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.

 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)

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.

 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.

 Modeling the Factorization of x2+bx+c

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

Content correlation last revised: 11/13/2008

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.