1: Number, Number Sense and Operations

1.A: Use scientific notation to express large numbers and numbers less than one.

1.A.1: Use scientific notation to express large numbers and small numbers between 0 and 1.

Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

1.C: Apply properties of operations and the real number system, and justify when they hold for a set of numbers.

1.C.4: Explain and use the inverse and identity properties and use inverse relationships (addition/subtraction, multiplication/division, squaring/square roots) in problem solving situations.

Modeling One-Step Equations
Solving Two-Step Equations

1.E: Compare, order and determine equivalent forms of real numbers.

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

1.G: Estimate, compute and solve problems involving real numbers, including ratio, proportion and percent, and explain solutions.

1.G.6: Estimate, compute and solve problems involving rational numbers, including ratio, proportion and percent, and judge the reasonableness of solutions.

Adding Fractions (Fraction Tiles)
Adding and Subtracting Integers
Adding on the Number Line
Beam to Moon (Ratios and Proportions)
Dividing Fractions
Dividing Mixed Numbers
Estimating Population Size
Estimating Sums and Differences
Geometric Probability
Improper Fractions and Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Part-to-part and Part-to-whole Ratios
Percent of Change
Percents, Fractions, and Decimals
Rational Numbers, Opposites, and Absolute Values
Sums and Differences with Decimals

1.H: Find the square root of perfect squares, and approximate the square root of non-perfect squares.

1.H.7: Find the square root of perfect squares, and approximate the square root of non-perfect squares as consecutive integers between which the root lies; e.g., [square root of 130] is between 11 and 12.

Square Roots

1.I: Estimate, compute and solve problems involving scientific notation, square roots and numbers with integer exponents.

1.I.3: Apply order of operations to simplify expressions and perform computations involving integer exponents and radicals.

Order of Operations

1.I.8: Add, subtract, multiply, divide and compare numbers written in scientific notation.

Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

2: Measurement

2.A: Solve increasingly complex non-routine measurement problems and check for reasonableness of results.

2.A.6: Solve and determine the reasonableness of the results for problems involving rates and derived measurements, such as velocity and density, using formulas, models and graphs.

Household Energy Usage

2.B: Use formulas to find surface area and volume for specified three-dimensional objects accurate to a specified level of precision.

2.B.4: Derive formulas for surface area and volume and justify them using geometric models and common materials. For example, find:

2.B.4.b: that the volume of a pyramid (or cone) is one-third of the volume of a prism (or cylinder) with the same base area and height.

Pyramids and Cones

2.C: Apply indirect measurement techniques, tools and formulas, as appropriate, to find perimeter, circumference and area of circles, triangles, quadrilaterals and composite shapes, and to find volume of prisms, cylinders, and pyramids.

2.C.5: Determine surface area for pyramids by analyzing their parts.

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

2.C.9: Demonstrate understanding of the concepts of perimeter, circumference and area by using established formulas for triangles, quadrilaterals, and circles to determine the surface area and volume of prisms, pyramids, cylinders, spheres and cones. (Note: Only volume should be calculated for spheres and cones.)

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

2.E: Estimate and compute various attributes, including length, angle measure, area, surface area and volume, to a specified level of precision.

2.E.10: Use conventional formulas to find the surface area and volume of prisms, pyramids and cylinders and the volume of spheres and cones to a specified level of precision.

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

3: Geometry and Spatial Sense

3.B: Describe and apply the properties of similar and congruent figures; and justify conjectures involving similarity and congruence.

3.B.3: Use proportions in several forms to solve problems involving similar figures (part-to-part, part-to-whole, corresponding sides between figures).

Beam to Moon (Ratios and Proportions)

3.C: Recognize and apply angle relationships in situations involving intersecting lines, perpendicular lines and parallel lines.

3.C.2: Recognize the angles formed and the relationship between the angles when two lines intersect and when parallel lines are cut by a transversal.

Triangle Angle Sum

3.E: Draw and construct representations of two- and three-dimensional geometric objects using a variety of tools, such as straightedge, compass and technology.

3.E.6: Draw nets for a variety of prisms, pyramids, cylinders and cones.

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

3.F: Represent and model transformations in a coordinate plane and describe the results.

3.F.5: Draw the results of translations, reflections, rotations and dilations of objects in the coordinate plane, and determine properties that remain fixed; e.g., lengths of sides remain the same under translations.

Dilations
Rotations, Reflections, and Translations
Translations

4: Patterns, Functions and Algebra

4.A: Generalize and explain patterns and sequences in order to find the next term and the nth term.

4.A.2: Generalize patterns and sequences by describing how to find the nth term.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

4.B: Identify and classify functions as linear or nonlinear, and contrast their properties using tables, graphs or equations.

4.B.3: Identify functions as linear or nonlinear based on information given in a table, graph or equation.

Absolute Value with Linear Functions
Arithmetic Sequences
Exponential Functions
Function Machines 1 (Functions and Tables)
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
Simple and Compound Interest
Slope-Intercept Form of a Line
Standard Form of a Line

4.C: Translate information from one representation (words, table, graph or equation) to another representation of a relation or function.

4.C.1: Relate the various representations of a relationship; i.e., relate a table to graph, description and symbolic form.

Function Machines 1 (Functions and Tables)
Introduction to Functions

4.D: Use algebraic representations, such as tables, graphs, expressions, functions and inequalities, to model and solve problem situations.

4.D.7: Use symbolic algebra (equations and inequalities), graphs and tables to represent situations and solve problems.

Absolute Value Equations and Inequalities
Comparing and Ordering Decimals
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Linear Inequalities in Two Variables
Points, Lines, and Equations
Solving Equations on the Number Line
Square Roots
Using Algebraic Equations
Using Algebraic Expressions

4.D.8: Write, simplify and evaluate algebraic expressions (including formulas) to generalize situations and solve problems.

Dividing Exponential Expressions
Multiplying Exponential Expressions
Operations with Radical Expressions
Order of Operations
Simple and Compound Interest
Solving Equations by Graphing Each Side
Solving Equations on the Number Line
Using Algebraic Equations

4.E: Analyze and compare functions and their graphs using attributes, such as rates of change, intercepts and zeros.

4.E.6: Describe the relationship between the graph of a line and its equation, including being able to explain the meaning of slope as a constant rate of change and y-intercept in real-world problems.

Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

4.F: Solve and graph linear equations and inequalities.

4.F.7: Use symbolic algebra (equations and inequalities), graphs and tables to represent situations and solve problems.

Absolute Value with Linear Functions
Exploring Linear Inequalities in One Variable
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Linear Inequalities in Two Variables
Modeling and Solving Two-Step Equations
Point-Slope Form of a Line
Points, Lines, and Equations
Solving Equations by Graphing Each Side
Square Roots
Standard Form of a Line
Systems of Linear Inequalities (Slope-intercept form)
Using Algebraic Expressions

4.F.9: Solve linear equations and inequalities graphically, symbolically and using technology.

Compound Inequalities
Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Solving Equations by Graphing Each Side
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable
Solving Two-Step Equations
Systems of Linear Inequalities (Slope-intercept form)

4.G: Solve quadratic equations with real roots by graphing, formula and factoring.

4.G.12: Solve simple quadratic equations graphically; e.g., y = x ² - 16.

Quadratics in Polynomial Form
Roots of a Quadratic

4.H: Solve systems of linear equations involving two variables graphically and symbolically.

4.H.10: Solve 2 by 2 systems of linear equations graphically and by simple substitution.

Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

4.H.11: Interpret the meaning of the solution of a 2 by 2 system of equations; i.e., point, line, no solution.

Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

4.J: Describe and interpret rates of change from graphical and numerical data.

4.J.13: Compute and interpret slope, midpoint and distance given a set of ordered pairs.

Cat and Mouse (Modeling with Linear Systems)
Distance Formula
Point-Slope Form of a Line
Slope

4.J.15: Describe and compare how changes in an equation affects the related graphs; e.g., for a linear equation changing the coefficient of x affects the slope and changing the constant affects the intercepts.

Points, Lines, and Equations
Radical Functions

4.J.16: Use graphing calculators or computers to analyze change; e.g., interest compounded over time as a nonlinear growth pattern.

Translating and Scaling Functions

5: Data Analysis and Probability

5.A: Create, interpret and use graphical displays and statistical measures to describe data; e.g., box-and-whisker plots, histograms, scatterplots, measures of center and variability.

5.A.1: Use, create and interpret scatterplots and other types of graphs as appropriate.

Correlation
Least-Squares Best Fit Lines
Polling: City
Real-Time Histogram
Solving Using Trend Lines
Stem-and-Leaf Plots
Trends in Scatter Plots

5.B: Evaluate different graphical representations of the same data to determine which is the most appropriate representation for an identified purpose.

5.B.2: Evaluate different graphical representations of the same data to determine which is the most appropriate representation for an identified purpose; e.g., line graph for change over time, circle graph for part-to-whole comparison, scatterplot for relationship between two variants.

Box-and-Whisker Plots

5.C: Compare the characteristics of the mean, median and mode for a given set of data, and explain which measure of center best represents the data.

5.C.5: Explain the mean's sensitivity to extremes and its use in comparison with the median and mode.

Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Populations and Samples
Stem-and-Leaf Plots

5.D: Find, use and interpret measures of center and spread, such as mean and quartiles, and use those measures to compare and draw conclusions about sets of data.

5.D.4: Compare two sets of data using measures of center (mean, mode, median) and measures of spread (range, quartiles, interquartile range, percentiles).

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)
Real-Time Histogram

5.E: Evaluate the validity of claims and predictions that are based on data by examining the appropriateness of the data collection and analysis.

5.E.8: Describe how the relative size of a sample compared to the target population affects the validity of predictions.

Polling: City
Polling: Neighborhood
Populations and Samples

5.G: Describe sampling methods and analyze the effects of method chosen on how well the resulting sample represents the population.

5.G.7: Identify different ways of selecting samples, such as survey response, random sample, representative sample and convenience sample.

Polling: City
Polling: Neighborhood
Populations and Samples

5.H: Use counting techniques, such as permutations and combinations, to determine the total number of options and possible outcomes.

5.H.10: Calculate the number of possible outcomes for a situation, recognizing and accounting for when items may occur more than once or when order is important.

Permutations and Combinations

5.I: Design an experiment to test a theoretical probability, and record and explain results.

Independent and Dependent Events

5.J: Compute probabilities of compound events, independent events, and simple dependent events.

5.J.11: Demonstrate an understanding that the probability of either of two disjoint events occurring can be found by adding the probabilities for each and that the probability of one independent event following another can be found by multiplying the probabilities.

Independent and Dependent Events

5.K: Make predictions based on theoretical probabilities and experimental results.

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

6: Mathematical Processes

6.A: Formulate a problem or mathematical model in response to a specific need or situation, determine information required to solve the problem, choose method for obtaining this information, and set limits for acceptable solution.

Estimating Population Size

6.B: Apply mathematical knowledge and skills routinely in other content areas and practical situations.

Estimating Population Size
Unit Conversions

6.C: Recognize and use connections between equivalent representations and related procedures for a mathematical concept; e.g., zero of a function and the x-intercept of the graph of the function, apply proportional thinking when measuring, describing functions, and comparing probabilities.

Unit Conversions

6.D: Apply reasoning processes and skills to construct logical verifications or counter-examples to test conjectures and to justify and defend algorithms and solutions.

Biconditional Statements
Conditional Statements

6.F: Use precise mathematical language and notations to represent problem situations and mathematical ideas.

Using Algebraic Expressions