Quarter 1 Overview Equations, Inequalities, Absolute Value Students must master creating, solving, and In 7 th grade, students will have developed a Write, solve, and interpret multi-step equations analyzing multi-step equations and basic understanding of how to solve multistep Solve literal equations for a specified variable inequalities in order to have a solid equations and inequalities. Write, solve, and graph inequalities foundation for the remainder of the Algebra In 6 th grade, students were introduced to the Write and graph compound inequalities 1 curriculum. concept of absolute value, and 7 th grade the Solve and graph absolute value equations and inequalities concept of absolute value was revisited. Functions Introducing and formalizing the language of This concept is the first building block in Identify functions and use function notation functions. understanding the relationship between Interpret key features of graphs unique inputs for every output. Understand and interpret rate of change and slope from a table, graph, equation, and from a contextual situation Arithmetic Sequences Introducing sequences and making Building upon understanding of patterns and Write a formula (explicit) for an arithmetic sequence connections to linear functions. relationships between independent and Determine the recursive for a arithmetic sequence dependent variables.
Quarter 2 Overview Linear Functions The students must make the connection that Students are building from the foundation of Be able to write, interpret, and manipulate between the various forms of a linear equation the slope of a line represents a constant rateof-change proportional relationships from 7 th grade. In 6 th grade students create equations from tables Write the equation of a line in slope-intercept The students need to explore functions, linear and graphs, then identify independent and form, point-slope form, and standard form functions and their behavior in a variety of dependent variables. Write a linear equation given a graph or a table ways: numerical, graphical, analytical, and Analyze key features of a function given its graph verbal. Extensions of Linear Concepts Provides contextual situations where Write, read, and interpret graphs of linear inequalities in two variables piecewise functions, and systems of equations and inequalities can be applied. Create, interpret, and solve a system of linear Giving students opportunities to work with systems by graphing, substitution, and functions in a variety of ways: graphical, elimination numerical, analytical, and verbal. Identify and interpret solutions to systems of linear inequalities Use function notation to read, interpret, and create a piecewise function Create, interpret, and solve absolute value functions and step functions. Equations from Data Create a scatterplot and be able to determine the equation of a trend line Use technology to perform a linear regression and calculate the correlation coefficient Distinguish between correlation and causation Developing a linear model, interpreting its components, using the model for prediction, and recognizing its limitations Students will apply understanding of linear equations to support learning of equations of trend lines. These concepts will build on the knowledge of the previous concept of linear functions. The students will already have a basic understanding of how to write, interpret, and manipulate the various forms of a linear equation. This will help with linear inequalities, piecewise functions, and linear systems. The students will already have a basic understanding of how to write, interpret, and manipulate the various forms of a linear equation, which will support with piecewise functions, absolute functions, step functions, linear inequalities, and linear systems of equations and inequalities. Students have been learning to write and graph linear equations this quarter.
Quarter 3 Overview Exponent Laws Develop and extend students In 6 th grade, students are introduced to expressions and Introduce squares and square roots, and cubes and cube roots understanding of exponents to build an understanding of nonlinear functions. equations with exponents incorporated in them. They use repeated multiplication to change from standard Develop the properties of exponents form to exponential form. The properties of exponents Simplify expressions involving exponents are introduced, for the first time, during this concept. Radicals Develop and extend students This is the first building block involving square roots, Write and simplify radical expressions understanding of radicals to support cube roots, or any radicals. In 6 th grade, students have Understand what is meant by rational exponents work with nonlinear functions and to support concepts in Geometry. Operations with radicals is not a tested standard. worked with factors, which supports in simplifying radicals. Exponential Functions Write a formula (explicit) for a geometric sequence Determine the recursive process for a geometric sequence Understand the definition of exponential function Graph and analyze exponential growth and decay functions Describe key features of graphs Polynomials Identify the parts of a polynomial Be able to perform operations (add, subtract, and multiply) on polynomials Identify and factor the GCF of the terms from the polynomial Factoring polynomials when a=1 and when a>1 Quadratics Model a real-world situation with a quadratic function Identify, interpret, and graph the key features of a quadratic function from both vertex and standard forms Understand the effects that transformations have on the different parent functions Introducing geometric sequences and the formulas for calculating their terms Exponential growth and decay will be the basis for studying exponential functions. Introduce the vocabulary needed to understand polynomials Develop and extend students understanding of performing operations on polynomials Introduce and master the different methods of factoring polynomials. Prepare students for Algebra 2 by modeling motion using quadratic relationships, making connections between multiple ways to represent mathematical information numerically, graphically, verbally, and algebraically. The process of identifying patterns from arithmetic sequences will support identifying patterns in geometric sequences. Exponential functions are introduced, for the first time, during this concept and will be developed further in Algebra 2. In 7 th grade, students are introduced to the concepts of combining like terms, distributive property, and equivalent expressions. In 6 th grade, students are use area models, which help with multiplying and factoring polynomials. In 6 th grade, students worked with the concept of greatest common factor. Factoring out a common factor from a binomial is also introduced, and this is extended in 7 th grade. Students have moved from a table to a graph when covering linear functions in quarter 2. This will help when converting from a table to a graph for quadratic functions.
Quarter 3 Overview Solving Quadratics (Continued in Quarter 4) Introduction of various methods to Students have prior knowledge on solving equations Graphing solve quadratic equations. Increase from quarter one and from 7 th grade. Students have Square root method student s ability to solve a wide variety worked with simplifying radicals and factoring this Factoring of equations and to choose the most quarter, which will support them with the various Completing the square appropriate solution method. methods for solving quadratic equations. Quadratic formula
Quarter 4 Overview Solving Quadratics (Continued from Quarter 3) Introduction of various methods to solve Students have prior knowledge on solving Graphing quadratic equations. Increase student s equations from quarter one and from 7 th Square root method ability to solve a wide variety of equations and grade. Students have worked with Factoring to choose the most appropriate solution simplifying radicals and factoring this quarter, Completing the square method. which will support them with the various Quadratic formula methods for solving quadratic equations. Applying and Modeling Quadratic Equations Write a quadratic function to fit data Use a quadratic model to solve problems Interpret solutions of a quadratic equation in real-world context Construct linear, quadratic, and exponential models for data Graph, interpret, and compare linear, quadratic, exponential, and piecewise-defined functions Equations from Data Use technology to perform quadratic and exponential regressions Compare and contrast linear, quadratic, and exponential regressions Distinguish between scatter plots that show a linear relationship and those where the relationship is not linear Systems of Equations Write a function to model a real-world situation Solve a system of equations by graphing Write a system of equations to model a realworld situation Solve a system of equations algebraically Statistics Computational comparison of center and spread Determining outliers and creating modified box plots Determining appropriate measures of variability Students will be able to apply and extend learning of graphing and solving quadratic equations. The learning about quadratic and exponential functions will support the learning of quadratic and exponential regressions for comparisons with linear regressions. Students will be able to apply understandings of linear and quadratic functions to nonlinear systems of equations. Develop student understanding of statistics. Students would have solved quadratic equations in Quarter 3. Students would have constructed linear and exponential functions in Quarter 2 and 3. Students would have used technology to perform linear regressions in Quarter 2. Students would have learned about linear regressions in Quarter 2. Students learned how to solve linear systems in quarter 2. Students learned how to solve quadratic equations in quarter 3 Students should understand the concepts of central tendencies, dot plots, box plots, histograms, and stem and leaf plots from 6 th and 7 th grade.
Quarter 4 Overview Introduction to Geometry Introduce and develop the concepts of In 7 th grade, students are introduced to angle Pythagorean Theorem geometry. relationships and circle relationships. Parallel lines and Transversals In 6 th and 7 th grade students examine volume Transformations of shapes on a coordinate plane of prisms. Volume of shapes (cone, cylinder, sphere)