proportions)
Percents and Proportions
Points in the Coordinate Plane
Proportions and Common Multipliers

6.M.4: Find areas of triangles and parallelograms. Recognize that shapes with the same number of sides but different appearances can have the same area. Develop strategies to find the area of more complex shapes.

Area of Parallelograms
Area of Triangles
Balancing Blocks (Volume)
Chocomatic (Multiplication, Arrays, and Area)
Classifying Quadrilaterals
Classifying Triangles
Fido's Flower Bed (Perimeter and Area)
Perimeter and Area of Rectangles

6.M.5: Identify, measure, and describe circles and the relationships of the radius, diameter, circumference, and area (e.g., d = 2r, p = C/d), and use the concepts to solve problems.

Circumference and Area of Circles

6.M.6: Find volumes and surface areas of rectangular prisms.

Balancing Blocks (Volume)
Prisms and Cylinders
Surface and Lateral Areas of Prisms and Cylinders

6.M.7: Find the sum of the angles in simple polygons (up to eight sides) with and without measuring the angles.

Polygon Angle Sum
Triangle Angle Sum

6.D: Data Analysis, Statistics, and Probability

6.D.1: Describe and compare data sets using the concepts of median, mean, mode, maximum and minimum, and range.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Sight vs. Sound Reactions
Stem-and-Leaf Plots

6.D.2: Construct and interpret stem-and-leaf plots, line plots, and circle graphs.

Graphing Skills
Mean, Median, and Mode
Stem-and-Leaf Plots

6.D.4: Predict the probability of outcomes of simple experiments (e.g., tossing a coin, rolling a die) and test the predictions. Use appropriate ratios between 0 and 1 to represent the probability of the outcome and associate the probability with the likelihood of the event.

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