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    Envisions 

     

    Standards for Mathematical Practice

     

    Students will:

     

    * Make sense of problems and persevere in solving them

    *Reason abstractly and quantitatively

    *Construct viable arguments and critique the reasoning of others

    *Model with mathematics

    *Use appropriate tools strategically

    *Attend to precision

    *Look for and make use of structure

    *Look for and express regularity in repeated reasoning

     

    Common Core Domains

     

    *Ratios and Proportional Relationships

    *The Number System

    *Expressions and Equations

    *Functions

    *Geometry

    *Statistics and Probability

     

    Text is Envision

     

    Our Course of Study - We will choose from the following:

     

    Unit 1: Real Numbers

     

    Understand Irrational Numbers

    • Classify a number as rational or irrational

    • Understand the concepts of square roots and perfect squares

    Evaluate Square Roots  

    • Evaluate square roots to solve problems.

    • Evaluate perfect squares 

    Solve Equations Using Square Roots 

    • Solve equations involving perfect squares  

    • Solve equations involving imperfect squares  

    Power or Products Property, Product of Powers Property, Quotient of Powers Property

    • Multiply and divide expressions with integer exponents.

    • Find the power of a power.

    Negative Exponent Property, Zero Exponent Property

    • Simplify exponential expressions using the Zero Exponential Property and the Negative Exponent Property.

    Use Powers of 10 to Estimate Quantities

    • Estimate and compare very large and very small quantities using powers of 10.

    Understand Scientific Notation

    • Write very large and very small numbers in scientific notation.

    • Convert scientific notation to standard form.

     

     

    Unit 2: Analyze and Solve Linear Equations

    Combine Like Terms to Solve Equations

    • Combine like terms.

    • Solve equations with like terms on one side of the equation.

    • Make sense of scenarios and represent them with equations.

    Solve equations with Variables on Both Sides

    • Solve equations with like terms on both sides of the equation.

    • Make sense of scenarios and represent them with equations.

    Solve Multistep Equations

    • Plan multiple solution pathways and choose one to find the solution.

    Equations with No Solutions or Infinitely Many Solutions

    • Determine the number of solutions to an equation.

    Compare Proportional Relationships

    • Analyze equations, linear graphs, and tables to find unit rates and compare proportional relationships.

    Connect Proportional Relationships and Slope

    • Find the slope of a line using different strategies.

    • Interpret a slope in context and relate it to steepness on a graph.

    Analyze Linear Equations: y=mx

    • Understand how the constant of proportionality and the slope relate in a linear equation.

    • Write a linear equation in the form y=mx when the slope is given.

    • Graph a linear equation in the form y=mx.

    Understand the y-intercept of a Line

    • Interpret and extend the table or graph of a linear relationship to find its y-intercept.

    • Analyze graphs in context to determine and explain the meaning of the y-intercept.

    Analyze Linear Equations: y=mx+b

    • Graph a line from an equation in the form y=mx+b.

    • Write an equation that represents the given graph of a line.

     

     

    Unit 3: Use Functions to Model Relationships

    Understand Relations and Functions

    • Identify whether a relation is a function.

    • Interpret a function.

    Connect Representations of Functions

    • Identify functions in different representations: equations, tables, and graphs.

    • Identify linear and nonlinear functions in different representations.

    Compare Linear and Nonlinear Functions

    • Compare properties of linear functions in different representations.

    • Compare properties of linear and nonlinear functions in different representations.

    Construct Functions to Model Linear Relationships

    • Construct a linear function to model a relationship using an equation in the form y=mx+b.

    Intervals of Increase and Decrease

    • Describe qualitatively the behavior of a function by analyzing its graph.

    • Describe the graph of a function at each interval.

    Sketch Functions from Verbal Descriptions

    • Draw a qualitative graph of a function based on a verbal description.

    • Analyze and interpret the sketch of a graph of a function.

     

    Unit 4: Investigate Bivariate Data

    Construct and Interpret Scatter Plots

    • Construct a scatter plot graph to model paired data.

    • Utilize a scatter plot to identify and interpret the relationship between paired data.

    Analyze Linear Associations

    • Recognize whether the paired data has a linear association, a nonlinear association, or no association.

    • Draw a trend line to determine whether a linear association is positive or negative and strong or weak.

    Use Linear Models to Make Predictions

    • Use the slope and y-intercept of a trend line to make a prediction.

    • Make a prediction when no equation is given by drawing trend lines and writing the equation of the linear model.

    Interpret Two-Way Frequency Tables

    • Organize paired categorical data into a two-way frequency table.

    • Compare and make conjectures about data displayed in a two-way frequency table.

    Interpret Two-Way Relative Frequency Tables

    • Construct two-way frequency tables and two-way relative frequency tables.

    • Compare and make conjectures about data displayed in a two-way relative frequency table.

    Unit 5: Analyze and Solve Systems of Linear Equations

    Estimate Solutions by Inspection

    • Examine graphs of linear systems of equations to determine the number of solutions, based on number of intersection points.

    • Compare the equations in a linear system to look for a relationship between the number of solutions and the slope and y-intercepts of the equations.

    Solve Systems by Graphing

    • Create and examine graphs of linear systems of equations to determine the solution.

    Solve Systems by Substitution

    • Understand how substitution can be used to solve a linear system of equations.

    • Apply this understanding to solve a system of linear equations with one solution, no solutions, or infinitely many solutions.

    Solve Systems by Elimination

    • Understand how the process of elimination can be used to solve a system of linear equations with no solutions, one solution, or infinitely many solutions.

    • Apply this understanding to solve mathematical and real-world problems.

     

    Unit 6: Congruence and Similarity

    Analyze Translations

    • Understand translations

    • Translate a figure on a coordinate plane.

    • Describe a translation.

    Analyze Reflections

    • Understand and describe a reflection.

    • Reflect two-dimensional figures.

    Analyze Rotations

    • Identify and perform a rotation.

    • Determine how a rotation affects a two-dimensional figure.

    Compose Transformations

    • Understand a sequence of transformations.

    • Describe and perform a sequence of transformations.

    Understand Congruent Figures

    • Understand congruence of figures using a series of transformations.

    • Identify congruent figures.

    Describe Dilations

    • Understand dilations.

    • Dilate to enlarge or reduce a figure in a coordinate plane.

    Understand Similar Figures

    • Understand similarity.

    • Complete a similarity transformation.

    • Identify similar figures.

    Angles, Lines, and Transversals

    • Understand the relationships of angles formed by parallel lines and a transversal.

    • Find unknown angle measures.

    Interior and Exterior Angles of Triangles

    • Understand the relationship of the interior angles of a triangle.

    • Find unknown angle measures.

    Angle-Angle Triangle Similarity

    • Determine whether triangles are similar.

    • Solve problems involving similar triangles.

     

    Unit 7: Understand and Apply the Pythagorean Theorem

    Understand the Pythagorean Theorem

    • Understand the Pythagorean Theorem

    • Given two side lengths of a right triangle, use the Pythagorean Theorem to find the length of the third side.

    Understand the Converse of the Pythagorean Theorem

    • Understand why the Converse of the Pythagorean Theorem is true.

    • Apply the Converse of the Pythagorean Theorem to identify right triangles.

    • Use the Converse of the Pythagorean Theorem to analyze two-dimensional shapes.

    Apply the Pythagorean Theorem to Solve Problems

    • Apply the Pythagorean Theorem and its converse to solve real-world problems.

    • Apply the Pythagorean Theorem to solve problems that involve three dimensions.

    Find Distance in the Coordinate Plane

    • Apply the Pythagorean Theorem to find the distance between two points on a map or coordinate plate.

    • Find the perimeter of a figure on a coordinate plane.

    • Identify the coordinates of the third vertex of a triangle on the coordinate plane.

     

    Unit 8: Solve Problems Involving Surface Area and Volume

    Find Surface Area of Three-Dimensional Figures

    • Find the surface areas of cylinders, cones, and spheres.

    Find Volume of Cylinders

    • Recognize the relationship between  the volume of a rectangular prism and the volume of a cylinder.

    • Solve real-world problems involving the volume of a cylinder.

    • Use the formula for the volume of a cylinder to find an unknown measure.

    Find Volume of Cones

    • Recognize the relationship between the volume of a cylinder and the volume of a cone.

    • Use the Pythagorean Theorem when solving volume problems.

    • Find the volume of a cone. Given the circumference of the base, find the volume of a cone.

    Find Volume of Spheres

    • Recognize the relationship between the volume of a cone and the volume of a sphere.

    • Find the volume of a sphere. Given the surface area, find the volume of a sphere.

    • Find the volume of a composite figure.