CLAUDIO, LAURA

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

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

Click here for Homework

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Homework and all assignments are found in Google Classroom.

Homework will be assigned nightly except Fridays and holidays. All homework assignments will be graded for completion. In order to obtain credit, you must show all your work. If you do not complete your homework one night, you can complete the assignment and hand it in the next day for 1/2 credit. 

Link to course: 8th grade Math (Savvas)

Please check Genesis for up-to-date grades and any missing assignments: Link to Genesis: 

All homework and assignments can be found here: Google Classroom