#### 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.

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

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

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

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

#### 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.

6.2.2: Understand integers.

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 =.

6.2.4: Apply an algorithm to add and subtract fractions.

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

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

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

#### 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.

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

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

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

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

#### 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.

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

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

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

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

6.4.8: Classify shapes as similar.

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

#### 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.

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.

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

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

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

6.5.6: Use proportions to determine unit rates.

#### 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.

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

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

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.

Correlation last revised: 5/24/2018

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