1: Number, Number Sense and Operations

1.A: Represent and compare numbers less than 0 through familiar applications and extending the number line.

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

1.B: Compare, order and convert among fractions, decimals and percents.

1.B.1: Demonstrate an understanding of place value using powers of 10 and write large numbers in scientific notation.

Unit Conversions 2 - Scientific Notation and Significant Digits

1.B.3: Describe differences between rational and irrational numbers; e.g., use technology to show that some numbers (rational) can be expressed as terminating or repeating decimals and other (irrational) as non-terminating and non-repeating decimals.

Rational Numbers, Opposites, and Absolute Values

1.C: Develop meaning for percents, including percents greater than 100 and less than 1.

Percent of Change
Percents, Fractions, and Decimals

1.D: Use models and pictures to relate concepts of ratio, proportion and percent.

Beam to Moon (Ratios and Proportions)
Part-to-part and Part-to-whole Ratios
Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Proportions and Common Multipliers

1.E: Use order of operations, including use of parenthesis and exponents to solve multi-step problems, and verify and interpret the results.

1.E.4: Use order of operations and properties to simplify numerical expressions involving integers, fractions and decimals.

Estimating Sums and Differences
Order of Operations

1.G: Apply and explain the use of prime factorizations, common factors, and common multiples in problem situations.

1.G.9: Represent and solve problem situations that can be modeled by and solved using concepts of absolute value, exponents and square roots (for perfect squares).

Rational Numbers, Opposites, and Absolute Values

1.H: Use and analyze the steps in standard and non-standard algorithms for computing with fractions, decimals and integers.

1.H.8: Develop and analyze algorithms for computing with percents and integers, and demonstrate fluency in their use.

Adding and Subtracting Integers
Adding on the Number Line
Addition of Polynomials

1.I: Use a variety of strategies, including proportional reasoning, to estimate, compute, solve and explain solutions to problems involving integers, fractions, decimals and percents.

1.I.6: Simplify numerical expressions involving integers and use integers to solve real-life problems.

Order of Operations

1.I.7: Solve problems using the appropriate form of a rational number (fraction, decimal or percent).

Fraction Garden (Comparing Fractions)
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
Toy Factory (Set Models of Fractions)

1.I.9: Represent and solve problem situations that can be modeled by and solved using concepts of absolute value, exponents and square roots (for perfect squares).

Rational Numbers, Opposites, and Absolute Values

2: Measurement

2.B: Convert units of length, area, volume, mass and time within the same measurement system.

2.B.2: Convert units of area and volume within the same measurement system using proportional reasoning and a reference table when appropriate; e.g., square feet to square yards, cubic meters to cubic centimeters.

Unit Conversions

2.C: Identify appropriate tools and apply appropriate techniques for measuring angles, perimeter or circumference and area of triangles, quadrilaterals, circles and composite shapes, and surface area and volume of prisms and cylinders.

2.C.6: Use strategies to develop formulas for finding area of trapezoids and volume of cylinders and prisms.

Prisms and Cylinders
Pyramids and Cones

2.C.7: Develop strategies to find the area of composite shapes using the areas of triangles, parallelograms, circles and sectors.

Area of Parallelograms
Area of Triangles

2.E: Use problem solving techniques and technology as needed to solve problems involving length, weight, perimeter, area, volume, time and temperature.

2.E.4: Solve problems involving proportional relationships and scale factors; e.g., scale models that require unit conversions within the same measurement system.

Beam to Moon (Ratios and Proportions)
Dilations
Estimating Population Size
Part-to-part and Part-to-whole Ratios
Percents and Proportions
Proportions and Common Multipliers
Similar Figures
Unit Conversions

2.E.5: Analyze problem situations involving measurement concepts, select appropriate strategies, and use an organized approach to solve narrative and increasingly complex problems.

Estimating Population Size

2.F: Analyze and explain what happens to area and perimeter or surface area and volume when the dimensions of an object are changed.

2.F.9: Describe what happens to the surface area and volume of a three-dimensional object when the measurements of the object are changed; e.g., length of sides are doubled.

Surface and Lateral Areas of Prisms and Cylinders

2.G: Understand and demonstrate the independence of perimeter and area for two-dimensional shapes and of surface area and volume for three-dimensional shapes.

2.G.8: Understand the difference between surface area and volume and demonstrate that two objects may have the same surface area, but different volumes or may have the same volume, but different surface areas.

Surface and Lateral Areas of Prisms and Cylinders

3: Geometry and Spatial Sense

3.B: Draw circles, and identify and determine the relationships among the radius, diameter, center and circumference.

Chords and Arcs
Circumference and Area of Circles

3.C: Specify locations and plot ordered pairs on a coordinate plane.

City Tour (Coordinates)
Elevator Operator (Line Graphs)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Linear Functions
Point-Slope Form of a Line
Points in the Coordinate Plane
Points, Lines, and Equations
Slope

3.D: Identify, describe and classify types of line pairs, angles, two-dimensional figures and three-dimensional objects using their properties.

3.D.2: Determine sufficient (not necessarily minimal) properties that define a specific two-dimensional figure or three-dimensional object. For example:

3.D.2.b: Develop a set of properties that eliminates all but the desired figure; e.g., only squares are quadrilaterals with all sides congruent and all angles congruent.

Classifying Quadrilaterals
Special Parallelograms

3.E: Use proportions to express relationships among corresponding parts of similar figures.

3.E.1: Use proportional reasoning to describe and express relationships between parts and attributes of similar and congruent figures.

Beam to Moon (Ratios and Proportions)

3.E.6: Determine and use scale factors for similar figures to solve problems using proportional reasoning.

Beam to Moon (Ratios and Proportions)
Dilations

3.F: Describe and use the concepts of congruence, similarity and symmetry to solve problems.

3.F.7: Identify the line and rotation symmetries of two-dimensional figures to solve problems.

Holiday Snowflake Designer
Quilting Bee (Symmetry)

3.G: Describe and use properties of triangles to solve problems involving angle measures and side lengths of right triangles.

3.G.3: Use and demonstrate understanding of the properties of triangles. For example:

3.G.3.a: Use Pythagorean Theorem to solve problems involving right triangles.

Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard

3.G.3.b: Use triangle angle sum relationships to solve problems.

Isosceles and Equilateral Triangles
Polygon Angle Sum
Triangle Angle Sum

3.G.5: Apply properties of congruent or similar triangles to solve problems involving missing lengths and angle measures.

Similar Figures

3.H: Predict and describe results (size, position, orientation) of transformations of two-dimensional figures.

3.H.8: Perform translations, reflections, rotations and dilations of two-dimensional figures using a variety of methods (paper folding, tracing, graph paper).

Dilations
Holiday Snowflake Designer
Rock Art (Transformations)
Similar Figures

3.I: Identify and draw three-dimensional objects from different views (top, side, front and perspective).

3.I.9: Draw representations of three-dimensional geometric objects from different views.

3D and Orthographic Views

3.J: Apply properties of equality and proportionality to solve problems involving congruent or similar figures; e.g., create a scale drawing.

3.J.6: Determine and use scale factors for similar figures to solve problems using proportional reasoning.

Beam to Moon (Ratios and Proportions)
Dilations

4: Patterns, Functions and Algebra

4.A: Describe, extend and determine the rule for patterns and relationships occurring in numeric patterns, computation, geometry, graphs and other applications.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Function Machines 1 (Functions and Tables)
Geometric Sequences

4.B: Represent, analyze and generalize a variety of patterns and functions with tables, graphs, words and symbolic rules.

4.B.1: Represent and analyze patterns, rules and functions with words, tables, graphs and simple variable expressions.

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Introduction to Functions
Linear Functions
Points, Lines, and Equations

4.B.2: Generalize patterns by describing in words how to find the next term.

Arithmetic Sequences
Geometric Sequences

4.C: Use variables to create and solve equations and inequalities representing problem situations.

Modeling and Solving Two-Step Equations
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable

4.D: Use symbolic algebra to represent and explain mathematical relationships.

4.D.9: Recognize a variety of uses for variables; e.g., placeholder for an unknown quantity in an equation, generalization for a pattern, formula.

Using Algebraic Expressions

4.E: Use rules and variables to describe patterns, functions and other relationships.

4.E.3: Recognize and explain when numerical patterns are linear or nonlinear progressions; e.g., 1, 3, 5, 7... is linear and 1, 3, 4, 8, 16... is nonlinear.

Function Machines 1 (Functions and Tables)

4.F: Use representations, such as tables, graphs and equations, to model situations and to solve problems, especially those that involve linear relationships.

4.F.5: Represent linear equations by plotting points in the coordinate plane.

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

4.F.6: Represent inequalities on a number line or a coordinate plane.

Absolute Value Equations and Inequalities
Compound Inequalities
Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Rational Numbers, Opposites, and Absolute Values
Solving Linear Inequalities in One Variable

4.G: Write, simplify and evaluate algebraic expressions.

4.G.1: Represent and analyze patterns, rules and functions with words, tables, graphs and simple variable expressions.

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Introduction to Functions
Linear Functions
Points, Lines, and Equations

4.G.7: Justify that two forms of an algebraic expression are equivalent, and recognize when an expression is simplified; e.g., 4m = m + m + m + m or a [dot] 5 + 4 = 5a + 4.

Exponents and Power Rules
Modeling the Factorization of ax²+bx+c
Operations with Radical Expressions
Order of Operations

4.K: Graph linear equations and inequalities.

4.K.5: Represent linear equations by plotting points in the coordinate plane.

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

4.K.6: Represent inequalities on a number line or a coordinate plane.

Absolute Value Equations and Inequalities
Compound Inequalities
Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Rational Numbers, Opposites, and Absolute Values
Solving Linear Inequalities in One Variable

5: Data Analysis and Probability

5.A: Read, create and use line graphs, histograms, circle graphs, box-and-whisker plots, stem-and-leaf plots, and other representations when appropriate.

5.A.1: Read, create and interpret box-and-whisker plots, stem-and-leaf plots, and other types of graphs, when appropriate.

Box-and-Whisker Plots
Distance-Time Graphs
Forest Ecosystem
Graphing Skills
Reaction Time 2 (Graphs and Statistics)
Stem-and-Leaf Plots

5.C: Evaluate interpretations and conclusions as additional data are collected, modify conclusions and predictions, and justify new findings.

Describing Data Using Statistics
Reaction Time 2 (Graphs and Statistics)

5.D: Compare increasingly complex displays of data, such as multiple sets of data on the same graph.

5.D.5: Compare data from two or more samples to determine how sample selection can influence results.

Movie Reviewer (Mean and Median)
Polling: City
Populations and Samples
Reaction Time 2 (Graphs and Statistics)

5.E: Collect, organize, display and interpret data for a specific purpose or need.

5.E.2: Analyze how decisions about graphing affect the graphical representation; e.g., scale, size of classes in a histogram, number of categories in a circle graph.

Box-and-Whisker Plots
Graphing Skills

5.F: Determine and use the range, mean, median and mode to analyze and compare data, and explain what each indicates about the data.

5.F.3: Analyze a set of data by using and comparing combinations of measures of center (mean, mode, median) and measures of spread (range, quartile, interquartile range), and describe how the inclusion or exclusion of outliers affects those measures.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram

5.H: Find all possible outcomes of simple experiments or problem situations, using methods such as lists, arrays and tree diagrams.

Permutations and Combinations

5.I: Describe the probability of an event using ratios, including fractional notation.

5.I.7: Compute probabilities of compound events; e.g., multiple coin tosses or multiple rolls of number cubes, using such methods as organized lists, tree diagrams and area models.

Independent and Dependent Events

5.J: Compare experimental and theoretical results for a variety of simple experiments.

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

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

5.K.8: Make predictions based on theoretical probabilities, design and conduct an experiment to test the predictions, compare actual results to predicted results, and explain differences.

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

6: Mathematical Processes

6.A: Clarify problem-solving situation and identify potential solution processes; e.g., consider different strategies and approaches to a problem, restate problem from various perspectives.

Estimating Population Size

6.C: Use more than one strategy to solve a problem, and recognize there are advantages associated with various methods.

Estimating Population Size

6.G: Relate mathematical ideas to one another and to other content areas; e.g., use area models for adding fractions, interpret graphs in reading, science and social studies.

Estimating Population Size
Unit Conversions

6.K: Recognize and use mathematical language and symbols when reading, writing and conversing with others.

Using Algebraic Expressions