1: The student understands and applies the concepts and procedures of mathematics.

1.1: Understand and apply concepts and procedures from number sense.

1.1.1: Understand the concept and symbolic representation of rational numbers.

1.1.1.c: Explain the meaning of square root of a whole number and provide examples.

Square Roots

1.1.2: Understand the relative values of rational numbers.

1.1.2.a: Order rational numbers including integers, whole number powers, and square roots, and explain why one rational number is greater than, equal to, or less than another.

Square Roots

1.1.2.b: Order rational numbers including integers, whole number powers, and square roots based on a picture of a real world model, locations on a number line, or symbolic representation.

Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Square Roots

1.1.2.c: Explain why one given rational number including integers, whole-number powers, and square roots is greater than, equal to, or less than another rational number.

Square Roots

1.1.3: Understand and use the distributive property and the properties of addition and multiplication on rational numbers.

1.1.3.b: Use the distributive property to simplify expressions that include integers.

Solving Equations By Graphing Each Side

1.1.3.c: Use the distributive property to factor expressions.

Factoring Special Products
Modeling the Factorization of x²+bx+c

1.1.3.e: Use the addition and multiplication properties, including the distributive property, to assist with computations.

Adding Real Numbers

1.1.4: Apply the concepts of ratio, percent, and direct proportion.

1.1.4.a: Determine an unknown value for a dimension or a number of events or objects using ratio or proportion.

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Geometric Probability - Activity A
Part:Part and Part:Whole Ratios
Perimeters and Areas of Similar Figures
Polling: Neighborhood
Proportions and Common Multipliers
Similar Figures - Activity A
Similar Polygons

1.1.4.b: Determine an unknown value for a dimension or a number of events or objects using percents.

Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Percents and Proportions

1.1.4.c: Select and use the most advantageous representation of ratios or percents in a given situation.

Estimating Population Size
Part:Part and Part:Whole Ratios
Polling: Neighborhood

1.1.4.d: Determine a ratio or percent in a given situation.

Estimating Population Size
Part:Part and Part:Whole Ratios
Percents and Proportions
Polling: Neighborhood

1.1.5: Understand the meaning of addition, subtraction, multiplication, division, powers, and square roots on rational numbers.

1.1.5.b: Explain the meaning of taking whole number powers of integers or square roots of whole numbers using words, pictures, or models.

Square Roots

1.1.5.c: Represent a situation involving multiplication or division of integers, whole number powers of integers, or square roots of whole numbers.

Square Roots

1.1.5.d: Explain how the result of dividing a rational number by a fraction between 0 and 1 is different from the result of dividing the same number by a fraction greater than 1.

Dividing Fractions
Dividing Mixed Numbers

1.1.5.e: Translate a given situation, picture, or illustration into a numeric expression or equation involving decimals, fractions, integers, whole number powers, and square roots of whole numbers.

Square Roots
Using Algebraic Equations
Using Algebraic Expressions

1.1.5.f: Select and/or use an appropriate operation to show understanding of whole number powers and square roots.

Square Roots

1.1.5.g: Convert between equivalent forms of rational numbers including whole number powers and square roots of perfect squares.

Improper Fractions and Mixed Numbers
Percents, Fractions and Decimals
Square Roots

1.1.6: Apply strategies or uses computational procedures using order of operations and addition, subtraction, multiplication, division, powers, and square roots on rational numbers.

1.1.6.a: Compute with rational numbers using order of operations.

Dividing Fractions
Dividing Mixed Numbers
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Order of Operations
Sums and Differences with Decimals

1.1.6.b: Compute using whole number powers and/or square roots of perfect squares.

Adding Real Numbers
Square Roots

1.1.6.d: Complete multi-step computations using two or more different operations with rational numbers.

Dividing Fractions
Dividing Mixed Numbers
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

1.1.7: Apply strategies and uses tools to complete tasks involving computation of rational numbers.

1.1.7.c: Describe strategies for mental computation with integers using powers and square roots.

Adding and Subtracting Integers with Chips
Square Roots

1.1.8: Apply estimation strategies involving computation of rational numbers using addition, subtraction, multiplication, division, powers, and square roots to predict results or determine reasonableness of answers.

1.1.8.b: Use a variety of estimation strategies to predict results prior to computation.

Estimating Population Size
Estimating Sums and Differences

1.1.8.c: Use a variety of estimation strategies to verify the reasonableness of calculated results.

Estimating Population Size
Estimating Sums and Differences

1.1.8.d: Compute to check the reasonableness of estimated answers for a given situation.

Adding Real Numbers

1.1.8.e: Explain an appropriate adjustment when an estimate and a computation do not agree.

Estimating Sums and Differences

1.1.8.f: Explain or describe a strategy for estimation involving computation with decimals, fractions, and integers, using +, -, x, Ö, powers, and square roots.

Adding and Subtracting Integers with Chips
Square Roots

1.2: Understand and apply concepts and procedures from measurement.

1.2.1: Understand how a change in one linear dimension affects surface area and volume of rectangular prisms and cylinders and how changes in two linear dimensions affect perimeter and area of rectangles.

1.2.1.a: Determine and/or describe the impact that a change in one dimension has on volume and surface area in right cylinders and rectangular prisms.

Area of Parallelograms - Activity A
Minimize Perimeter
Perimeter, Circumference, and Area - Activity B
Prisms and Cylinders - Activity A
Rectangle: Perimeter and Area
Special Quadrilaterals
Surface and Lateral Area of Prisms and Cylinders

1.2.1.b: Determine and/or describe a change in a linear dimension given a change in volume and/or surface area of rectangular prisms and cylinders.

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Surface and Lateral Area of Prisms and Cylinders

1.2.1.c: Determine and/or describe the impact on perimeter and/or area of a rectangle caused by a change in two dimensions.

Area of Parallelograms - Activity A
Circle: Circumference and Area
Minimize Perimeter
Perimeter, Circumference, and Area - Activity B
Prisms and Cylinders - Activity A
Rectangle: Perimeter and Area
Special Quadrilaterals

1.2.2: Understand and use rate, slope, and other derived units of measurement.

1.2.2.a: Explain the concept of a rate or slope in a given situation.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Slope - Activity B

1.2.2.c: Calculate a rate of change or slope in a situation.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Slope - Activity B

1.2.3: Explain why different situations require different levels of precision.

1.2.3.a: Describe or explain why different situations require different levels of precision.

Triple Beam Balance

1.2.3.b: Compare situations that require different levels of precision.

Triple Beam Balance

1.2.3.c: Select and describe an appropriate unit of measure for the precision needed in a given situation.

Triple Beam Balance

1.2.5: Use formulas, including the Pythagorean Theorem, to determine measurements related to triangles, rectangular prisms, and right cylinders.

1.2.5.a: Explain how to use a formula to calculate and label the surface area and volume of a prism or cylinder.

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

1.2.5.b: Use the Pythagorean Theorem to determine and label a missing dimension of a right triangle or prism.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Prisms and Cylinders - Activity A
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B

1.2.5.c: Determine and label surface areas of right cylinders and right prisms.

Prisms and Cylinders - Activity A
Surface and Lateral Area of Prisms and Cylinders

1.2.5.d: Determine and label dimensions of a triangle, prism, or cylinder based on a given perimeter, circumference, area, and/or volume.

Area of Parallelograms - Activity A
Circle: Circumference and Area
Minimize Perimeter
Perimeter, Circumference, and Area - Activity B
Prisms and Cylinders - Activity A
Surface and Lateral Area of Prisms and Cylinders

1.2.6: Apply strategies to obtain reasonable estimates of surface area and volume of right cylinders and rectangular prisms, and the lengths of sides of right triangles.

1.2.6.b: Use estimation to determine and label volume and surface area for right cylinders and right prisms and explain why an approximation is appropriate.

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Surface and Lateral Area of Prisms and Cylinders

1.2.6.c: Use estimation strategies to determine and label the approximate length of the third side of a right triangle given the lengths of two sides.

Classifying Triangles
Triangle Angle Sum - Activity A

1.2.6.d: Use estimation strategies to determine and labels the approximate distance or height in a situation using similar triangles or the Pythagorean Theorem.

Distance Formula - Activity A
Estimating Sums and Differences
Geoboard: The Pythagorean Theorem
Perimeters and Areas of Similar Figures
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B
Similar Figures - Activity A
Similar Polygons

1.3: Understand and apply concepts and procedures from geometric sense.

1.3.1: Understand properties of cylinders, cones, and pyramids.

1.3.1.a: Identify or describe cylinders, cones, or pyramids.

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Surface and Lateral Area of Pyramids and Cones

1.3.1.b: Classify and label cylinders, cones, or pyramids.

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

1.3.1.c: Draw nets of cylinders, prisms, and pyramids.

Prisms and Cylinders - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

1.3.1.d: Identify and label rays, lines, end points, line segments, vertices, and angles in three-dimensional shapes and figures.

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

1.3.2: Use the properties of similarity; uses the Pythagorean Theorem to determine if a triangle is a right triangle.

1.3.2.a: Sort, classify, and label similar and congruent figures.

Congruence in Right Triangles
Constructing Congruent Segments and Angles
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures - Activity A
Similar Polygons

1.3.2.b: Use properties of similarity to draw, describe, sort, classify, and/or label two-dimensional figures in illustrations or real life.

Classifying Quadrilaterals - Activity A
Parallelogram Conditions
Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons
Special Quadrilaterals

1.3.2.c: Draw a shape similar to a given complex shape.

Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons

1.3.2.e: Use the Pythagorean Theorem to determine if a triangle is a right triangle.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B

1.3.3: Describe the relative position of points on a coordinate grid.

1.3.3.a: Locate a missing vertex given the coordinates of the vertices of a polygon.

Points in the Coordinate Plane - Activity A

1.3.3.b: Explain a method for finding the missing side of a triangle in a real-world setting.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B

1.3.4: Apply a combination of translations, reflections, and/or rotations to 2-dimensional figures.

1.3.4.a: Use any combination of rotations, reflections, and/or translations to draw or locate congruent figures on a grid.

Reflections
Rotations, Reflections and Translations
Translations

1.3.4.b: Use ordered pairs or labels to describe the location of a picture or an object transformed by any combination of translations, reflections, and/or rotations on a coordinate grid.

Points in the Coordinate Plane - Activity A
Reflections
Rotations, Reflections and Translations
Translations

1.4: Understand and apply concepts and procedures from probability and statistics.

1.4.1: Understand the concept of compound events.

1.4.1.a: Determine and explain when events are compound.

Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events

1.4.1.b: Describe the difference between compound events involving "and" or "or".

Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events

1.4.1.c: Describe or represent compound events.

Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events

1.4.2: Use procedures to determine the probability of compound events.

1.4.2.a: Determine the sample space for simple experiments involving independent or compound events.

Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events

1.4.2.b: Calculate the probability of two independent events occurring simultaneously using various methods including organized lists, tree diagrams, counting procedures, and area models.

Compound Independent Events
Compound Independent and Dependent Events
Geometric Probability - Activity A
Independent and Dependent Events
Permutations
Permutations and Combinations

1.4.2.c: Explain the relationship between theoretical and empirical probability of compound events.

Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events
Polling: City
Probability Simulations
Theoretical and Experimental Probability

1.4.2.d: Predict the probability of outcomes of experiments and relates the predictions to empirical results.

Compound Independent Events
Compound Independent and Dependent Events
Geometric Probability - Activity A
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

1.4.2.e: Design a situation that would produce a given probability.

Geometric Probability - Activity A

1.4.2.f: Design a game using compound probabilities with equal chances of winning for all players.

Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events

1.4.3: Describe how different samples of a population may affect the data collected.

1.4.3.a: Describe bias in population samples and explains a procedure for selecting an unbiased representative sample.

Polling: Neighborhood

1.4.3.c: Determine whether claims made about results are based on biased data due to sampling.

Polling: Neighborhood

1.4.4: Identify clusters and outliers in data and determine effects on the measures of central tendency.

1.4.4.a: Identify clusters and outliers and determine how they may affect measures of central tendency.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

1.4.4.b: Modify a set of data so that the median is a more reasonable measure of central tendency than the mean.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

1.4.4.c: Examine variations in data, including clusters and outliers, to select the most appropriate measure of central tendency to describe a given set of data.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

1.4.4.d: Determine and/or use the mean, median, mode, and/or range for a set of data.

Box-and-Whisker Plots
Describing Data Using Statistics
Line Plots
Mean, Median and Mode

1.4.5: Read and interpret data presented in diagrams, tables of ordered pairs, and scatter plots and makes predictions based on the data.

1.4.5.a: Describe trends or patterns in data presented in a table of ordered pairs or a scatter plot.

Arithmetic and Geometric Sequences
Correlation
Finding Patterns
Geometric Sequences
Scatter Plots - Activity A
Solving Using Trend Lines

1.4.5.b: Read and interpret the data in Venn Diagrams, tables of ordered pairs, and/or scatter plots.

Correlation
Scatter Plots - Activity A
Solving Using Trend Lines

1.4.5.d: Draw trend lines with or without technology and makes predictions about real-world situations.

Solving Using Trend Lines

1.4.5.e: Explain whether stem-and-leaf plot, box-and-whisker plot, or scatter plot is more appropriate for a given set of data, a particular situation, or purpose, or answers a question most effectively.

Box-and-Whisker Plots
Correlation
Scatter Plots - Activity A
Solving Using Trend Lines
Stem-and-Leaf Plots

1.4.5.f: Determine whether claims made about results are based on biased representations of data.

Box-and-Whisker Plots
Histograms
Line Plots
Scatter Plots - Activity A
Stem-and-Leaf Plots

1.4.5.g: Predict an outcome given a linear relationship involving non-negative rational numbers.

Linear Functions
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A

1.5: Understand and apply concepts and procedures from algebraic sense.

1.5.1: Apply knowledge of linear and non-linear relationships to recognize, extend, and create patterns and sequences in tables and graphs.

1.5.1.a: Extend, represent, or create linear and non-linear patterns and sequences using tables and graphs.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Finding Patterns
Geometric Sequences
Linear Functions
Using Tables, Rules and Graphs

1.5.1.c: Use technology to generate graphic representations of linear and non-linear relationships.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Cubic Function Activity
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Linear Functions
Point-Slope Form of a Line - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Rational Functions
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs

1.5.1.d: Extend a pattern by supplying missing terms in the beginning, middle, or end of a linear or non-linear pattern.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences
Linear Functions

1.5.2: Determine a rule for linear and non-linear functions represented in tables, graphs, patterns or situations.

1.5.2.a: Determine a rule, developed from a table, graph, or situation, using words or algebraic symbols.

Cubic Function Activity
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Introduction to Functions
Linear Functions
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Rational Functions
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs

1.5.2.b: Develop a rule that describes a recursive pattern in terms of current and previous values such as the Fibonacci sequence.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

1.5.2.c: Describe a rule and/or construct a table to represent a pattern.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences
Linear Functions
Using Tables, Rules and Graphs

1.5.2.d: Use technology to develop a table or graph from a given rule.

Cubic Function Activity
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Introduction to Functions
Linear Functions
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Rational Functions
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs

1.5.3: Express relationships between quantities using equality and inequality symbols.

1.5.3.a: Express relationships between quantities including whole number exponents and square roots using =, "not equal to", <, >, "less than or equal to" and "greater than or equal to".

Square Roots

1.5.3.b: Describe a situation represented by an equation or inequality involving whole number exponents and/or square roots.

Square Roots
Using Algebraic Equations

1.5.3.c: Use equality and inequality symbols to express relationships between rational numbers using square roots and powers in a given situation.

Simplifying Radicals - Activity A
Square Roots

1.5.4: Use variables to write expressions, linear equations, and inequalities that represent situations involving relationships with rational numbers.

1.5.4.a: Use variables to write an expression, equation, or inequality to represent a given situation.

Using Algebraic Equations
Using Algebraic Expressions

1.5.4.b: Describe a situation that corresponds to a given expression, equation or inequality.

Using Algebraic Equations

1.5.4.c: Describe a situation involving a linear relationship that matches a given graph.

Arithmetic Sequences
Linear Functions
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs

1.5.4.d: Translate among different representations of linear equations, using symbols, graphs, tables, diagrams, or written descriptions.

Cubic Function Activity
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Linear Functions
Point-Slope Form of a Line - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Rational Functions
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs

1.5.4.e: Explain the meaning of a variable in a formula, expression, equation, or inequality.

Using Algebraic Equations
Using Algebraic Expressions

1.5.6: Apply a variety of properties to solve multi-step equations and one-step inequalities with one variable.

1.5.6.a: Solve multi-step single-variable equations involving parentheses, like terms, or variables on both sides of the equal sign.

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Two-Step Equations

1.5.6.b: Write and solve multi-step single variable equations involving parentheses, like terms, or variables on both sides of the equal sign.

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Two-Step Equations
Using Algebraic Equations

1.5.6.c: Solve, or write and solve, one-step inequalities.

Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Using Algebraic Equations

1.5.6.d: Explain or show the meaning of the solution to an equation.

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Two-Step Equations

3: The student uses mathematical reasoning.

3.1: Analyze information.

3.1.1: Analyze numerical, measurement, geometric, probability, statistical, and/or algebraic information from a variety of sources.

3.1.1.a: Analyze mathematical information or results.

Biconditional Statement
Conditional Statement

3.1.1.b: Compare mathematical information represented in tables, charts, graphs, text, diagrams, figures, or pictures.

Biconditional Statement
Conditional Statement
Populations and Samples

3.1.1.d: Differentiate between valid and invalid analysis of mathematical information or results.

Biconditional Statement
Conditional Statement

3.3: Verify results.

3.3.1: Justify results using evidence.

3.3.1.a: Justify results using evidence and information from the problem situation and/or known facts, patterns, and relationships.

Introduction to Functions

3.3.2: Evaluate reasonableness of results.

3.3.2.b: Verify that the solution to a real-world problem makes sense in relation to the situation.

Biconditional Statement
Conditional Statement

4: The student communicates knowledge and understanding in both everyday and mathematical language.

4.1: Gather information.

4.1.2: Extract numerical, measurement, geometric, probability, statistical, and/or algebraic information from multiple sources.

4.1.2.a: Extract and use mathematical information from various sources such as pictures, symbols, text, tables, charts, diagrams, models, and graphs including scatter plots, stem-and-leaf plots, and box-and-whisker plots for a purpose.

Box-and-Whisker Plots
Scatter Plots - Activity A
Solving Using Trend Lines
Stem-and-Leaf Plots

4.2: Organize, represent, and share information.

4.2.2: Represent numerical, measurement, geometric, probability, statistical, and/or algebraic information in graphs or other appropriate forms.

4.2.2.a: Represent mathematical information using tables, charts, scatter plots, stem-and-leaf plots, box-and-whisker plots, pictures, models, drawings, or other appropriate forms including title, labels, appropriate and consistent scales, and accurate display of data.

Box-and-Whisker Plots
Scatter Plots - Activity A
Stem-and-Leaf Plots