6.1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

6.1.1: Generate and solve complex abstract problems that involve modeling physical, social, and/or mathematical phenomena.

Estimating Population Size

6.1.2: Evaluate conjectures and pose follow-up questions to prove or disprove conjectures.

Biconditional Statements

6.1.4: Understand equivalent symbolic expressions as distinct symbolic forms that represent the same relationship.

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

6.1.6: Use correct and clearly written or spoken words, variables, and notations to communicate about significant mathematical tasks.

Using Algebraic Expressions

6.1.7: Generalize connections among a variety of representational forms and real-world situations.

Estimating Population Size

6.2: The student will demonstrate through the mathematical processes an understanding of the concepts of whole-number percentages, integers, and ratio and rate; the addition and subtraction of fractions; accurate, efficient, and generalizable methods of multiplying and dividing fractions and decimals; and the use of exponential notation to represent whole numbers.

6.2.1: Understand whole-number percentages through 100.

Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals

6.2.2: Understand integers.

Adding and Subtracting Integers
Integers, Opposites, and Absolute Values

6.2.3: Compare rational numbers and whole-number percentages through 100 by using the symbols "less than or equal to", "greater than or equal to", <, >, and =.

Comparing and Ordering Decimals
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

6.2.4: Apply an algorithm to add and subtract fractions.

Adding Fractions (Fraction Tiles)
Estimating Sums and Differences
Fractions Greater than One (Fraction Tiles)
Fractions with Unlike Denominators
Improper Fractions and Mixed Numbers

6.2.5: Generate strategies to multiply and divide fractions and decimals.

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

6.2.6: Understand the relationship between ratio/rate and multiplication/division.

Beam to Moon (Ratios and Proportions)
Factor Trees (Factoring Numbers)
No Alien Left Behind (Division with Remainders)
Proportions and Common Multipliers
Road Trip (Problem Solving)
Solving Algebraic Equations II

6.2.8: Represent the prime factorization of numbers by using exponents.

Finding Factors with Area Models

6.3: The student will demonstrate through the mathematical processes an understanding of writing, interpreting, and using mathematical expressions, equations, and inequalities.

6.3.1: Analyze numeric and algebraic patterns and pattern relationships.

Finding Patterns
Function Machines 1 (Functions and Tables)

6.3.2: Apply order of operations to simplify whole-number expressions.

Order of Operations

6.3.3: Represent algebraic relationships with variables in expressions, simple equations, and simple inequalities.

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

6.3.4: Use the commutative, associative, and distributive properties to show that two expressions are equivalent.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Modeling the Factorization of x²+bx+c
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

6.3.5: Use inverse operations to solve one-step equations that have whole-number solutions and variables with whole-number coefficients.

Solving Equations on the Number Line

6.4: The student will demonstrate through the mathematical processes an understanding of shape, location, and movement within a coordinate system; similarity, complementary, and supplementary angles; and the relationship between line and rotational symmetry.

6.4.1: Represent with ordered pairs of integers the location of points in a coordinate grid.

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

6.4.3: Generalize the relationship between line symmetry and rotational symmetry for two-dimensional shapes.

Holiday Snowflake Designer
Quilting Bee (Symmetry)

6.4.4: Construct two-dimensional shapes with line or rotational symmetry.

Holiday Snowflake Designer
Quilting Bee (Symmetry)

6.4.5: Identify the transformation(s) used to move a polygon from one location to another in the coordinate plane.

Rotations, Reflections, and Translations

6.4.6: Explain how transformations affect the location of the original polygon in the coordinate plane.

Rotations, Reflections, and Translations

6.4.8: Classify shapes as similar.

Similarity in Right Triangles

6.4.9: Classify pairs of angles as either complementary or supplementary.

Investigating Angle Theorems

6.5: The student will demonstrate through the mathematical processes an understanding of surface area; the perimeter and area of irregular shapes; the relationships among the circumference, diameter, and radius of a circle; the use of proportions to determine unit rates; and the use of scale to determine distance.

6.5.1: Explain the relationships among the circumference, diameter, and radius of a circle.

Circumference and Area of Circles

6.5.2: Apply strategies and formulas with an approximation of pi (3.14, or 22/7) to find the circumference and area of a circle.

Circumference and Area of Circles

6.5.3: Generate strategies to determine the surface area of a rectangular prism and a cylinder.

Surface and Lateral Areas of Prisms and Cylinders

6.5.4: Apply strategies and procedures to estimate the perimeters and areas of irregular shapes.

Balancing Blocks (Volume)
Fido's Flower Bed (Perimeter and Area)

6.5.5: Apply strategies and procedures of combining and subdividing to find the perimeters and areas of irregular shapes.

Area of Triangles
Fido's Flower Bed (Perimeter and Area)

6.5.6: Use proportions to determine unit rates.

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

6.6: The student will demonstrate through the mathematical processes an understanding of the relationships within one population or sample.

6.6.1: Predict the characteristics of one population based on the analysis of sample data.

Polling: City
Polling: Neighborhood

6.6.2: Organize data in frequency tables, histograms, or stem-and-leaf plots as appropriate.

Describing Data Using Statistics
Histograms
Mascot Election (Pictographs and Bar Graphs)
Stem-and-Leaf Plots

6.6.3: Analyze which measure of central tendency (mean, median, or mode) is the most appropriate for a given purpose.

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

6.6.4: Use theoretical probability to determine the sample space and probability for one- and two-stage events such as tree diagrams, models, lists, charts, and pictures.

Geometric Probability
Independent and Dependent Events
Permutations and Combinations
Probability Simulations
Theoretical and Experimental Probability