The fundamental purpose of this course is to formalize and extend the mathematics that students learned in the middle grades. The critical areas, called units, deepen and extend understanding of linear and exponential relationships by contrasting them with each other and by applying linear models to data that exhibit a linear trend, and students engage in methods for analyzing, solving, and using quadratic functions. The Standards for Mathematical Practice apply throughout each course, and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations.
Unit 1- Relationships Between Quantities and Reasoning with Equations: By the end of eighth grade students have learned to solve linear equations in one variable and have applied graphical and algebraic methods to analyze and solve systems of linear equations in two variables. This unit builds on these earlier experiences by asking students to analyze and explain the process of solving an equation. Students develop fluency writing, interpreting, and translating between various forms of linear equations and inequalities, and using them to solve problems. They master the solution of linear equations and apply related solution techniques and the laws of exponents to the creation and solution of simple exponential equations. All of this work is grounded on understanding quantities and on relationships between them.
SKILLS TO MAINTAIN:
Reinforce understanding of the properties of integer exponents. The initial experience with exponential expressions, equations, and functions involves integer exponents and builds on this understanding.
Unit 2- Linear and Exponential Relationships: In earlier grades, students define, evaluate, and compare functions, and use them to model relationships between quantities. In this unit, students will learn function notation and develop the concepts of domain and range. They explore many examples of functions, including sequences; they interpret functions given graphically, numerically, symbolically, and verbally, translate between representations, and understand the limitations of various representations. Students build on and informally extend their understanding of integer exponents to consider exponential functions. They compare and contrast linear and exponential functions, distinguishing between additive and multiplicative change. Students explore systems of equations and inequalities, and they find and interpret their solutions. They interpret arithmetic sequences as linear functions and geometric sequences as exponential functions.
Unit 3- Descriptive Statistics: This unit builds upon students prior experiences with data, providing students with more formal means of assessing how a model fits data. Students use regression techniques to describe and approximate linear relationships between quantities. They use graphical representations and knowledge of the context to make judgments about the appropriateness of linear models. With linear models, they look at residuals to analyze the goodness of fit.
Unit 4- Expressions and Equations: In this unit, students build on their knowledge from unit 2, where they extended the laws of exponents to rational exponents. Students apply this new understanding of number and strengthen their ability to see structure in and create quadratic and exponential expressions. They create and solve equations, inequalities, and systems of equations involving quadratic expressions.
Unit 5- Quadratic Functions and Modeling: In this unit, students consider quadratic functions, comparing the key characteristics of quadratic functions to those of linear and exponential functions. They select from among these functions to model phenomena. Students learn to anticipate the graph of a quadratic function by interpreting various forms of quadratic expressions. In particular, they identify the real solutions of a quadratic equation as the zeros of a related quadratic function. Students expand their experience with functions to include more specialized functions, absolute value, step, and those that are piece wise-defined.
A/G- Algebra 1 students become fluent in solving characteristic problems involving the analytic geometry of lines, such as writing down the equation of a line given a point and a slope. Such fluency can support them in solving less routine mathematical problems involving linearity, as well as in modeling linear phenomena (including modeling using systems of linear inequalities in two variables).
A-APR.1- Fluency in adding, subtracting, and multiplying polynomials supports students throughout their work in Algebra, as well as in their symbolic work with functions. Manipulation can be more mindful when it is fluent.
A-SSE.1b- Fluency in transforming expressions and chunking (seeing parts of an expression as a single object) is essential in factoring, completing the square, and other mindful algebraic calculations.
English Language Development ELD Standards Special Notes Section:
Teachers are required to provide listening, speaking, reading and writing instruction that allows English language learners (ELL) to communicate information, ideas and concepts for academic success in the content area of Mathematics. For the given level of English language proficiency and with visual, graphic, or interactive support, students will interact with grade level words, expressions, sentences and discourse to process or produce language necessary for academic success. The ELD standard should specify a relevant content area concept or topic of study chosen by curriculum developers and teachers which maximizes an ELL's need for communication and social skills. To access an ELL supporting document which delineates performance definitions and descriptors, please click on the following link:
For additional information on the development and implementation of the ELD standards, please contact the Bureau of Student Achievement through Language Acquisition at email@example.com.
Additional Instructional Resources:
A.V.E. for Success Collection is provided by the Florida Association of School Administrators: http://www.fasa.net/4DCGI/cms/review.html?Action=CMS_Document&DocID=139. Please be aware that these resources have not been reviewed by CPALMS and there may be a charge for the use of some of them in this collection.
Florida Standards Implementation Guide Focus Section:
The Mathematics Florida Standards Implementation Guide was created to support the teaching and learning of the Mathematics Florida Standards. The guide is compartmentalized into three components: focus, coherence, and rigor.Focus means narrowing the scope of content in each grade or course, so students achieve higher levels of understanding and experience math concepts more deeply. The Mathematics standards allow for the teaching and learning of mathematical concepts focused around major clusters at each grade level, enhanced by supporting and additional clusters. The major, supporting and additional clusters are identified, in relation to each grade or course. The cluster designations for this course are below.
MAFS.912.N-RN.1 Extend the properties of exponents to rational exponents.
MAFS.912.A-APR.1 Perform arithmetic operations on polynomials.
MAFS.912.A-CED.1 Create equations that describe numbers or relationships.
MAFS.912.A-REI.1 Understand solving equations as a process of reasoning and explain the reasoning.
MAFS.912.A-REI.2 Solve equations and inequalities in one variable.
MAFS.912.A-REI.4 Represent and solve equations and inequalities graphically.
MAFS.912.A-SSE.1 Interpret the structure of expressions.
MAFS.912.F-IF.1 Understand the concept of a function and use function notation.
MAFS.912.F-IF.2 Interpret functions that arise in applications in terms of the context.
MAFS.912.S-ID.3 Interpret linear models.
MAFS.912.N-Q.1 Reason quantitatively and use units to solve problems.
MAFS.912.A-APR.2 Understand the relationship between zeros and factors of polynomials.
MAFS.912.A-SSE.2 Write expressions in equivalent forms to solve problems.
MAFS.912.F-BF.1 Build a function that models a relationships between two quantities.
MAFS.912.F-IF.3 Analyze functions using different representations.
MAFS.912.F-LE.1 Construct and compare linear, quadratic, and exponential models and solve problems.
MAFS.912.F-LE.2 Interpret expressions for functions in terms of the situation they model.
MAFS.912.S-ID.2 Summarize, represent, and interpret data on two categorical and quantitative variables.
MAFS.912.N-RN.2 Use properties and rational and irrational numbers.
MAFS.912.A-REI.3 Solve systems of equations.
MAFS.912.F-BF.2 Build new functions from existing functions.
MAFS.912.S-ID.1 Summarize, represent, and interpret data on a single count or measurement variable.
Note: Clusters should not be sorted from major to supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting and additional clusters.