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
Adult General Education Program: The Florida Department of Education administers the Adult General Education (AGE)Program in accordance with the statutory framework outlined in the following state and federal laws: Florida Statute 1004.02, F.S., Florida Statute 1004.93, F.S., and Title II of the Workforce Investment and Opportunity Act (WIOA), also known as the federal Adult Education and Family Literacy Act (AEFLA).

As administered by the Florida Department of Education, Adult General Education encompasses the following programs, services, and activities:
•	Academic Skills Building (ASB) Program
•	Adult Basic Education (ABE) Program
•	Adult High School (AHS) Program
•	Adult English for Speakers of Other Languages (ESOL) Program
•	General Education Development (GED®) Program
•	Integrated Education and Training (IET) Service Approach
•	Integrated English Literacy and Civics Education (IELCE) Service Approach
•	2-Generation and Family Literacy Service Approaches
•	Workforce Preparation Activities

The Adult General Education Program is designed to serve the following objectives:
•	Provide literacy instruction to adults to obtain the knowledge and skills necessary for employment and economic self-sufficiency.
•	Facilitate adult learners to attain a secondary school diploma and transition to postsecondary education and training, including career pathways.
•	Empower parents to obtain the education and skills that are necessary to participate as full partners in the educational development of their children and to achieve sustainable economic opportunities for their families.
•	Deliver English language instruction to adult English language learners whose native language is other than English or who live in a family or community environment where a language other than English is the dominant language, to achieve competence in reading, writing, speaking, and comprehension of the English language.

Academic Skills Building Program: The Academic Skills Building (ASB) Program is a non-credit program within Adult General Education designed to maintain alignment and ensure educational continuity with Florida’s K12 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 in the ASB program may enroll in one or both courses. 

In alignment with Florida Statute 1004.02, 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 in order to:
•	Attain advanced proficiency in Reasoning Through Language Arts 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 Reasoning Through Language Arts and ASB Mathematics, if they meet the following criteria for enrollment:
•	Have the goal to attain advanced proficiency in Reasoning Through Language Arts and/or Mathematics.
•	Obtain a pre-test score that places them at NRS ABE Levels 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 Reasoning Through Language Arts and Math. As a stand-alone program, ASB is intended to be offered separately 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 ABE NRS levels 1-4 are not suited for enrollment in the ASB Program, which is specifically tailored for students at ABE NRS Levels 5 and 6, equivalent to one and two levels above ABE NRS Level 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 Adult High School 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 NRS levels 1-6 are not suited for enrollment in the ASB Program. This program is specifically tailored for students at ABE NRS Levels 5 and 6, equivalent to one and two levels above Adult ESOL NRS level 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 Math curriculum frameworks and standards of the are based on Florida’s B.E.S.T. standards and as such they are designed to support the adult education learner in becoming proficient in the skills taught in the ASB RLA and Math Program.

STUDENTS
Per State Board Rule 6A-6.014, students eligible to enroll in the ASB Program are those who: 
•	Are age 16 years or older.
•	Are not enrolled in the K12 educational system.
•	Do not have a high school diploma and score into NRS ABE Levels 5 or 6 on a state-approved test.
•	May have a high school diploma but score into NRS ABE Levels 5 or 6 on a state approved test.

EDUCATIONAL FUNCTIONING LEVELS
The term “Educational Functioning Level” as defined by WIOA refers to the literacy levels in Academic Skills Building (ASB), Adult Basic Education (ABE), and Adult English for Speakers of Other Languages (ESOL). These levels are detailed in the National Reporting System (NRS) Guidelines and encompass a set of skills and competencies that students demonstrate in specific skill areas, as specified by the National Reporting System (Code of Federal Regulations Title 34 Subtitle B Chapter IV Part 462).

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

NRS efls	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 DOE 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 Educational Functioning Level

Course Title and Number	NRS efls	Recommended Maximum Hours	
ASB Mathematics
School Districts:  9900501
Florida College System:  ASB0100-ASB0199	ABE Level 5	450 Hours	
	ABE Level 6	450 Hours	

CURRICULUM AND INSTRUCTION
The ASB Mathematics curriculum framework opens by presenting instructors with the Anchor Standards encompassing seven strands: Number Sense and Operations, Fractions, Algebraic Reasoning, Function, Measurement, Geometric Reasoning, and Data and Probability. Emphasizing the term “framework,” it serves as the cornerstone for designing curriculum, aiding agencies and teachers in the selection or creation of instructional materials, techniques, and continuous assessment. The Florida DOE disseminates the ASB Mathematics curriculum framework to agencies statewide, empowering local agency personnel to craft a curriculum relevant to the objectives of their students and instructors. Below is a structured outline of elements to consider when creating the local agency’s curriculum:

1.	Educational Outcomes:
•	Clearly define the educational outcomes that students are expected to achieve upon completion of the course. 
2.	Core Instructional Materials:
•	Develop or select a set of core instructional materials (both print and digital) that are aligned with the defined educational outcomes. This can include textbooks, workbooks, online resources, and multimedia materials.
3.	Needs Assessment Tools:
•	Create a series of needs assessment tools to help teachers identify the specific learning needs and educational goals of individual students. This will aid in prioritizing standards and tailoring instruction to meet the diverse needs of learners.
4.	Supplementary Workbooks:
•	Provide supplementary workbooks that provide exercises for skill-building on topics such as number sense and operations, fractions, algebraic reasoning, measurement, geometric reasoning, and data and probability, within the context of academia, careers, and the workforce.
5.	Pacing Guides and Matrices:
•	Develop pacing guides and matrices that clearly outline the scope and sequence of the curriculum. This helps in organizing the content over the duration of the course and ensures a logical progression of skills.
6.	Recommended Resources:
•	Compile a list of recommended websites, films, and digital learning tools that can be utilized by teachers to supplement the curriculum. Ensure that these resources are relevant, up-to-date, and support the diverse needs of adult learners.
7.	Overview of Content:
•	Provide an overview of the content to be covered in the course, including math standards and any additional content created or collected by instructors.
8.	Learning Activities:
•	Describe a variety of learning activities that can be used regularly for reinforcement. Include a mix of individual and group activities, hands-on projects, and real-world application exercises.

It is recommended to continuously assess and update the agency’s curriculum based on feedback, changes in educational standards, and the evolving needs of learners. Regular collaboration with instructors and seeking input from the Florida DOE Bureau of Adult Education can further enhance the quality and effectiveness of the agency’s curriculum.

Instructors are not obligated to follow the standards sequentially. The distinct needs of each group of students can guide instruction, empowering instructors to modify the sequence of teaching the standards and benchmarks.

ASSESSMENT
The Florida DOE has approved the following tests for the ASB Mathematics course: 
•	CASAS Mathematics GOALS
•	TABE 11&12 Mathematics 

References for Assessment and Reporting: For complete information regarding assessment procedures and policies, see the Florida DOE Assessment Technical Assessment Paper. For guidelines on the procedures for reporting data related to student test results, see the Florida DOE Division of Career and Adult Education (DCAE) Office of Research and 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 Florida DOE defines a new student as someone not previously enrolled in the local agency during the current or preceding program year. New ABE Math 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 Division of Career and Adult Education (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 reading and listening. Subsequently, the agency is required to submit the post-test results to the Florida DOE 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 ABE Math course occurs when the student’s post-test scores exceed NRS ABE level 4. The agency is responsible for reporting the post-test results to the Florida DOE following the guidelines outlined by the DCAE Office of Research and Evaluation.

Documentation of Progression of ASB Math Students in IET Programs: Agencies are required to also submit documentation to FDOE when ASB Math 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 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.

ACCOMMODATIONS
Federal and state legislation requires the provision of accommodations for students with disabilities to meet individual needs and ensure equal access. Adult students with disabilities must self-identify, provide documentation, and request such services. Students with disabilities may need accommodations in areas such as instructional methods and materials, assignments and assessments, time demands and schedules, learning environment, assistive technology, and special communication systems. Documentation of the accommodations requested and provided should be maintained in a confidential file.

ADULT EDUCATION INSTRUCTOR CERTIFICATION 
As per Florida Statute 1012.39 (1)(b), F.S., each school district shall establish the minimal qualifications for part-time and full-time teachers in adult education agencies.
	
INTEGRATED EDUCATION AND TRAINING (IET)
The Florida DOE promotes the planning, development, and implementation of an IET service approach that provides concurrent and contextualized adult education and literacy activities in combination with workforce preparation activities and workforce training for a specific occupation or occupational cluster for the purpose of educational and career advancement. 

Florida’s IET service approach is well-suited for meeting the specific needs of ASB students. Agencies are encouraged to create opportunities that seamlessly integrate education and career-focused content and deliver workforce preparation and training for ASB students.

The IET service approach provides all levels of adult education students the opportunity to acquire the skills needed to:
•	Transition to and complete postsecondary education and training programs.
•	Obtain employment and advance in employment leading to economic self-sufficiency.
•	Exercise the rights and responsibilities of citizenship.

All IET Programs must include the following three components as noted in the following sections of WIOA.
•	Adult education and literacy activities (WIOA Section 203(2)).
•	Workforce preparation activities (WIOA Section 203(17)).
•	Workforce training services (one or more) for a specific occupation or occupation cluster (WIOA Section 134(c)(3)(D)).

To meet the “integrated” requirement of IET, all services must include the following:
•	Adult education and literacy activities run concurrently and contextually with workforce preparation activities and workforce training for a specific occupation or occupational cluster for the purpose of educational and career advancement.
•	Activities are of sufficient intensity and quality, and based on the most rigorous research available, particularly with respect to improving reading, writing, mathematics, and English proficiency of eligible individuals.
•	Occur simultaneously.
•	Use occupationally relevant instructional materials.

The integrated education and training program must have a single set of learning objectives that identifies specific adult education content, workforce preparation activities, and workforce training competencies, and the program activities function cooperatively. 

ACADEMIC SKILLS BUILDING STANDARDS BACKGROUND
In Program Year 2022-2023, the Florida DOE aligned its ABE Standards to Florida’s K-12 Benchmarks for Excellent Student Thinking (B.E.S.T.) Standards in accordance with Executive Order 19-32 dated January 31, 2019. This current version of the ABE Standards is the result of that alignment.  Professional curriculum writers developed the current set of standards with extensive input from a team of Florida Adult Education practitioners who thoroughly reviewed the standards. Thanks to their dedication and efforts, the current standards address the high-priority skills and content that students need to advance toward their postsecondary and career goals.

ASB MATHEMATICAL THINKING AND REASONING STANDARDS FOR ADULT EDUCATION
ASB Math students 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. 

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 Standards are separated into seven Strands: Each Standard has one or more Benchmarks. The instructor may present topic-centered and/or project-based lessons that integrate standards from several strands. Each level-specific standard corresponds to the same-numbered K-12 B.E.S.T. standard. In other words, each standard identifying broad college and career readiness skills has a corresponding level-specific standard illustrating specific level-appropriate expectations called a benchmark skill. Instructors may present topic-centered and/or project-based lessons that integrate standards from several 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	NRS Level	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 NRS LEVELS
Seven strands (also known as domains) comprise Florida’s ASB mathematic standards in the top two NRS Educational Functioning Levels: NRS ABE EFLs 5 and 6. Each EFL of the ASB Mathematical course has a limited number of standards. This allows mathematical instruction at each NRS 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. While the standards by design guide instruction, instructors may introduce, practice, reinforce, and develop fluency at lower and/or higher instructional levels.

Table 4: ASB Mathematics Strands/Domains across NRS Educational Functioning Levels and Grade Equivalents

 MATHEMATICS STRANDS/
DOMAINS	NRS Educational Functioning Levels and Grade Equivalents	
	NRS ABE Level 1
0 – 1.9	NRS ABE Level 2
2.0 – 3.9	NRS ABE Level 3
4.0 – 5.9	NRS ABE Level 4
6.0 – 8.9	NRS ABE Level 5
9.0 – 10.9	NRS ABE Level 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 NRS level.

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

NRS Level 5 instructional time 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 (NRS L4). 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 NRS Level 6
High Intermediate Basic Education, GE: 11.0 – 12.9   

NRS Level 6 instructional time 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 percent 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.