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 and use scientific notation.

1.1.1.b: Express and/or use equivalents among fractions, decimals, percents, integers, positive integer exponents, square roots, and/or numbers written in scientific notation.

Square Roots

1.1.4: Understand the concept of inverse proportion and apply direct and inverse proportion.

1.1.4.a: Explain, illustrate, or describe examples of inverse proportion.

Direct and Inverse Variation

1.1.4.b: Determine whether a real-world problem involves direct or inverse proportion.

Determining a Spring Constant
Direct Variation
Direct and Inverse Variation

1.1.4.c: Use direct or inverse proportion to determine an unknown number of objects or an unknown value in a given situation.

Determining a Spring Constant
Direct Variation
Direct and Inverse Variation

1.1.6: Complete multi-step computations with combinations of rational numbers using order of operations and addition, subtraction, multiplication, division, powers, and square roots.

1.1.6.a: Calculate using order of operations on rational numbers.

Fractions with Unlike Denominators

1.1.8: Apply estimation strategies in situations involving multi-step computations of rational numbers using addition, subtraction, multiplication, division, powers, and square roots to predict or determine reasonableness of answers.

1.1.8.b: Use a variety of estimation strategies to predict or to verify the reasonableness of calculated results.

Estimating Population Size

1.1.8.c: Describe a strategy used for estimation using multi-step computations.

Estimating Population Size

1.2: Understand and apply concepts and procedures from measurement.

1.2.1: Understand the relationship between change in one or two linear dimension(s) and corresponding change in perimeter, area, surface area, and volume.

1.2.1.a: Determine and/or describe the impact of a change in two linear dimensions on perimeter, area, surface 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
Pyramids and Cones - Activity A
Rectangle: Perimeter and Area
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

1.2.1.b: Describe how changes in one or more linear dimensions affect perimeter, area, and/or volume in real world situations.

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

1.2.1.c: Determine the change in one or more linear dimensions given a change in perimeter, area, surface 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
Pyramids and Cones - Activity A
Rectangle: Perimeter and Area
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

1.2.3: Apply unit conversions within measurement systems, U.S. or metric, to maintain an appropriate level of precision.

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

Triple Beam Balance

1.2.5: Use formulas to determine measurements related to right prisms, cylinders, cones, or pyramids.

1.2.5.a: Use formulas to determine and label the volume of a compound figure.

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

1.2.5.b: Use formulas to determine and label the surface area of a compound figure.

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

1.2.6: Understand and apply estimation strategies to obtain reasonable measurements at an appropriate level of precision.

1.2.6.a: Determine when approximate measurements are sufficient and estimate a reasonable measurement at an appropriate level of precision.

Triple Beam Balance

1.2.6.d: Select and use a procedure to find a reasonable estimate for and label the volumes of prisms and cylinders.

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

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

1.3.1: Understand the properties of and the relationships among 1-dimensional, 2-dimensional, and 3-dimensional shapes and figures.

1.3.1.a: Make and test conjectures about 2-dimensional and 3-dimensional shapes and their individual attributes and relationships using physical, symbolic, and technological models.

Classifying Quadrilaterals - Activity B
Classifying Triangles
Parallelogram Conditions
Polygon Angle Sum - Activity A
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Special Quadrilaterals
Triangle Angle Sum - Activity A

1.3.1.b: Use the relationship between similar figures to determine the scale factor.

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

1.3.1.c: Match or draw a 3-dimensional figure that could be formed by folding a given net.

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

1.3.2: Use the properties of and relationships among 1-dimensional, 2-dimensional, and 3-dimensional shapes and figures including prisms, cylinders, cones, and pyramids.

1.3.2.a: Match or draw 3-dimensional objects from different views using the same properties and relationships.

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

1.3.2.b: Sort, classify, and label prisms, cylinders, cones, and 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

1.3.2.c: Sort, classify, and label 2-dimensional and 3-dimensional shapes according to characteristics including faces, edges, and vertices, using actual and virtual modeling.

Classifying Quadrilaterals - Activity B
Classifying Triangles
Parallelogram Conditions
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Special Quadrilaterals
Triangle Angle Sum - Activity A

1.3.2.d: Construct geometric figures, including angle bisectors, perpendicular bisectors, and triangles given specific characteristic, using a variety of tools and technologies.

Construct Parallel and Perpendicular Lines
Constructing Congruent Segments and Angles

1.3.2.f: Create a three-dimensional scale drawing with particular geometric properties.

Classifying Triangles

1.3.3: Use geometric properties to determine and plot points on a coordinate grid.

1.3.3.a: Determine geometric properties of two-dimensional objects using coordinates on a grid.

Classifying Triangles

1.3.4: Apply multiple transformations - translations, reflections, and/or rotations to 2-dimensional figures. Apply single dilations to 2-dimensional figures.

1.3.4.a: Use multiple translations, reflections, and/or rotations to create congruent figures on a coordinate grid.

Constructing Congruent Segments and Angles
Reflections
Rotations, Reflections and Translations
Translations

1.3.4.b: Use dilation of a given figure to form a similar figure.

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

1.3.4.c: Determine the final coordinates of a point after multiple transformations.

Rotations, Reflections and Translations

1.3.4.d: Describe a combination of two translations, reflections, and/or rotations to transform one figure to another figure with or without a coordinate grid.

Reflections
Rotations, Reflections and Translations
Translations

1.3.4.e: Determine rotational symmetry of a figure.

Holiday Snowflake Designer

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

1.4.1: Understand the concepts of dependent and independent events.

1.4.1.a: Describe whether the outcome of a first event affects the probability of a later event.

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

1.4.1.b: Describe the difference between dependent and independent events.

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

1.4.1.c: Describe the relationship between theoretical probability and empirical frequency of dependent events using simulations with and without technology.

Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

1.4.2: Use procedures to compute the probability of dependent and independent events.

1.4.2.a: Determine the sample space for independent or dependent events.

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

1.4.2.b: Determine probabilities of dependent and independent events.

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

1.4.2.c: Determine the outcomes and probability of multiple independent or dependent events.

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

1.4.2.d: Modify or revise a simple game based on independent probabilities so that all players have an equal probability of winning.

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

1.4.3: Determine possible sources of bias in questions, data collection methods, samples, and/or measures of central tendency and describe how such bias can be controlled.

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

Polling: Neighborhood

1.4.5: Use bivariate data in tables and displays to predict mathematical relationships.

1.4.5.b: Determine whether an equation for a line is appropriate for a given set of data and supports the judgment with data.

Point-Slope Form of a Line - Activity A

1.4.5.c: Match an equation with a set of data or a graphic display.

Box-and-Whisker Plots
Line Plots
Stem-and-Leaf Plots

1.4.5.d: Identify trends in a set of data in order to make a prediction based on the information.

Solving Using Trend Lines

1.4.6: Determine and explain how the same set of data can support different points of view.

1.4.6.a: Explain how the same set of data can support different points of view.

Populations and Samples

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

1.5.1: Apply knowledge of patterns or sequences to represent linear functions (W) and/or exponential functions.

1.5.1.a: Represent, extend, or create a pattern or sequence between sets of numbers representing a linear function.

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

1.5.1.b: Identify, extend, or create a geometric sequence or pattern.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

1.5.1.c: Translate among equivalent numerical, graphical, and algebraic forms of a linear function.

Introduction to Functions
Linear Functions
Point-Slope Form of a Line - Activity A
Polynomials and Linear Factors
Slope-Intercept Form of a Line - Activity A
Using Algebraic Equations
Using Tables, Rules and Graphs

1.5.1.e: Describe or represent linear and exponential patterns in words or algebraic symbols.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Exponential Functions - Activity A
Finding Patterns
Geometric Sequences
Linear Functions

1.5.2: Determine an equation or rule for a linear function represented in a pattern, table, graph, or model.

1.5.2.a: Determine an equation of a line from a set of ordered pairs.

Defining a Line with Two Points
Point-Slope Form of a Line - Activity A
Standard Form of a Line

1.5.2.c: Write an equation or rule to describe a sequence.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences
Using Algebraic Equations
Using Algebraic Expressions

1.5.2.d: Write an equation for a line given a graph of the line.

Defining a Line with Two Points
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line

1.5.2.e: Write a rule for a recursive geometric pattern.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

1.5.2.f: Write an expression, equation, or inequality with two variables representing a linear and/or non-linear model of a real-world problem.

Using Algebraic Equations
Using Algebraic Expressions

1.5.2.g: Write an equation for a reasonable line to describe a set of bivariate data from a table or scatter plot.

Correlation
Lines of Best Fit Using Least Squares - Activity A
Point-Slope Form of a Line - Activity A
Solving Using Trend Lines

1.5.4: Use variables to write expressions, linear equations and inequalities that represent situations involving rational numbers, whole number powers, and square roots. Uses variables to write non-linear equations.

1.5.4.a: Use variables to write expressions and equations to represent situations that can be described using repeated addition or repeated multiplication.

Using Algebraic Equations
Using Algebraic Expressions

1.5.4.b: Write equations in recursive form for additive or multiplicative models.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences
Using Algebraic Equations

1.5.4.c: Match an expression or equation to a given real-world situation and explain the meaning of a variable.

Using Algebraic Equations
Using Algebraic Expressions

1.5.4.d: Differentiate between and explain correct vs. incorrect representations of algebraic situations.

Linear Functions

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

Using Algebraic Equations
Using Algebraic Expressions

1.5.5: Apply algebraic properties to simplify expressions involving whole number exponents.

1.5.5.a: Write and/or simplify expressions including applying the distributive property.

Solving Equations By Graphing Each Side
Using Algebraic Equations
Using Algebraic Expressions

1.5.5.b: Simplify an expression involving exponents.

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

1.5.6: Apply properties to solve multi-step equations and systems of equations.

1.5.6.a: Rearrange formulas to solve for a particular variable.

Solving Formulas for any Variable

1.5.6.b: Determine the solution to a system of linear equations using tables, graphs, and/or symbols.

Modeling Linear Systems - Activity A
Solving Linear Systems by Graphing
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A

1.5.6.c: Interpret solutions of systems of equations.

Solving Linear Systems by Graphing
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A

1.5.6.d: Solve, or write and solve, multi-step equations.

Modeling and Solving Two-Step Equations
Solving Two-Step Equations
Using Algebraic Equations

1.5.6.e: Solve, or write and solve, linear inequalities.

Linear Inequalities in Two Variables - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Using Algebraic Equations

3: The student uses mathematical reasoning.

3.1: Analyze information.

3.1.1: Analyze, compare, and integrate mathematical information from multiple sources.

3.1.1.a: Analyze mathematical information or results.

Biconditional Statement
Conditional Statement

3.1.1.b: Integrate information from two or more sources.

Biconditional Statement
Conditional Statement

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 inductive or deductive reasoning.

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

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

3.3.3: Validate thinking about mathematical ideas.

3.3.3.a: Justify or refute claims and supporting arguments using data, models, known facts, patterns, relationships, counter examples, and/or proportional reasoning

Introduction to Functions

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

4.2: Organize, represent, and share information.

4.2.2: Represent mathematical information in graphs or other appropriate forms.

4.2.2.a: Represent mathematical information using pictures, tables, Venn diagrams, scatter plots, 2- or 3-dimensional drawings, or other appropriate including title, labels, appropriate and consistent scales, and accurate display of data.

Scatter Plots - Activity A