Grade Level Expectations
1.1.4: Apply understanding of direct and inverse proportion to solve problems.
1.1.4.a: Explain a method for determining whether a real-world problem involves direct proportion or inverse proportion.
1.1.4.b: Explain a method for solving a real-world problem involving direct proportion
1.1.4.c: Explain a method for solving a real-world problem involving inverse proportion.
1.1.4.d: Solve problems using direct or inverse models (e.g., similarity, age of car vs. worth).
1.1.4.e: Explain, illustrate, or describe examples of direct proportion.
1.1.4.f: Explain, illustrate, or describe examples of inverse proportion.
1.1.4.g: Use direct or inverse proportion to determine a number of objects or a measurement in a given situation.
1.1.6: Apply strategies to compute fluently with rational numbers in all forms including whole number exponents.
1.1.6.a: Complete multi-step computations using order of operations in situations involving combinations of rational numbers including whole number exponents and square roots of square numbers.
Fractions with Unlike Denominators
Square Roots
1.1.8: Apply estimation strategies to determine the reasonableness of results in situations involving multi-step computations with rational numbers including whole number powers and square and cube roots.
1.1.8.d: Describe various strategies used during estimation involving integers, rational numbers.
1.2.1: Analyze how changes in one or two dimensions of an object affect perimeter, area, surface area, and volume.
1.2.1.a: Describe and compare the impact that a change in one or more dimensions has on objects (e.g., how doubling one dimension of a cube affects the surface area and volume).
Circle: Circumference and Area
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
1.2.1.b: Describe how changes in the dimensions of objects affect perimeter, area, and volume in real-world situations (e.g., how does the change in the diameter of an oil drum affect the area and 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
1.2.1.c: Solve problems by deriving the changes in two dimensions necessary to obtain a desired surface area and/or volume (e.g., given a box with certain dimensions, make the volume of the box y cubic units by changing two dimensions of the box).
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
1.2.1.d: Compare a given change in one or two dimensions on the perimeter, area, surface areas, or volumes of two objects.
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.e: Determine the change in one dimension given a change in perimeter, area, volume, or surface area.
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
1.2.5: Apply formulas to calculate measurements of right prisms or right circular cylinders.
1.2.5.a: Explain how to use a formula for finding the volume of a prism or cylinder.
Prisms and Cylinders - Activity A
1.2.5.b: Use a formula to find the volume of a prism or cylinder.
Prisms and Cylinders - Activity A
1.2.5.c: Use a formula to derive a dimension of a right prism or right cylinder given other measures.
Prisms and Cylinders - Activity A
Surface and Lateral Area of Prisms and Cylinders
1.2.5.d: Use formulas to describe and compare the surface areas and volumes of two or more right prisms and/or right cylinders.
Prisms and Cylinders - Activity A
Surface and Lateral Area of Prisms and Cylinders
1.2.5.e: Use formulas to obtain measurements needed to describe a right cylinder or right prism.
Hyperbola - Activity A
Prisms and Cylinders - Activity A
Surface and Lateral Area of Prisms and Cylinders
1.2.6: Understand and apply strategies to obtain reasonable measurements at an appropriate level of precision.
1.2.6.b: Estimate a reasonable measurement at an appropriate level of precision.
1.2.6.e: Apply a process that can be used to find a reasonable estimate for the volume of prisms, pyramids, cylinders, and cones.
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Surface and Lateral Area of Pyramids and Cones
1.2.6.f: Estimate volume and surface area for right cylinders and right prisms.
Prisms and Cylinders - Activity A
Surface and Lateral Area of Prisms and Cylinders
1.3.1: Understand the relationship among characteristics of one-dimensional, two-dimensional, and threedimensional figures.
1.3.1.a: Identify and label one- and twodimensional characteristics (rays, lines, end points, line segments, vertices, and angles) in three-dimensional figures.
1.3.1.c: Draw and label with names and symbols nets of right prisms and right cylinders.
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: Describe everyday objects in terms of their geometric characteristics.
1.3.1.e: Describe or classify various shapes based on their characteristics.
Classifying Quadrilaterals - Activity B
Classifying Triangles
Congruence in Right Triangles
Parallelogram Conditions
Prisms and Cylinders - Activity A
Proving Triangles Congruent
Pyramids and Cones - Activity A
Special Quadrilaterals
1.3.1.f: Make and test conjectures about twodimensional and three-dimensional shapes and their individual attributes and relationships using physical, symbolic, and technological models (e.g., diagonal of a rectangle or prism is the longest interior segment; what figures make up cross-sections of a given three-dimensional shape?).
Congruence in Right Triangles
Prisms and Cylinders - Activity A
Proving Triangles Congruent
Special Quadrilaterals
1.3.2: Apply understanding of geometric properties and relationships.
1.3.2.a: Use geometric properties and relationships to describe, compare, and draw two-dimensional and three-dimensional shapes and figures.
Classifying Quadrilaterals - Activity B
Classifying Triangles
Congruence in Right Triangles
Parallelogram Conditions
Proving Triangles Congruent
Special Quadrilaterals
1.3.2.b: Construct geometric figures using a variety of tools and technologies (e.g., angle bisectors, perpendicular bisectors, triangles given specific characteristics).
Construct Parallel and Perpendicular Lines
Constructing Congruent Segments and Angles
1.3.2.d: Use the properties of two-dimensional and three-dimensional shapes to solve mathematical problems (e.g., find the width of a river based on similar triangles; given a set of parallel lines, a transversal, and an angle, find the other angles).
Investigating Angle Theorems - Activity A
Similar Figures - Activity A
Similar Polygons
Triangle Angle Sum - Activity A
1.3.2.e: Compare two-dimensional and threedimensional shapes according to characteristics including faces, edges, and vertices, using actual and virtual modeling.
Congruence in Right Triangles
Proving Triangles Congruent
1.3.3: Apply understanding of geometric properties and location of points.
1.3.3.f: Identify, interpret, and use the meaning of slope of a line as a rate of change using physical, symbolic, and technological models.
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
1.3.4: Apply understanding of multiple transformations to figures.
1.3.4.a: Apply multiple transformations to create congruent and similar figures in any or all of the four quadrants.
Constructing Congruent Segments and Angles
Dilations
Perimeters and Areas of Similar Figures
Reflections
Rotations, Reflections and Translations
Similar Figures - Activity A
Similar Polygons
1.3.4.b: Use multiple transformations (combinations of translations, reflections, or rotations) to draw an image.
Dilations
Reflections
Rotations, Reflections and Translations
Translations
1.3.4.c: Use dilation (expansion or contraction) of a given shape to form a similar shape.
1.3.4.d: Determine the final coordinates of a point after a series of transformations.
Rotations, Reflections and Translations
1.3.4.e: Examine figures to determine rotational symmetry about the center of the shape.
1.3.4.f: Define a set of transformations that would map one onto the other given two similar shapes.
Dilations
Reflections
Rotations, Reflections and Translations
1.3.4.g: Create a design with or without technology using a combination of two or more transformations with one or two two-dimensional figures.
Dilations
Reflections
Rotations, Reflections and Translations
1.4.1: Understand the concept of conditional probability.
1.4.1.a: Compare the probabilities of dependent and independent events.
Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events
1.4.1.c: Explain the difference between dependent and independent events.
Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events
1.4.1.d: Explain and give examples of compound events.
Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events
1.4.2: Apply understanding of dependent and independent events to calculate probabilities.
1.4.2.a: Determine probabilities of dependent and independent events.
Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events
1.4.2.b: Generate the outcomes and probability of multiple independent and dependent events using a model or procedure (e.g., tree diagram, area model, counting procedures).
Binomial Probabilities
Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events
Permutations
Permutations and Combinations
1.4.2.d: Explain 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
Polling: City
Probability Simulations
Theoretical and Experimental Probability
1.4.2.e: Create a simple game based on independent probabilities wherein 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
1.4.2.f: Create a simple game based on compound probabilities.
Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events
1.4.2.g: Determine the sample space for independent or dependent events.
Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events
1.4.4: Understand and apply techniques to find the equation for a reasonable linear model.
1.4.4.b: Determine the equation of a line that fits the data displayed on a scatter plot.
Correlation
Lines of Best Fit Using Least Squares - Activity A
Solving Using Trend Lines
1.4.4.f: Create a graph based on the equation for a line.
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
1.4.5: Analyze a linear model to judge its appropriateness for a data set.
1.4.5.a: Determine whether a straight line is an appropriate way to describe a trend in a set of bivariate data.
Correlation
Solving Using Trend Lines
1.4.5.b: Determine whether the underlying model for a set of data is linear.
Correlation
Solving Using Trend Lines
1.4.6: Apply understanding of statistics to make, analyze, or evaluate a statistical argument.
1.4.6.a: Identify trends in a set of data in order to make a prediction based on the information.
1.4.6.c: State possible factors that may influence a trend but not be reflected in the data (e.g., population growth of deer vs. availability of natural resources or hunting permits).
1.5.1: Apply processes that use repeated addition (linear) or repeated multiplication (exponential).
1.5.1.a: Recognize, extend, or create a pattern or sequence between sets of numbers and/or linear patterns.
Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences
Linear Functions
1.5.1.b: Identify, extend, or create a geometric or arithmetic 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.
Linear Functions
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs
1.5.2: Analyze a pattern, table, graph, or model involving repeated addition (linear) or repeated multiplication (exponential) to write an equation or rule.
1.5.2.a: Find the equation of a line in a variety of ways (e.g., from a table, graph, slopeintercept, point-slope, two points).
Defining a Line with Two Points
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs
1.5.2.c: Identify or write an equation or rule to describe a pattern, sequence, and/or a linear function.
Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences
Linear Functions
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Using Algebraic Equations
Using Algebraic Expressions
1.5.2.d: Write an equation for a line given a set of information (e.g., two points, point-slope, etc.).
Defining a Line with Two Points
Point-Slope Form of a Line - Activity A
Slope - Activity B
Standard Form of a Line
1.5.2.e: Write a recursive definition of a geometric pattern (e.g., Start and New = Old * Number).
Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences
1.5.2.f: Represent systems of equations and inequalities graphically.
Inequalities Involving Absolute Values
Linear Inequalities in Two Variables - Activity A
Linear Programming - Activity A
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Systems of Linear Inequalities (Slope-intercept form) - Activity A
1.5.2.h: Write an expression, equation, or inequality with two variables representing a linear model of a real-world problem.
Using Algebraic Equations
Using Algebraic Expressions
1.5.4: Apply understanding of equations, tables, or graphs to represent situations involving relationships that can be written as repeated addition (linear) or repeated multiplication (exponential).
1.5.4.a: Represent variable quantities through expressions, equations, inequalities, graphs, and tables to represent linear situations involving whole number powers and square and cube roots.
Defining a Line with Two Points
Inequalities Involving Absolute Values
Introduction to Functions
Linear Functions
Linear Inequalities in Two Variables - Activity A
Linear Programming - Activity A
Point-Slope Form of a Line - Activity A
Quadratic and Absolute Value Functions
Slope-Intercept Form of a Line - Activity A
Solving Equations By Graphing Each Side
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Square Roots
Standard Form of a Line
Systems of Linear Inequalities (Slope-intercept form) - Activity A
Using Tables, Rules and Graphs
1.5.4.b: Identify and use variable quantities to read and write expressions and equations to represent situations that can be described using repeated addition (e.g., models that are linear in nature).
1.5.4.c: Identify and use variable quantities to read and write expressions and equations to represent situations that can be described using repeated multiplication (e.g., models that are exponential such as savings accounts and early stages of population growth).
Using Algebraic Equations
Using Algebraic Expressions
1.5.4.d: Recognize and write equations in recursive form for additive models (e.g., starting value, New = Old + some number).
Arithmetic Sequences
Arithmetic and Geometric Sequences
1.5.4.e: Recognize and write equations in recursive form for multiplicative models (e.g., starting value, New = Old x some number).
Arithmetic and Geometric Sequences
Geometric Sequences
1.5.4.f: Select an expression or equation to represent a given real world situation.
Using Algebraic Equations
Using Algebraic Expressions
1.5.5: Apply procedures to simplify expressions.
1.5.5.a: Simplify expressions and evaluate formulas involving exponents.
Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions
1.5.5.b: Justify a simplification of an expression involving exponents.
Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions
1.5.6: Apply procedures to solve equations and systems of equations.
1.5.6.a: Rearrange formulas to solve for a particular variable (e.g., given A =.5bh, solve for h).
Solving Formulas for any Variable
1.5.6.b: Solve real-world situations involving linear relationships and verify that the solution makes sense in relation to the problem.
Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Two-Step Equations
1.5.6.c: Find the solution to a system of linear equations using tables, graphs, and 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.d: 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.e: Solve multi-step equations.
Modeling and Solving Two-Step Equations
Solving Two-Step Equations
1.5.6.f: Use systems of equations to analyze and solve real-life problems.
Solving Linear Systems by Graphing
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A
1.5.6.g: Determine when two linear options yield the same outcome (e.g., given two different investment or profit options, determine when both options will yield the same result).
3.1.1: Synthesize information from multiple sources in order to answer questions.
3.1.1.a: Use the properties of two-dimensional and three-dimensional figures to solve mathematical problems (e.g., find the width of a river based on similar triangles; given a set of parallel lines, a transversal, and an angle, find the other angles).
Investigating Angle Theorems - Activity A
Similar Figures - Activity A
Similar Polygons
Triangle Angle Sum - Activity A
3.2.1: Apply skill of conjecturing and analyze conjectures by formulating a proof or constructing a counter example.
3.2.1.a: Make and test conjectures about twodimensional and three-dimensional figures and their individual attributes and relationships using physical, symbolic, and technological models (e.g., diagonal of a rectangle or prism is the longest interior segment; what figures make up cross-sections of a given three-dimensional shape).
Congruence in Right Triangles
Prisms and Cylinders - Activity A
Proving Triangles Congruent
Special Quadrilaterals
3.2.2: Analyze information to draw conclusions and support them using inductive and deductive reasoning.
3.2.2.a: Compare and describe the volume of cylinders, cones, and prisms when an attribute is changed (e.g., the area of the base, the height of solid).
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
3.3.1: Analyze results using inductive and deductive reasoning.
3.3.1.a: Compare and contrast similar twodimensional figures and shapes using properties of two-dimensional figures and shapes.
Congruence in Right Triangles
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures - Activity A
Similar Polygons
3.3.1.b: Find a reasonable estimate for the volume of prisms, pyramids, cylinders, and cones.
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Surface and Lateral Area of Pyramids and Cones
4.1.2: Synthesize mathematical information for a given purpose from multiple, selfselected sources.
4.1.2.a: State possible factors that may influence a trend but not be reflected in the data (e.g., population growth of deer vs. availability of natural resources or hunting permits).
4.2.2: Understand how to express ideas and situations using mathematical language and notation.
4.2.2.c: Describe and compare the impact that a change in one or more dimensions has on objects (e.g., doubling the edge of a cube affects the surface area).
Circle: Circumference and Area
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
4.2.2.d: Explain 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
Polling: City
Probability Simulations
Theoretical and Experimental Probability
5.1.1: Apply multiple mathematical concepts and procedures in a given problem or situation.
5.1.1.b: Determine the final coordinates of a point after a series of transformations.
Rotations, Reflections and Translations
5.1.2: Understand how to use different mathematical models and representations in the same situation.
5.1.2.a: Identify, interpret, and use the meaning of slope of a line as a rate of change using concrete, symbolic, and technological models.
Direct Variation
Direct and Inverse Variation
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
5.1.2.b: Construct one-dimensional, twodimensional, and three-dimensional geometric figures using a variety of tools and technologies (e.g., angle bisectors, perpendicular bisectors, triangles given specific characteristics).
Construct Parallel and Perpendicular Lines
Constructing Congruent Segments and Angles
5.1.2.c: Find the equation of a line in a variety of ways (e.g., from a table, graph, slopeintercept, point-slope, two points).
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs
5.1.2.d: Find the solution to a system of linear equations using tables, graphs and symbols.
Modeling Linear Systems - Activity A
Solving Linear Systems by Graphing
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A
5.3.1: Understand situations in which mathematics can be used to solve problems with local, national, or international implications.
5.3.1.a: Explain a method for determining whether a real world problem involves direct proportion or inverse proportion.
5.3.1.b: Describe how changes in the dimensions of objects affect perimeter, area, and volume in real-world situations (e.g., how does the change in the diameter of an oil drum affect the area and 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
Correlation last revised: 11/13/2008