6A: Students who meet the standard can demonstrate knowledge and use of numbers and their many representations in a broad range of theoretical and practical settings. (Representations)

6A.1: Recognize and use exponential, scientific, and calculator notation.

Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

6A.2: Represent, order, and compare rational numbers using a variety of methods and materials.

Comparing and Ordering Decimals

6A.3: Place rational numbers on a number line.

Fraction Garden (Comparing Fractions)
Rational Numbers, Opposites, and Absolute Values

6B: Students who meet the standard can investigate, represent and solve problems using number facts, operations, and their properties, algorithms, and relationships. (Operations and properties)

6B.1: Determine the least common multiple and greatest common factor of a set of numbers using prime factorization containing exponents.

Finding Factors with Area Models

6B.3: Simplify arithmetic expressions containing integers using the field properties and order of operations.

Order of Operations

6B.4: Describe and use the inverse relationships of squaring and finding square roots to simplify computations and solve problems.

Square Roots

6D: Students who meet the standard can solve problems using comparison of quantities, ratios, proportions, and percents.

6D.1: Develop, use, analyze, and explain methods for solving number sentences or word problems involving proportions with rational numbers.

Estimating Population Size

6D.2: Solve problems that involve percents, including percent increase and decrease, regardless of the piece of information that is missing.

Percent of Change
Percents, Fractions, and Decimals
Real-Time Histogram
Time Estimation

7A: Students who meet the standard can measure and compare quantities using appropriate units, instruments, and methods. (Performance and conversion of measurements)

7A.1: Solve simple scale conversions, contractions, and dilations (e.g., maps and diagrams).

Dilations
Points in the Coordinate Plane

7C: Students who meet the standard can select and use appropriate technology, instruments, and formulas to solve problems, interpret results, and communicate findings. (Progression from selection of appropriate tools and methods to application of measurements

7C.1: Solve simple problems involving rates and other derived measurements such as velocity and density.

Household Energy Usage

7C.2: Solve problems involving angle measurement in polygons and circles.

Chords and Arcs
Inscribed Angles
Triangle Angle Sum

7C.3: Develop and describe surface area and volume formulas for cones and cylinders by relating pyramids to cones and prisms to cylinders.

Prisms and Cylinders
Pyramids and Cones
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

7C.4: Solve problems involving time, temperature, mass, speed, distance, density, and monetary values.

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

7C.5: Solve problems involving scale drawings, models, maps, or blueprints.

Points in the Coordinate Plane

7C.7: Determine the surface area of three-dimensional figures.

Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

8A: Students who meet the standard can describe numerical relationships using variables and patterns. (Representations and algebraic manipulations)

8A.3: Determine a specific term of a pattern of numbers or drawings.

Finding Patterns

8A.4: Create arithmetic and geometric sequences to fit a given set of conditions.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

8A.5: Recognize and generate equivalent forms for linear equations, including transforming linear equations into standard and slope-intercept form.

Linear Inequalities in Two Variables
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

8B: Students who meet the standard can interpret and describe numerical relationships using tables, graphs, and symbols. (Connections of representations including the rate of change)

8B.1: Graph linear equations and inequalities on the Cartesian plane.

Absolute Value Equations and Inequalities
Linear Functions
Linear Inequalities in Two Variables
Parabolas
Point-Slope Form of a Line
Points, Lines, and Equations
Systems of Linear Inequalities (Slope-intercept form)

8B.2: Graph a set of points and describe the relationship as linear or nonlinear.

Points, Lines, and Equations

8B.3: Describe the relationships between symbolic expressions and graphs of lines using the appropriate vocabulary for the intercepts and slope of the line.

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

8B.4: Graph absolute values on a number line.

Absolute Value Equations and Inequalities

8B.5: Determine the slope of a line from a graph.

Cat and Mouse (Modeling with Linear Systems)
Elevator Operator (Line Graphs)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Point-Slope Form of a Line
Slope
Slope-Intercept Form of a Line
Standard Form of a Line

8C: Students who meet the standard can solve problems using systems of numbers and their properties. (Problem solving; number systems, systems of equations, inequalities, algebraic functions)

8C.1: Solve arithmetic and simple algebraic equations using properties of real numbers, equality and inequality, and justify the procedures.

Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Two-Step Equations

8D: Students who meet the standard can use algebraic concepts and procedures to represent and solve problems. (Connection of 8A, 8B, and 8C to solve problems)

8D.1: Solve algebraic equations or word problems that involve linear equations or inequalities using algebraic or graphical representations.

Linear Inequalities in Two Variables
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Equations by Graphing Each Side
Solving Linear Inequalities in One Variable
Solving Two-Step Equations
Systems of Linear Inequalities (Slope-intercept form)

8D.2: Solve absolute value equations or inequalities in one variable using algebraic or graphical representations.

Absolute Value Equations and Inequalities
Compound Inequalities

8D.3: Create word problems that meet given conditions and represent linear relationships.

Standard Form of a Line

9A: Students who meet the standard can demonstrate and apply geometric concepts involving points, lines, planes, and space. (Properties of single figures, coordinate geometry and constructions)

9A.4: Determine if a triangle is possible using side lengths and the triangle inequality.

Triangle Inequalities

9A.5: Solve pictorial or word problems that involve geometric relationships within a single geometric shape or figure, including the Pythagorean theorem.

Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Surface and Lateral Areas of Pyramids and Cones

9A.6: Analyze the results of a combination of reflections, rotations, and translations of a figure, and determine alternate motions that could produce the same results.

Rock Art (Transformations)

9A.7: Combine simple construction techniques to construct squares, equilateral triangles, or other simple combinations of equal segments, angles, etc.

Constructing Congruent Segments and Angles

9B: Students who meet the standard can identify, describe, classify and compare relationships using points, lines, planes, and solids. (Connections between and among multiple geometric figures)

9B.2: Solve problems involving similar figures.

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

9B.3: Examine the congruence or similarity of objects using transformations.

Circles
Dilations
Reflections
Rock Art (Transformations)
Rotations, Reflections, and Translations
Translations

9C: Students who meet the standard can construct convincing arguments and proofs to solve problems. (Justifications of conjectures and conclusions)

9C.1: Create and critique arguments concerning geometric ideas and relationships, such as congruence, similarity, the Pythagorean relationship, or formulas for surface areas or volume of simple three-dimensional objects.

Pythagorean Theorem
Pythagorean Theorem with a Geoboard

9D: Students who meet the standard can use trigonometric ratios and circular functions to solve problems.

9D.1: Recognize Pythagorean Triples.

Pythagorean Theorem
Pythagorean Theorem with a Geoboard

9D.2: Identify the basic trigonometric ratios in terms of lengths of the sides of a right triangle and an acute angle.

Cosine Function
Sine Function

9D.3: Solve for missing side lengths using the trigonometric ratios in right triangles.

Cosine Function
Sine Function

9D.4: Determine and justify the side length relationships present in 45 degrees-45 degrees-90 degrees triangles and 30 degrees-60 degrees-90 degrees triangles.

Cosine Function
Isosceles and Equilateral Triangles
Sine Function

10A: Students who meet the standard can organize, describe and make predictions from existing data. (Data analysis)

10A.1: Construct, read, interpret, infer, predict, draw conclusions, and evaluate data from various displays, including histograms and scatter plots.

Box-and-Whisker Plots
Correlation
Graphing Skills
Histograms
Least-Squares Best Fit Lines
Polling: City
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram
Solving Using Trend Lines
Stem-and-Leaf Plots
Trends in Scatter Plots

10A.2: Determine the best measure of central tendency from mean, median, or mode.

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

10A.3: Discuss how data can be manipulated to represent different points of view based on the use of different measures of central tendency and based on different graphical displays.

Polling: City
Populations and Samples
Reaction Time 2 (Graphs and Statistics)

10A.5: Analyze graphical displays of data for possible misleading characteristics.

Graphing Skills

10B: Students who meet the standard can formulate questions, design data collection methods, gather and analyze data and communicate findings. (Data Collection)

10B.1: Formulate a question, design a study to answer the question, and collect data.

Correlation
Describing Data Using Statistics
Movie Reviewer (Mean and Median)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram
Time Estimation

10B.2: Analyze potential methods of collecting information and decide which methods would produce the most reliable and accurate data.

Polling: City
Polling: Neighborhood
Populations and Samples
Reaction Time 2 (Graphs and Statistics)

10B.3: Analyze instruments used for surveys for errors and bias.

Polling: Neighborhood

10B.4: Analyze potential experiments or simulations for errors and bias.

Polling: City
Polling: Neighborhood

10C: Students who meet the standard can determine, describe and apply the probabilities of events. (Probability including counting techniques)

10C.2: Design and conduct experiments or simulations for probability, including the possible use of technology to simulate events.

Binomial Probabilities
Geometric Probability
Independent and Dependent Events
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

10C.3: Discuss the difference in empirical and theoretical probability.

Geometric Probability
Independent and Dependent Events
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

10C.4: Compute probabilities for simple compound events using a variety of methods, including area models.

Independent and Dependent Events
Theoretical and Experimental Probability

10C.5: Identify situations where dependent and independent events occur.

Binomial Probabilities
Independent and Dependent Events

10C.6: Determine probabilities using simple counting techniques.

Probability Simulations

10C.7: Discuss situations where permutations and combinations should be used in counting outcomes.

Binomial Probabilities
Permutations and Combinations