Author: Ila Waite-Burns;Florida Department of Education
Last saved by: Brown, Maia
Company: Florida Department of Education

2026-2027

Florida Department of Education
Adult General Education Curriculum Framework 

ACADEMIC SKILLS BUILDING MATHEMATICS
Program Title | Academic Skills Building (ASB)
Program Number | 9900500
Course Title | Academic Skills Building Mathematics

Course Number

School Districts: 9900501
Florida College System: ASB0100-ASB0199

CIP Number | 1532010101
Grade Equivalent | 9.0 – 12.9
Grade Level | 30, 31
Standard Length | Varies

PURPOSE

Academic Skills Building Program: The ASB Program is designed to maintain alignment and ensure educational continuity with Florida’s K-12 Benchmarks for Excellent Student Thinking (B.E.S.T.) Standards. The ASB Program consists of two courses, ASB Reasoning through Language Arts (RLA) and ASB Mathematics. Students may enroll in each course independently or in both courses simultaneously.

In alignment with Florida Statute 1004.02, Florida Statutes (F.S.), and the federal Adult Education and Family Literacy Act, the primary objective of the ASB Program is to provide academic and workforce preparation services to individuals who have a high school diploma, but find themselves needing to enhance their educational skills to:

http://www.leg.state.fl.us/Statutes/index.cfm?App_mode=Display_Statute&URL=1000-1099/1004/Sections/1004.02.html

https://www.congress.gov/113/bills/hr803/BILLS-113hr803enr.pdf

•	Attain advanced proficiency in RLA and/or Mathematics.
•	Pursue a secondary career and technical education certificate.
•	Achieve or advance in employment.

Although the primary objective of the ASB Program is to provide academic and workforce preparation services to students who have attained a high school diploma, agencies may enroll individuals who have not attained a high school diploma in one or both courses of the program, ASB RLA and ASB Mathematics, if they meet the following criteria for enrollment:

•	Have the goal to attain advanced proficiency in RLA and/or Mathematics.
•	Obtain pre-test scores that place them within Educational Functioning Level (EFL) 5 or 6.
•	Obtain or advance in employment.

The ASB Program is designed to function independently of other adult education programs, allowing students to concentrate on the specific educational skills they require in the skill areas of RLA and Mathematics. As a stand-alone program, ASB is intended to be offered independently from the ABE, AHS, Adult ESOL and GED® Programs.

•	ABE ≠ ASB: It is not intended that students be enrolled simultaneously in ABE and ASB. The ASB Standards are written at a substantially higher level than the ABE Standards, demanding a greater level of rigor and cognitive effort. As a result, students testing at EFLs 1-4 are not suited for enrollment in the ASB Program, which is specifically tailored for students at EFLs 5 and 6, equivalent to one and two levels above EFL 4. 
•	AHS ≠ ASB: It is not intended that students be enrolled simultaneously in AHS and ASB. The ASB Standards are written at a comparable level of rigor and cognitive demand as those of the AHS Program. However, the ASB Program is not structured to prepare students to obtain a State of Florida high school diploma through concurrent or sequential enrollment in the AHS Program. There are noteworthy distinctions in the standards between the ASB Program and the AHS Program. The AHS program mirrors Florida's B.E.S.T K-12 high school standards precisely and teachers in the AHS Program must hold certification in the courses they teach. In contrast, the standards in ASB's RLA and Mathematics courses represent a subset derived from Florida’s B.E.S.T. K-12 high school standards, designed to assist adult education learners in acquiring specific skills as outlined by state-approved adult education assessments.
•	Adult ESOL ≠ ASB: It is not intended that students be enrolled simultaneously in Adult ESOL and ASB. The ASB Standards are written at a substantially higher level than the Adult ESOL Standards, demanding a greater level of rigor and cognitive effort. As a result, students operating at Adult ESOL EFLs 1-6 are not suited for enrollment in the ASB Program. This program is specifically tailored for students at EFLs 5 and 6, equivalent to one and two levels above Adult ESOL EFL 6.
•	GED® ≠ ASB: It is not intended that students be enrolled simultaneously in GED® and ASB. The ASB Program does not aim to facilitate obtaining a State of Florida high school equivalent through concurrent or sequential enrollment in the GED® Preparation Program. Furthermore, as a standalone program, ASB is not designed to prepare students to pass the GED® tests. The ASB Standards are written at a comparable level of rigor and cognitive demand as those of the GED® Program. However, the curriculum frameworks and standards of the GED® Preparation Program are based on the GED® Tests and their sole purpose is to prepare students to pass the full battery of the GED® Tests. The ASB RLA and Mathematics curriculum frameworks and standards are based on Florida’s B.E.S.T. Standards. As such, they are designed to support the adult education learner in becoming proficient in the skills taught in the ASB RLA and the ASB Mathematics courses.

STUDENTS

Per State Board Rule 6A-6.014, Florida Administrative Code (F.A.C.) - General Requirements for Adult General Education, students eligible to enroll in the ASB Program are those who: 

https://www.flrules.org/gateway/ruleno.asp?id=6A-6.014

•	Are 16 years of age or older.
•	Are not enrolled in the K-12 educational system.
•	May or may not have a high school diploma.
•	Obtain pre-test scores that place them within EFL Level 5 or 6.

Table 1: EFLs for ASB Mathematics Course showing the relation of levels to the Grade Equivalent for each EFL

efl | Course Title and Level | Grade Equivalent
ABE Level 5 | ASB Mathematics Level 5 | 9.0 – 10.9
ABE Level 6 | ASB Mathematics Level 6 | 11.0 – 12.9

PROGRAM LENGTH

_The _maximum _number _of _instructional _hours _recommended _by _the _Florida _Department _of _Education _(FDOE) _is _450 _hours _per _EFL. _Acknowledging _the _individualized _nature _of _learning, _some _students _may _finish _an _EFL _in _fewer _(or _more) _hours _than _the _recommended _maximum _duration _indicated.

Table 2: Recommended Maximum Number of Hours by EFL

Course Title and Number | EFL | Recommended Maximum Hours

_ASB _Mathematics
•	School Districts: 9900501
•	Florida College System: ASB0100-ASB0199

ABE Level 5

450 Hours

| ABE Level 6 | 450 Hours

ASSESSMENT
For guidance on the assessment guidelines and requirements for ASB Math, see State Board Rule 6.A-6.014, F.A.C.

https://www.flrules.org/gateway/ruleno.asp?id=6A-6.014

References for Assessment and Reporting: For complete information regarding assessment procedures and policies, see the FDOE Assessment Technical Assistance Paper. For guidelines on the procedures for reporting data related to student test results, see the FDOE Division of Career and Adult Education (DCAE) Office of Research and Evaluation.

https://www.fldoe.org/academics/career-adult-edu/career-adult-edu-technical-assistance-.stml

https://www.fldoe.org/academics/career-adult-edu/research-evaluation/

Pre-testing: Federal and state regulations mandate that local adult education agencies conduct pre-tests for all new students within the initial 12 hours of enrollment activity. The FDOE defines a new student as someone not previously enrolled in the local agency during the current or preceding program year. New ASB Mathematics students are required to pre-test in the Math skill area. The agency is responsible for submitting the pre-test results to the FDOE in accordance with the guidelines outlined by the DCAE Office of Research and Evaluation.

Post-testing: Once a student completes the recommended instructional hours specified by the test publisher, the local agency will administer post-tests in mathematics. Subsequently, the agency is required to submit the post-test results to the FDOE in accordance with the guidelines established by the DCAE Office of Research and Evaluation.

Course Completion: For state and federal reporting purposes, completion of the ASB Mathematics course occurs when the student’s post-test scores exceed EFL 6. The agency is responsible for reporting the post-test results to the FDOE following the guidelines outlined by the DCAE Office of Research and Evaluation.

Documentation of Progression of ASB Mathematics Students in IET Programs: Agencies are required to also submit documentation to FDOE when ASB Mathematics students, participating in a state approved IET program, make progress through one or more of the following methods:

_•	_Enroll _in _a _postsecondary _program _after _exit _and _by _the _end _of _the _program _year.
_•	_Earn _an _industry _certification _on _the _Master _Credential _List.
_•	_Earn _an _industry _certification _on _the _Perkins _Recognized _Postsecondary _Credential _List.
_•	_Complete _one _year _of _an _apprenticeship _program.

	

_ASB _MATHEMATICAL _THINKING _AND _REASONING _STANDARDS _FOR _ADULT _EDUCATION

_Students _enrolled _in _the _ASB _Mathematics _course _are _expected _to _engage _with _mathematics _through _the _Mathematics _Thinking _and _Reasoning _(MTR) _Standards. _These _standards _are _written _in _clear _language _so _all _stakeholders _can _understand _them, _and _students _can _use _them _as _self-monitoring _tools. _The _MTR _Standards _promote _deeper _learning _and _understanding _of _mathematics. _The _clarifications _are _included _to _guide _teachers _in _the _integration _of _the _MTR _Standards _within _mathematics _instruction. 

Language exact copy from the Florida K-12 B.E.S.T. Standards

_Mathematical _Thinking _and _Reasoning _Standards

_MA.ABE.MTR.1.1

_Actively _participate _in _effortful _learning _both _individually _and _collectively. _Mathematicians _who _participate _in _effortful _learning _both _individually _and _with _others: _Analyze _the _problem _in _a _way _that _makes _sense _given _the _task. _Ask _questions _that _will _help _with _solving _the _task. _Build _perseverance _by _modifying _methods _as _needed _while _solving _a _challenging _task. _Stay _engaged _and _maintain _a _positive _mindset _when _working _to _solve _tasks. _Help _and _support _each _other _when _attempting _a _new _method _or _approach.

_Clarifications: _Teachers _who _encourage _students _to _participate _actively _in _effortful _learning _both _individually _and _with _others: _Cultivate _a _community _of _growth _mindset _learners. _Foster _perseverance _in _students _by _choosing _tasks _that _are _challenging. _Develop _students’ _ability _to _analyze _and _problem-solve. _Recognize _students’ _effort _when _solving _challenging _problems.

_MA.ABE.MTR.2.1

_Demonstrate _understanding _by _representing _problems _in _multiple _ways. _Mathematicians _who _demonstrate _understanding _by _representing _problems _in _multiple _ways: _Build _understanding _through _modeling _and _using _manipulatives. _Represent _solutions _to _problems _in _multiple _ways _using _objects, _drawings, _tables, _graphs _and _equations. _Progress _from _modeling _problems _with _objects _and _drawings _to _using _algorithms _and _equations. _Express _connections _between _concepts _and _representations. _Choose _a _representation _based _on _the _given _context _or _purpose.

_Clarifications: _Teachers _who _encourage _students _to _demonstrate _understanding _by _representing _problems _in _multiple _ways: _Help _students _make _connections _between _concepts _and _representations. _Provide _opportunities _for _students _to _use _manipulatives _when _investigating _concepts. _Guide _students _from _concrete _to _pictorial _to _abstract _representations _as _understanding _progresses. _Show _students _that _various _representations _can _have _different _purposes _and _can _be _useful _in _different _situations.

_MA.ABE.MTR.3.1

_Complete _tasks _with _mathematical _fluency. _Mathematicians _who _complete _tasks _with _mathematical _fluency: _Select _efficient _and _appropriate _methods _for _solving _problems _within _the _given _context. _Maintain _flexibility _and _accuracy _while _performing _procedures _and _mental _calculations. _Complete _tasks _accurately _and _with _confidence. _Adapt _procedures _to _apply _them _to _a _new _context. _Use _feedback _to _improve _efficiency _when _performing _calculations.

_Clarifications: _Teachers _who _encourage _students _to _complete _tasks _with _mathematical _fluency: _Provide _students _with _the _flexibility _to _solve _problems _by _selecting _a _procedure _that _allows _them _to _solve _them _efficiently _and _accurately. _Offer _multiple _opportunities _for _students _to _practice _efficient _and _generalizable _methods. _Provide _opportunities _for _students _to _reflect _on _the _method _they _used _and _determine _if _a _more _efficient _method _could _have _been _used.

_MA.ABE.MTR.4.1

_Engage _in _discussions _that _reflect _on _the _mathematical _thinking _of _self _and _others. _Mathematicians _who _engage _in _discussions _that _reflect _on _the _mathematical _thinking _of _self _and _others: _Communicate _mathematical _ideas, _vocabulary _and _methods _effectively. _Analyze _the _mathematical _thinking _of _others. _Compare _the _efficiency _of _a _method _to _those _expressed _by _others. _Recognize _errors _and _suggest _how _to _correctly _solve _the _task. _Justify _results _by _explaining _methods _and _processes. _Construct _possible _arguments _based _on _evidence. 

_Clarifications: _Teachers _who _encourage _students _to _engage _in _discussions _that _reflect _on _the _mathematical _thinking _of _self _and _others: _Establish _a _culture _in _which _students _ask _questions _of _the _teacher _and _their _peers, _and _error _is _an _opportunity _for _learning. _Create _opportunities _for _students _to _discuss _their _thinking _with _peers. _Select, _sequence _and _present _student _work _to _advance _and _deepen _understanding _of _correct _and _increasingly _efficient _methods. _Develop _students’ _ability _to _justify _methods _and _compare _their _responses _to _the _responses _of _their _peers.

_MA.ABE.MTR.5.1

_Use _patterns _and _structure _to _help _understand _and _connect _mathematical _concepts. _Mathematicians _who _use _patterns _and _structure _to _help _understand _and _connect _mathematical _concepts: _Focus _on _relevant _details _within _a _problem. _Create _plans _and _procedures _to _logically _order _events, _steps _or _ideas _to _solve _problems. _Decompose _a _complex _problem _into _manageable _parts. _Relate _previously _learned _concepts _to _new _concepts. _Look _for _similarities _among _problems. _Connect _solutions _of _problems _to _more _complicated _large-scale _situations.

_Clarifications: _Teachers _who _encourage _students _to _use _patterns _and _structure _to _help _understand _and _connect _mathematical _concepts: _Help _students _recognize _the _patterns _in _the _world _around _them _and _connect _these _patterns _to _mathematical _concepts. _Support _students _to _develop _generalizations _based _on _the _similarities _found _among _problems. _Provide _opportunities _for _students _to _create _plans _and _procedures _to _solve _problems. _Develop _students’ _ability _to _construct _relationships _between _their _current _understanding _and _more _sophisticated _ways _of _thinking.

_MA.ABE.MTR.6.1

_Assess _the _reasonableness _of _solutions. _Mathematicians _who _assess _the _reasonableness _of _solutions: _Estimate _to _discover _possible _solutions. _Use _benchmark _quantities _to _determine _if _a _solution _makes _sense. _Check _calculations _when _solving _problems. _Verify _possible _solutions _by _explaining _the _methods _used. _Evaluate _results _based _on _the _given _context.

_Clarifications: _Teachers _who _encourage _students _to _assess _the _reasonableness _of _solutions: _Have _students _estimate _or _predict _solutions _prior _to _solving. _Prompt _students _to _continually _ask, _“Does _this _solution _make _sense? _How _do _you _know?”  _Reinforce _that _students _check _their _work _as _they _progress _within _and _after _a _task. _Strengthen _students’ _ability _to _verify _solutions _through _justifications.

_MA.ABE.MTR.7.1

_Apply _mathematics _to _real-world _contexts. _Mathematicians _who _apply _mathematics _to _real-world _contexts: _Connect _mathematical _concepts _to _everyday _experiences. _Use _models _and _methods _to _understand, _represent _and _solve _problems. _Perform _investigations _to _gather _data _or _determine _if _a _method _is _appropriate. _Redesign _models _and _methods _to _improve _accuracy _or _efficiency.

_Clarifications: _Teachers _who _encourage _students _to _apply _mathematics _to _real-world _contexts: _Provide _opportunities _for _students _to _create _models, _both _concrete _and _abstract, _and _perform _investigations. _Challenge _students _to _question _the _accuracy _of _their _models _and _methods. _Support _students _as _they _validate _conclusions _by _comparing _them _to _the _given _situation. _Indicate _how _various _concepts _can _be _applied _to _other _disciplines.

_ASB _MATHEMATICS _STANDARDS _CODING _SCHEME

_The _ASB _Mathematics _curriculum _framework _has _these _components: _Strands, _Standards _and _Benchmarks. _The _Strands _include _Number _Sense _and _Operations, _Fractions, _Algebraic _Reasoning, _Function, _Measurement, _Geometric _Reasoning _and _Data _and _Probability. _Each _Standard _is _associated _with _one _or _more _Benchmarks. _The _instructor _may _present _topic-centered _and/or _project-based _lessons _that _integrate _standards _from _multiple _strands. 

Table 3: Coding Scheme for the ASB Mathematics Standards

_ASB _Mathematics _Curriculum _Framework _Coding _Scheme
_Domains/Strands:

_NSO _= _Number _Sense _and _Operations 
_FR _= _Fractions 
_AR _= _Algebraic _Reasoning 
_F _= _Function
_M _= _Measurement
_GR _= _Geometric _Reasoning
_DP _= _Data _and _Probability

_Subject | _efl | _Strand | _Standard | _Benchmark
_Mathematics | _L3 | _NSO | _1a | _1

Examples:
Standard: MA.L5.GR.2c Understand similarity and congruence using models and transformations
Benchmark: MA.L5.GR.2c.1 Describe and apply the effect of a single transformation on two-dimensional figures using coordinates and the coordinate plane.
Benchmark: MA.L5.GR.2c.2 Solve mathematical and real-world problems involving proportional relationships between similar triangles.

ASB MATHEMATICAL STRANDS AND EFLs

Seven strands (also known as domains) comprise Florida’s ASB Mathematic Standards in the top two EFLs: EFLs 5 and 6. Each EFL of the ASB Mathematics course has a limited number of standards. This allows mathematical instruction at each level to have a narrow and deep focus that allows the student to develop an understanding of the following areas:

•	Mathematical Foundations
•	Mathematical Concepts
•	Mathematical Procedural skills
•	Mathematical Fluency. 

The shaded areas in Table 4 below indicate that the domain does not have a standard or primary focus for instruction at that instructional level. Instructors may introduce, practice, reinforce and develop fluency at lower and/or higher instructional levels.

Table 4: ASB Mathematics Strands/Domains across EFLs and Grade Equivalents

MATHEMATICS STRANDS/
DOMAINS

EFLs and Grade Equivalents

| EFL 1 0 – 1.9 | EFL 2 2.0 – 3.9 | EFL 3 4.0 – 5.9 | EFL 4 6.0 – 8.9 | EFL 5 9.0 – 10.9 | EFL 6 11.0 – 12.9
Number Sense and Operations (NSO) | 0 – 1.9 | 2.0 – 3.9 | 4.0 – 5.9 | 6.0 – 8.9 | 9.0 – 10.9 | 11 – 12.9
Fractions (FR) | | 2.0 – 3.9 | 4.0 – 5.9 | | |
Algebraic Reasoning (AR) | 0 – 1.9 | 2.0 – 3.9 | 4.0 – 5.9 | 6.0 – 8.9 | 9.0 – 10.9 | 11 – 12.9
Function* (F) | | | | *7.0 – 8.9 | 9.0 – 10.9 | 11 – 12.9
Measurement (M) | 0 – 1.9 | 2.0 – 3.9 | 4.0 – 5.9 | | |
Geometric Reasoning (GR) | 0 – 1.9 | 2.0 – 3.9 | 4.0 – 5.9 | 6.0 – 8.9 | 9.0 – 10.9 | 11 – 12.9
Data and Probability (DP) | 0 – 1.9 | 2.0 – 3.9 | 4.0 – 5.9 | 6.0 – 8.9 | 9.0 – 10.9 | 11 – 12.9
* In the Function Domain, the suggested instruction should begin at the midpoint of the EFL.

ASB MATHEMEMATICS (MA) STANDARDS
Mathematics Standards EFL 5
High Intermediate Basic Education, GE: 9.0 – 10.9   

EFL Level 5 emphasizes solving real-world problems involving operations with rational numbers, linear equations volume and surface area, as well applications of proportional reasoning in geometry.

Mathematics instruction begins with emphasizing students' ability to reason about and solve real world and mathematical problems that involve the four operations with rational numbers (EFL 4). Students extend their number sense to include problem-solving irrational numbers.  Instruction emphasizes the use of horizontal number lines and absolute value to addition and subtraction with negative and positive rational numbers. 

Instruction includes extending the concept of proportions to recognizing real world and mathematical problems that can be modeled using linear functions as well as patterns in linear functions, graphs and tables.

This level begins to build a foundation for the use of algebraic and graphical representations to solve real world and mathematical problems, involving linear equations, inequalities and pairs of simultaneous linear equations. Instruction also emphasizes the use of linear functions to describe, analyze and model linear relationships between quantities.

Instruction emphasizes how to solve real world and mathematical problems that involve volume and surface area of 3-dimensional geometric figures, such as prisms and pyramids. Students use informal arguments to establish facts about various angle relationships such as the relationships between angles created when parallel lines are cut by a transversal. Applications of the Pythagorean Theorem to determine lengths in real-world contexts and distances in the coordinate plane are also emphasized.

Lastly, instruction provides some attention to making comparisons using measures of center and measures of variability for numerical data. Students also develop, use and evaluate probability models. Students can use scatter plots for bivariate measurement data to interpret patterns of association between two quantities (such as clustering, outliers, positive or negative association, linear or nonlinear association). 

Mathematics Standards EFL 6
High Intermediate Basic Education, GE: 11.0 – 12.9   

EFL 6 emphasizes extending understanding to real numbers, as well as other types of functions, such as quadratic and exponential. 

Mathematics instruction begins with students simplifying algebraic expressions involving rational numbers and exponents. Students build toward working with numeric and algebraic expressions involving radicals. Students are able to assess the reasonableness of calculation results based on the limitations of technology and give results with the appropriate units.

Instruction emphasizes attention to basic understanding of polynomials as well as the four operations with polynomials. Students study the use of quadratic and exponential functions to represent and describe relationships between quantities. Students solve systems of linear equations and inequalities as well as one-variable quadratic and exponential equations. 

Instruction emphasizes constructing graphs and comparing and interpreting functions (including, but not limited to, linear, quadratic and exponential). Students are able to sketch graphs given a verbal description of the relationship and identify and interpret key features of the graphs of functions that arise in context. They are able to select or define a function that appropriately models a relationship and to compare properties of two functions, each represented in a different way (algebraically, graphically, numerically in tables or by verbal description). 

Instruction focuses on solving problems involving similarity and congruence criteria for triangles and use volume and surface area formulas for cylinders, pyramids, cones and spheres to solve problems. Concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTU’s per cubic foot) are emphasized.

Lastly, instruction focuses on summarizing, representing and interpreting data based on two categorical and quantitative variables, including by using frequency tables and 2-way tables to interpret bivariate categorical data. Students compare data sets by looking at commonalities and differences in shape, distribution, center and spread with attention to outliers. They can recognize possible associations and trends in data, in particular in linear models, and distinguish between correlation and causation. They interpret one- and two-variable data, including those with linear and nonlinear relationships. They interpret the slope (rate of change) and intercept (constant term) for a line of best fit and in the context of the data. They understand and account for extreme points of data in their analysis and interpret relative frequencies (joint, marginal and conditional). 

ASB MATHEMATICS (MA) 
Standards and Benchmark Skills
ASB Educational Functioning Levels 5 and 6

Number Sense and Operations
MA.L5.NSO (GE: 9.0 – 10.9)

MA.L5.NSO.1 Solve problems involving rational numbers and extend the understanding of rational numbers to irrational numbers.

MA.L5.NSO.1.1 Plot, order and compare rational and irrational numbers, represented in various forms.
MA.L5.NSO.1.2 Solve multi-step mathematical and real-world problems involving the order of operations with rational numbers, including exponents and radicals. As needed, represent problems using a horizontal number line and apply the concept of absolute value to assess the reasonableness of solutions.

Number Sense and Operations
MA.L6.NSO (GE: 11.0 – 12.9)

MA.L6.NSO.1 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

MA.L6.NSO.1.1 Apply the Laws of Exponents to evaluate numerical expressions and generate equivalent numerical expressions, with rational exponents and/or number bases, with procedural fluency.
MA.L6. NSO.1.2 Generate equivalent algebraic expressions using the properties of exponents.
MA.L6.NSO.1.3 Apply previous understanding of operations with rational numbers to add, subtract, multiply and divide numerical radicals.
MA.L6.NSO.1.4 Rewrite expressions involving radicals using the properties of exponents and understanding of operations with numerical radicals.

Fractions 
MA.L5.FR (GE: 9.0 – 10.9)

Not a focus standard at this level

Fractions 
MA.L6.FR (GE: 11.0 – 12.9)

Not a focus standard at this level

Algebraic Reasoning
MA.L5.AR (GE: 9.0 – 10.9)

MA.L5.AR.1 Rewrite and generate equivalent algebraic expressions and equations.

MA.L5.AR.1.1 Rewrite and generate equivalent algebraic expressions.
MA.L5.AR.1.2 Solve one-variable exponential equations using the properties of exponents. Interpret solutions as viable in terms of the context and identify any extraneous solutions.
MA.L5.AR.1.3 Rearrange equations or formulas to isolate a quantity of interest.
MA.L5.AR.1.4 Choose and interpret units consistently in formulas.

MA.L5.AR.2 Write and graph two-variable linear equations and inequalities to represent relationships between quantities from a table or a written description within a mathematical or real-world context.

MA.L5.AR.2.1 Write a linear two-variable equation to represent relationships between quantities from a graph, a written description or a table of values within a mathematical or real-world context. Determine if a linear relationship is also a proportional relationship.
MA.L5.AR.2.2 Given a table, equation or written description of a linear function, graph that function and determine and interpret its key features (includes slope intercept, point-slope and standard forms.)
MA.L5.AR.2.3 Write two-variable linear inequalities to represent relationships between quantities from a graph or a written description within a mathematical or real-world context.
MA.L5.AR.2.4 Given a mathematical or real-world context, graph the solution set to a two variable linear inequality.

MA.L5.AR.3 Solve mathematical and real-world problems that are modeled with linear functions and inequalities. Graph and interpret key features

MA.L5.AR.3.1 Solve and graph mathematical and real-world problems that are modeled with linear functions. Interpret key features and determine constraints in terms of the context. Key features are limited to domain, range, intercepts and rate of change.
MA.L5.AR.3.2 Given a real-world context, write and solve one-variable multi-step linear equations.
MA.L5.AR.3.3 Given a mathematical or real-world context, write and solve one-variable linear inequalities, including compound inequalities. Represent solutions algebraically or graphically.
Example real-world contexts: Problems involving money, business, converting between currencies using exchange rates and simple interest

MA.L5.AR.4 Develop an understanding of two-variable systems of equations.

MA.L5.AR.4.1 Given a mathematical or real-world context, represent constraints as systems of two linear equations or inequalities and solve. Interpret solutions to problems as viable or nonviable options.
MA.L5.AR.4.2 Graph the solution set of a system of two-variable linear inequalities.

Algebraic Reasoning
MA.L6.AR (GE: 11.0 – 12.9)

MA.L6.AR.1 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. Rewrite simple rational expressions in different forms.

MA.L6.AR.1.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction and multiplication.
MA.L6.AR.1.2 Add, subtract and multiply polynomial expressions with rational number coefficients. 
MA.L6.AR.1.3 Divide a polynomial expression by a monomial expression with rational number coefficients.
MA.L6.AR.1.4 Rewrite a polynomial expression as a product of polynomials over the real number system.

MA.L6.AR.2 Given a table, equation or written description of a quadratic or exponential function, graph that function and determine its key features

MA.L6.AR.2.1 Given a mathematical or real-world context, classify an exponential function as representing growth or decay. 
MA.L6.AR.2.2 Given an expression or equation representing a quadratic function, determine the vertex and zeros and interpret them in terms of a real-world context.
MA.L6.AR.2.3 Write an exponential or quadratic function to represent a relationship between two quantities from a graph, a written description or a table of values within a mathematical or real-world context. 
MA.L6.AR.2.4 Given a table, equation or written description of a quadratic or exponential function, graph that function and determine and interpret its key features. Key features are limited to domain, range, intercepts, positive or negative; end behavior; vertex; and symmetry. Note - logarithmic functions are not included.
Example real-world contexts: Problems involving money, business, simple interest, compound interest and continuously compounded interest

MA.L6.AR.3 Solve and graph mathematical and real-world problems that are modeled with exponential and quadratic functions. Interpret key features and determine constraints in terms of the context. (e.g. problems involving simple interest)

MA.L6.AR.3.1 Identify and interpret parts of an equation or expression that represent a quantity in terms of a mathematical or real-world context, including viewing one or more of its parts as a single entity. 
MA.L6.AR.3.2 Solve and graph mathematical and real-world problems that are modeled with exponential functions. Interpret key features and determine constraints in terms of the context. Key features are limited to domain, range, intercepts, positive or negative; end behavior; intervals where the function is increasing or decreasing; and symmetry. 
Example: Problems involving simple interest
MA.L6.AR.3.3 Given an expression or equation representing an exponential function, reveal the constant percent rate of change per unit interval using the properties of exponents. Interpret the constant percentage rate of change in terms of a real-world context.
MA.L6.AR.3.4 Solve and graph mathematical and real-world problems that are modeled with quadratic functions. Interpret key features and determine constraints in terms of the context. Key features are limited to domain, range, intercepts, positive or negative; vertex; intervals where the function is increasing or decreasing; and symmetry. 
Example: Problems involving simple interest
MA.L6.AR.3.4 Given a mathematical or real-world context, write and solve one-variable quadratic inequalities over the real number system. Represent solutions algebraically or graphically

MA.L6.AR.4 Given a mathematical or real-world context, write and solve a system of two variable linear equations or inequalities algebraically or graphically. Graph the solution set and interpret solutions as viable or nonviable options and represent constraints.

MA.L6.AR.4.1 Given a mathematical or real-world context, write and solve a system of two variable linear equations algebraically or graphically.
MA.L6.AR.4.2 Graph the solution set of a system of two-variable linear inequalities.
MA.L6.AR.4.3 Given a real-world context, represent constraints as systems of linear equations or inequalities. Interpret solutions to problems as viable or nonviable options

Functions
MA.L5.F (GE: 9.0 – 10.9)

MA.L5.F.1 Understand key features of linear functions and apply to solve and model real-world situations.

MA.L5.F.1.1 Given a set of ordered pairs, a table, a graph or mapping diagram, determine whether the relationship is a function. Identify the domain and range of the relation.
MA.L5.F.1.2 Given a function represented in function notation, evaluate the function for an input in its domain. For a real-world context, interpret the output. 
MA.L5.F.1.3 Calculate and interpret the average rate of change of a real-world situation represented graphically, algebraically or in a table over a specified interval.
MA.L5.F.1.4 Compare key features of linear functions each represented algebraically, graphically, in tables or written descriptions. Sketch a graph using key features such as rate of change, intercepts and intervals where the function is increasing or decreasing.

Functions
MA.L6.F (GE: 11.0 – 12.9)

MA.L6.F.1 Understand key features of linear, exponential and quadratic functions and apply them to solve and model real-world situations.

MA.L6.F.1.1 Given an equation or graph that defines a function, classify the function type. Given an input-output table, determine a function type that could represent it.
MA.L6.F.1.2 Compare key features of linear and nonlinear functions each represented algebraically, graphically, in tables or written descriptions. Sketch a graph using key features such as rate of change, intercepts and intervals where the function is increasing or decreasing.
MA.L6.F.1.3 Determine whether a linear, quadratic or exponential function best models a given real-world situation.
Example: Explain the relationship between simple interest and linear growth in contrast to the relationship between compound interest and exponential growth.

Measurement 
MA.L5.M (GE: 9.0 – 10.9)

Not a focus standard at this level

Measurement 
MA.L6.M (GE: 11.0 – 12.9)

Not a focus standard at this level

Geometric Reasoning 
MA.L5.GR (GE: 9.0 – 10.9)

MA.L5.GR.1c Solve mathematical and real-world problems involving postulates, relationships and theorems of lines and angles - including the Pythagorean Theorem and types of angle relationships specific to triangles. Apply precise definitions of geometric terms, as needed.

MA.L5.GR.1c.1 Apply the Pythagorean Theorem to solve mathematical and real-world problems involving unknown side lengths in right triangles.
MA.L5.GR.1c.2 Apply the Pythagorean Theorem to solve mathematical and real-world problems involving the distance between two points in a coordinate plane. Apply precise definitions of points, lines and distance along a line, as needed.
MA.L5.GR.1c.3 Solve mathematical problems involving the relationships between supplementary, complementary, vertical or adjacent angles as well as the relationships of interior and exterior angles of a triangle. Apply precise definitions of angles, perpendicular lines, parallel lines and line segments, as needed.

MA.L5.GR.2a Solve mathematical and real-world problems involving the surface area of three-dimensional figures limited to right-rectangular pyramids and prisms.

MA.L5.GR.2a.1 Solve mathematical and real-world problems involving the volume of right rectangular prisms with positive rational number edge lengths using a visual model and a formula.
MA.L5.GR.2a.2 Given a mathematical or real-world context, find the surface area of right rectangular prisms and right rectangular pyramids using the figure’s net.
MA.L1.GR.2a.3 Use units as a way to understand problems and to guide the solution of multi-step problems.

MA.L5.GR.2c Understand similarity and congruence using models and transformations.

MA.L5.GR.2c.1 Identify transformations that do or do not preserve distance.
MA.L5.GR.2c.2 Identify a sequence of transformations that will map a given figure onto itself or onto another congruent or similar figure.
MA.L5.GR.2c.3 Given a geometric figure and a sequence of transformations, draw the transformed figure on a coordinate plane.

Geometric Reasoning 
MA.L6.GR (GE: 11.0 – 12.9)

MA.L6.GR.1a Apply concepts of density based on modeling situations.

MA.L6.GR.1a.1 Solve mathematical and real-world problems involving dimensions and areas of geometric figures, including scale drawings and scale factors.
Example: Calculating persons per square mile.

MA.L6.GR.1b Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

MA.L6.GR.1b.1 Justify the criteria for triangle congruence using the definition of congruence in terms of rigid transformations.
MA.L6.GR.1b.2 Justify the criteria for triangle similarity using the definition of similarity in terms of non-rigid transformations. 
MA.L6.GR.1b.3 Prove triangle congruence or similarity using Side-Side-Side, Side-Angle-Side, Angle-Side-Angle, Angle-Angle-Side, Angle-Angle and Hypotenuse-Leg.
MA.L6.GR.1b.4 Solve mathematical and real-world problems involving congruence or similarity in two-dimensional figures.
	Example:

MA.L6.GR.2 Solve mathematical and real-world problems involving the volume and surface area of three-dimensional figures limited to cylinders, cones and spheres and apply concepts of density based on volume in modeling situations.

MA.L6.GR.2.1 Given a mathematical or real-world context, find the surface area of a right circular cylinder and cones using the figure’s net. Applying precise definitions of circles, as needed.
MA.L6.GR.2.2 Solve real-world problems involving surface area of right circular cylinders, cones and spheres.
MA.L6.GR.2.3 Solve mathematical and real-world problems involving volume of right circular cylinders, cones and spheres.
Example: Calculating BTUs per cubic foot

Data and Probability
MA.L5.DP (GE: 9.0 – 10.9)

MA.L5.DP.1a Interpret the data distributions, scale, different components and quantities in the various displays.

MA.L5.DP.1a.1 Determine an appropriate measure of center or measure of variation to summarize numerical data, represented numerically or graphically, taking into consideration the context and any outliers.
MA.L5.DP.1a.2 Given two numerical or graphical representations of data, use the measure(s) of center and measure(s) of variability to make comparisons, interpret results and draw conclusions about the two populations.

MA.L5.DP.1b Given a set of data, select an appropriate method to represent the data, depending on whether it is numerical or categorical data and on whether it is univariate or bivariate.

MA.L5.DP.1b.1 Given a set of data, select an appropriate method to represent the data, depending on whether it is numerical or categorical data and on whether it is univariate or bivariate.
MA.L5.DP.1b.2 Choose and interpret the scale and the origin in graphs and data displays.

MA.L5.DP.1c Given a scatter plot with a line of fit and residuals, determine the strength and direction of the correlation. Interpret strength and direction within a real world context.

MA.L5.DP.1c.1 Given a scatter plot within a real-world context, describe patterns of association, strength and direction.
MA.L5.DP.1c.2 Given a scatter plot with a linear association, determine the strength and direction of the correlation using a line of fit and residuals.

MA.L5.DP.2 Develop an understanding of probability. Find and compare experimental and theoretical probabilities.

MA.L5.DP.2.1 Given the probability of a chance event, interpret the likelihood of it occurring. Compare the probabilities of chance events.
MA.L5.DP.2.2 Find the theoretical probability of an event related to a simple experiment.
MA.L5.DP.2.3 Use a simulation of a simple experiment to find experimental probabilities and compare them to theoretical probabilities.

Data and Probability
MA.L6.DP (GE: 11.0 – 12.9)

MA.L6.DP.1a Solve problems involving univariate and bivariate numerical data. | MA.L6.DP.1a For two or more sets of numerical univariate data, calculate and compare the appropriate measures of center and measures of variability, accounting for possible effects of outliers. Interpret any notable features of the shape of the data distribution.
MA.L6.DP.1b Construct a two-way frequency table summarizing bivariate categorical data. Interpret joint and marginal frequencies and determine possible associations in terms of a real-world context. Explain the difference between correlation and causation in the contexts of categorical data. | MA.L6.DP.1b Construct a two-way frequency table summarizing bivariate categorical data. Interpret joint and marginal frequencies and determine possible associations in terms of a real-world context. Explain the difference between correlation and causation in the contexts of categorical data.

MA.L6.DP.1c Fit a linear function to bivariate numerical data that suggests a linear association and interpret the slope and 𝑦-intercept of the model. Use the model to solve real-world problems in terms of the context of the data.

MA.L6.DP.1c.1 Given a scatter plot with a linear association, informally fit a linear function. 
MA.L6.DP.1c.2 Given a scatter plot with a line of fit and residuals, determine the strength and direction of the correlation. Interpret strength and direction within a real-world context.
MA.L6.DP.1c.3 Fit a linear function to bivariate numerical data that suggests a linear association and interpret the slope and 𝑦-intercept of the model. Use the model to solve real-world problems in terms of the context of the data.

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