|MAFS.6.EE.1.2 (Archived Standard):|| Write, read, and evaluate expressions in which letters stand for numbers.
|MAFS.7.EE.2.3 (Archived Standard):|| Solve multi-step real-life and mathematical problems posed with
positive and negative rational numbers in any form (whole numbers,
fractions, and decimals), using tools strategically. Apply properties of
operations to calculate with numbers in any form; convert between
forms as appropriate; and assess the reasonableness of answers using
mental computation and estimation strategies. For example: If a woman
making $25 an hour gets a 10% raise, she will make an additional 1/10 of
her salary an hour, or $2.50, for a new salary of $27.50. If you want to place
a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches
wide, you will need to place the bar about 9 inches from each edge; this
estimate can be used as a check on the exact computation.|
|MAFS.7.EE.2.4 (Archived Standard):|| Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
|MAFS.7.NS.1.1 (Archived Standard):|| Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
|MAFS.7.NS.1.2 (Archived Standard):|| Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
|MAFS.7.RP.1.3 (Archived Standard):||Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.|
|MAFS.8.EE.1.1 (Archived Standard):||Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3² ×==1/3³=1/27.|
|MAFS.8.EE.1.4 (Archived Standard):||Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.|
|MAFS.8.EE.2.5 (Archived Standard):|| Graph proportional relationships, interpreting the unit rate as the
slope of the graph. Compare two different proportional relationships
represented in different ways. For example, compare a distance-time
graph to a distance-time equation to determine which of two moving
objects has greater speed.|
|MAFS.8.F.2.4 (Archived Standard):||Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.|
|MAFS.8.NS.1.1 (Archived Standard):||Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.|
|MAFS.8.NS.1.2 (Archived Standard):||Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.|
|MAFS.912.A-APR.1.1 (Archived Standard):|| Understand that polynomials form a system analogous to the integers,
namely, they are closed under the operations of addition, subtraction,
and multiplication; add, subtract, and multiply polynomials.|
|MAFS.912.A-APR.2.3 (Archived Standard):|| Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function
defined by the polynomial.|
|MAFS.912.A-APR.3.4 (Archived Standard):||Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x² + y²)² = (x² – y²)² + (2xy)² can be used to generate Pythagorean triples.|
|MAFS.912.A-APR.4.7 (Archived Standard):||Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.|
|MAFS.912.A-CED.1.1 (Archived Standard):||Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational, absolute, and exponential functions. ★|
|MAFS.912.A-CED.1.2 (Archived Standard):||Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. ★|
|MAFS.912.A-CED.1.3 (Archived Standard):||Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. ★|
|MAFS.912.A-CED.1.4 (Archived Standard):||Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R. ★|
|MAFS.912.A-REI.1.1 (Archived Standard):|| Explain each step in solving a simple equation as following from the
equality of numbers asserted at the previous step, starting from the
assumption that the original equation has a solution. Construct a
viable argument to justify a solution method. |
|MAFS.912.A-REI.1.2 (Archived Standard):||Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.|
|MAFS.912.A-REI.2.3 (Archived Standard):|| |
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
|MAFS.912.A-REI.2.4 (Archived Standard):|| Solve quadratic equations in one variable.
|MAFS.912.A-REI.3.5 (Archived Standard):||Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.|
|MAFS.912.A-REI.3.6 (Archived Standard):|| Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.|
|MAFS.912.A-REI.4.10 (Archived Standard):||Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).|
|MAFS.912.A-REI.4.11 (Archived Standard):||Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. ★|
|MAFS.912.A-SSE.1.1 (Archived Standard):|| Interpret expressions that represent a quantity in terms of its context. ★
|MAFS.912.A-SSE.1.2 (Archived Standard):|| Use the structure of an expression to identify ways to rewrite it. For
example, see x4- y4 as (x²)² – (y²)², thus recognizing it as a difference of
squares that can be factored as (x² – y²)(x² + y²).|
|MAFS.912.A-SSE.2.3 (Archived Standard):|| |
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.★
|MAFS.912.F-BF.1.1 (Archived Standard):|| Write a function that describes a relationship between two quantities. ★|
|MAFS.912.F-BF.2.3 (Archived Standard):|| Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x),
f(kx), and f(x + k) for specific values of k (both positive and negative);
find the value of k given the graphs. Experiment with cases and
illustrate an explanation of the effects on the graph using technology.
Include recognizing even and odd functions from their graphs and
algebraic expressions for them.|
|MAFS.912.F-IF.1.1 (Archived Standard):||Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).|
|MAFS.912.F-IF.2.4 (Archived Standard):||For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. ★|
|MAFS.912.F-IF.2.5 (Archived Standard):||Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble engines in a factory, then the positive integers would be an appropriate domain for the function. ★|
|MAFS.912.F-IF.2.6 (Archived Standard):||Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. ★|
|MAFS.912.F-IF.3.7 (Archived Standard):|| Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. ★|
|MAFS.912.F-IF.3.8 (Archived Standard):|| Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
|MAFS.912.G-GPE.2.5 (Archived Standard):|| Prove the slope criteria for parallel and perpendicular lines and use
them to solve geometric problems (e.g., find the equation of a line
parallel or perpendicular to a given line that passes through a given
|MAFS.912.N-Q.1.1 (Archived Standard):||Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. ★|
|MAFS.912.N-Q.1.2 (Archived Standard):|| Define appropriate quantities for the purpose of descriptive modeling. ★|
|MAFS.912.N-Q.1.3 (Archived Standard):||Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. ★|
|MAFS.912.N-RN.1.2 (Archived Standard):||Rewrite expressions involving radicals and rational exponents using the properties of exponents.|
|MAFS.912.S-ID.2.5 (Archived Standard):||Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. ★|
|MAFS.912.S-ID.2.6 (Archived Standard):|| Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. ★|
|MAFS.912.S-ID.3.7 (Archived Standard):||Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. ★|
|MAFS.K12.MP.1.1 (Archived Standard):|| |
Make sense of problems and persevere in solving them.
Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.
|MAFS.K12.MP.2.1 (Archived Standard):|| |
Reason abstractly and quantitatively.
Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.
|MAFS.K12.MP.3.1 (Archived Standard):|| |
Construct viable arguments and critique the reasoning of others.
Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.
|MAFS.K12.MP.4.1 (Archived Standard):|| |
Model with mathematics.
Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.
|MAFS.K12.MP.5.1 (Archived Standard):|| Use appropriate tools strategically. |
Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.
|MAFS.K12.MP.6.1 (Archived Standard):|| |
Attend to precision.
Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.
|MAFS.K12.MP.7.1 (Archived Standard):|| |
Look for and make use of structure.
Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x² + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.
|MAFS.K12.MP.8.1 (Archived Standard):|| |
Look for and express regularity in repeated reasoning.
Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x² + x + 1), and (x – 1)(x³ + x² + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.
|ELD.K12.ELL.MA.1:||English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics.|
|ELD.K12.ELL.SI.1:||English language learners communicate for social and instructional purposes within the school setting.|
General Course Information and Notes
GENERAL NOTESThis course is targeted for students who are not yet “college ready” in mathematics. This course incorporates the Florida Standards for Mathematical Practices as well as the following Florida Standards for Mathematical Content: Expressions and Equations, The Number System, Ratios and Proportional Relationships, Functions, Algebra, Geometry, Number and Quantity, Statistics and Probability, and the Florida Standards for High School Modeling. The standards align with the Mathematics Postsecondary Readiness Competencies deemed necessary for entry-level college courses.
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:
|Course Number: 1200410||
Course Path: Section: Grades PreK to 12 Education Courses > Grade Group: Grades 9 to 12 and Adult Education Courses > Subject: Mathematics > SubSubject: Algebra >
|Abbreviated Title: MATH COLL SUCCESS|
|Number of Credits: Half credit (.5)|
|Course Type: Core Academic Course||Course Level: 2|
|Course Status: Terminated|
|Grade Level(s): 9,10,11,12|
|Graduation Requirement: Mathematics|
| Mathematics (Grades 6-12)|