6: Demonstrate and apply a knowledge and sense of numbers, including numeration and operations (addition, subtraction, multiplication, division), patterns, ratios and proportions.

6.8.02: Read, write, recognize, model, and interpret integers, including translating numerical expressions.

Adding and Subtracting Integers
Order of Operations

6.8.03: Recognize, translate between, and apply multiple representations of rational numbers (decimals, fractions, mixed numbers, percents, and roots).

Comparing and Ordering Decimals
Dividing Mixed Numbers
Estimating Sums and Differences
Improper Fractions and Mixed Numbers
Multiplying with Decimals
Part-to-part and Part-to-whole Ratios
Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Proportions and Common Multipliers
Rational Numbers, Opposites, and Absolute Values
Square Roots
Sums and Differences with Decimals

6.8.04: Use scientific notation to represent numbers and solve problems.

Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

6.8.06: Order and compare rational numbers.

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

6.8.07: Identify and locate rational and irrational numbers (e.g., pi, the square root of 2, the square root of 5) on a number line.

Rational Numbers, Opposites, and Absolute Values

6.8.08: Solve problems involving descriptions of numbers, including characteristics and relationships (e.g., exponents, roots, prime/composite, prime factorization, greatest common factor, least common multiple).

Chocomatic (Multiplication, Arrays, and Area)
Finding Factors with Area Models
Operations with Radical Expressions
Square Roots

6.8.09: Solve problems and number sentences involving addition, subtraction, multiplication, and division using rational numbers, exponents, and roots.

Adding Fractions (Fraction Tiles)
Adding on the Number Line
Dividing Fractions
Dividing Mixed Numbers
Estimating Sums and Differences
Improper Fractions and Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Operations with Radical Expressions
Square Roots
Sums and Differences with Decimals

6.8.10: Identify and apply order of operations to simplify numeric expressions involving integers (including exponents and roots), fractions, and decimals.

Order of Operations

6.8.11: Identify and apply the following properties of operations with rational numbers:

6.8.11.a: the commutative and associative properties for addition and multiplication;

Adding and Subtracting Integers
Adding on the Number Line
Equivalent Algebraic Expressions I

6.8.11.b: the distributive property;

Equivalent Algebraic Expressions II
Square Roots

6.8.11.d: the additive and multiplicative inverse properties; and

Adding and Subtracting Integers
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

6.8.12: Describe the effect of multiplying and dividing by numbers, including the effect of multiplying or dividing a rational number by:

6.8.12.a: a number less than zero;

Adding and Subtracting Integers

6.8.12.c: a number between zero and one; and

Adding and Subtracting Integers

6.8.12.d: a number greater than one.

Adding and Subtracting Integers

6.8.13: Select, use, and justify appropriate operations, methods, and tools to compute or estimate with rational numbers. Verify solutions and determine the reasonableness of results.

Adding Fractions (Fraction Tiles)
Adding and Subtracting Integers
Adding on the Number Line
Dividing Fractions
Dividing Mixed Numbers
Estimating Sums and Differences
Improper Fractions and Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

6.8.14: Estimate the square or cube root of a number less than 1,000 between two whole numbers (e.g., the cubed root of 200 is between 5 and 6).

Square Roots

6.8.15: Use ratios to describe problem situations.

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Part-to-part and Part-to-whole Ratios
Road Trip (Problem Solving)

6.8.16: Use proportional reasoning to model and solve problems.

Beam to Moon (Ratios and Proportions)
Direct and Inverse Variation
Estimating Population Size
Geometric Probability
Part-to-part and Part-to-whole Ratios
Percents and Proportions
Proportions and Common Multipliers

6.8.17: Read, write, recognize, model, and interpret percents, including those less than 1% and greater than 100%.

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

6.8.18: Solve number sentences and problems involving fractions, decimals, and percents (e.g., percent increase and decrease, interest rates, tax, discounts, tips).

Comparing and Ordering Decimals
Compound Interest
Estimating Sums and Differences
Multiplying with Decimals
Percent of Change
Percents, Fractions, and Decimals
Proportions and Common Multipliers
Real-Time Histogram
Sums and Differences with Decimals
Time Estimation

7: Estimate, make and use measurements of objects, quantities and relationships and determine acceptable levels of accuracy.

7.8.02: Solve problems involving perimeter/circumference and area of polygons, circles, and composite figures using diagrams, models, and grids or by measuring or using given formulas (may include sketching a figure from its description).

Area of Parallelograms
Area of Triangles
Chocomatic (Multiplication, Arrays, and Area)
Circumference and Area of Circles
Perimeter and Area of Rectangles
Perimeters and Areas of Similar Figures

7.8.03: Compare and estimate length (including perimeter/circumference), area, volume, weight/mass, and angles (0° to 360°) using referents.

Area of Triangles

7.8.04: Solve problems involving the volume or surface area of a right rectangular prism, right circular cylinder, or composite shape using an appropriate formula or strategy.

Prisms and Cylinders
Surface and Lateral Areas of Prisms and Cylinders

7.8.05: Solve problems involving unit conversions within the same measurement system for length, weight/mass, capacity, square units, and measures expressed as rates (e.g., converting feet/second to yards/minute).

Unit Conversions

7.8.06: Solve problems involving scale drawings, maps, and indirect measurement (e.g., determining the height of a building by comparing its known shadow length to the known height and shadow length of another object).

Perimeters and Areas of Similar Figures
Points in the Coordinate Plane
Similar Figures

8: Use algebraic and analytical methods to identify and describe patterns and relationships in data, solve problems and predict results.

8.8.01: Analyze, extend, and create sequences or linear functions, and determine algebraic expressions to describe the nth term of a sequence.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Geometric Sequences

8.8.02: Write an expression using variables to represent unknown quantities.

Solving Equations on the Number Line
Using Algebraic Equations
Using Algebraic Expressions

8.8.03: Simplify algebraic expressions.

Dividing Exponential Expressions
Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Multiplying Exponential Expressions
Operations with Radical Expressions
Order of Operations
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

8.8.04: Recognize and generate equivalent forms of algebraic expressions.

Dividing Exponential Expressions
Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Exponents and Power Rules
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Multiplying Exponential Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

8.8.07: Represent linear equations and quantitative relationships on a rectangular coordinate system, and interpret the meaning of a specific part of a graph.

Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Linear Functions
Standard Form of a Line

8.8.08: Translate between different representations (table, written, graphical, or pictorial) of whole number relationships and linear expressions.

Arithmetic Sequences
Function Machines 1 (Functions and Tables)
Geometric Sequences
Points, Lines, and Equations

8.8.09: Interpret the meaning of slope and intercepts in linear situations.

Cat and Mouse (Modeling with Linear Systems)
Compound Interest
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Solving Equations by Graphing Each Side
Standard Form of a Line

8.8.10: Identify, graph, and interpret up to two inequalities with a single variable (including the intersection or union of these inequalities) on a number line.

Compound Inequalities

8.8.11: Represent and analyze problems with linear equations and inequalities.

Linear Inequalities in Two Variables
Solving Equations by Graphing Each Side

8.8.12: Solve linear equations and inequalities in one variable over the rational numbers (e.g., 5x+7= -13, 4x-3= -7x+8, -2x+3>-5).

Solving Algebraic Equations II
Solving Linear Inequalities in One Variable

9: Use geometric methods to analyze, categorize and draw conclusions about points, lines, planes and space.

9.8.01: Solve problems involving two- and three-dimensional shapes.

Classifying Quadrilaterals

9.8.02: Solve problems that require knowledge of triangle and quadrilateral properties (e.g., triangle inequality).

Classifying Quadrilaterals
Concurrent Lines, Medians, and Altitudes
Parallelogram Conditions
Similarity in Right Triangles
Special Parallelograms
Triangle Angle Sum
Triangle Inequalities

9.8.04: Identify, describe, and determine the radius, diameter, and circumference of a circle and their relationship to each other and to pi.

Circumference and Area of Circles

9.8.05: Graph points, and identify coordinates of points on the Cartesian coordinate plane (all four quadrants).

City Tour (Coordinates)
Points in the Coordinate Plane

9.8.06: Represent and identify geometric figures using coordinate geometry, including those resulting from transformations.

Dilations

9.8.07: Analyze the results of a combination of transformations, and determine a different transformation that could produce the same result.

Rock Art (Transformations)

9.8.08: Identify or analyze relationships of angles formed by intersecting lines (including parallel lines cut by a transversal) and angles formed by radii of a circle.

Inscribed Angles
Triangle Angle Sum

9.8.09: Solve problems involving vertical, complementary, and supplementary angles.

Investigating Angle Theorems
Triangle Angle Sum

9.8.11: Solve problems involving congruent and similar figures.

Perimeters and Areas of Similar Figures
Similar Figures
Similarity in Right Triangles

9.8.12: Relate absolute value to distance on the number line.

Absolute Value with Linear Functions
Rational Numbers, Opposites, and Absolute Values

10: Collect, organize and analyze data using statistical methods; predict results; and interpret uncertainty using concepts of probability.

10.8.01: Read, interpret (including possible misleading characteristics), and make predictions from data represented in a bar graph, line (dot) plot, Venn diagram (with two or three circles), chart/table, line graph, scatterplot, circle graph, stem-and-leaf plot, or histogram.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

10.8.02: Compare and contrast the effectiveness of different representations of the same data.

Correlation

10.8.03: Create a bar graph, chart/table, line graph, or circle graph and solve a problem using the data in the graph for a given set of data.

Earthquakes 1 - Recording Station
Reaction Time 1 (Graphs and Statistics)

10.8.04: Identify or draw a reasonable approximation of the line of best fit from a set of data or a scatter plot, and use the line to make predictions.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

10.8.05: Analyze and apply measures of central tendency (mode, range, median, and mean) in problem-solving situations.

Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Populations and Samples
Reaction Time 1 (Graphs and Statistics)

10.8.06: Solve problems involving the probability of an event composed of repeated trials, compound events (including independent events), or future events with or without replacement.

Independent and Dependent Events
Theoretical and Experimental Probability

10.8.07: Represent all possible outcomes (sample space) for simple or compound events (e.g., tables, grids, tree diagrams).

Independent and Dependent Events
Permutations and Combinations
Theoretical and Experimental Probability

10.8.08: Solve simple problems involving the number of ways objects can be arranged (permutations and combinations).

Permutations and Combinations