Author: Ila Waite-Burns;Florida Department of Education;Philip.Anderson@fldoe.org
Last saved by: Brown, Maia
Company: Florida Department of Education

2026-2027

Florida Department of Education
Adult General Education Curriculum Framework

ADULT BASIC EDUCATION MATHEMATICS
Program Title | Adult Basic Education (ABE)
Program Number | 9900000
Course Title | ABE Mathematics

Course Number

School Districts: 9900001
Florida College System: ABX0100-ABX0199

CIP Number | 1532010100
Grade Equivalent | 0.0 – 8.9
Grade Level | 30, 31

PURPOSE

_Adult _Basic _Education _Program: _The _ABE _Program _is _designed _to _maintain _alignment _and _ensure _educational _continuity _with _Florida’s _K12 _Benchmarks _for _Excellent _Student _Thinking _(B.E.S.T.) _Standards. _The _ABE _Program _consists _of _two _courses, _ABE _Reasoning _through _Language _Arts _(RLA) _and _ABE _Mathematics. _Students _may _enroll _in _each _course _independently _or _in _both _courses _simultaneously.

_In _accordance _with _s. _1004.02, _Florida _Statutes _(F.S.),  _the _ABE _Program _is _guided _by _the _following _objectives:

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

•	Provide educational services that will enable adults to acquire:
o	The skills necessary to attain basic and functional literacy.
o	A high school diploma by completing the AHS program or by passing a high school equivalency examination.
o	An educational foundation that will enable them to become more employable, productive and self-sufficient citizens.
•	Provide educational opportunities for adults who have earned a diploma or high school equivalency diploma but who lack the basic skills necessary to function effectively in everyday situations, to enter the job market or to enter career certificate instruction.

_The _ABE _Mathematics _Program _is _guided _by _the _following _objectives:

_•	_Provide _academic _instruction _and _education _services _below _the _postsecondary _level _that _increase _an _individual’s _ability _to:
_o	_Perform _mathematics _or _other _activities _necessary _for _the _attainment _of _a _secondary _school _diploma _or _its _recognized _equivalent.
_o	_Progress _to _postsecondary _education _and _training.
_o	_Obtain _employment.

_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 _ABE _Mathematics _course _are _those _who: 

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

•	Are 16 years of age or older.
•	May or may not have a high school diploma.
•	Are not enrolled in the K-12 educational system. 
•	Obtain pre-test scores that place them within Educational Functioning Level (EFL) 1 – 4.

_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

_ABE _Mathematics
•	School Districts: 9900001
•	Florida College System: ABX0100-ABX0199

ABE Level 1

_450

| ABE Level 2 | _450
| ABE Level 3 | _300
| ABE Level 4 | _300

ASSESSMENT 
For guidance on the assessment guidelines and requirements for ABE Mathematics, 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: Local adult education agencies must 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 ABE Mathematics students are required to pre-test in the mathematics 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 ABE Mathematics course occurs when the student’s post-test scores exceed EFL 4. 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.

ABE MATHEMATICAL THINKING AND REASONING SKILLS STANDARDS FOR ADULT EDUCATION

ABE Mathematical students are expected to engage with mathematics through the Mathematical 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. To obtain more information on the MTR Standards, refer to the FDOE Bureau of Standards and Instructional Support web page.

https://www.fldoe.org/academics/standards/subject-areas/math-science/mathematics/bestmath.stml

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.

_ABE _MATHEMATICS _STANDARDS _CODING _SCHEME

_The _ABE _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. 

_Table _3: _Coding _Scheme _of _ABE _Mathematics _Curriculum _Framework 

_ABE _Mathematics _Standards _Coding _Scheme
_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:
MA.L3.NSO.1a Understand the place value of multi-digit numbers.
MA.L3.NSO.1a.1 Express how the value of a digit in a multi-digit whole number changes if the digit moves one place to the left or right.
MA.L3.NSO.1a.2 Read and write multi-digit whole numbers from 0 to 1,000,000 using standard form, expanded form and word form.
MA.L3.NSO.1a.3 Plot, order and compare multi-digit whole numbers up to 1,000,000.
MA.L3.NSO.1a.4 Round whole numbers from 0 to 10,000 to the nearest 10,100 or 1,000.
MA.L3.NSO.1a.5 Plot, order and compare decimals up to the hundredths.

ABE MATHEMATICS STANDARDS STRANDS AND EFLs

The ABE Mathematics Standards are presented in two broad instructional groupings: 
1.	Basic = EFL 1 and 2 (Grade Equivalent 0.0 – 3.9)
2.	Intermediate = EFL 3 and 4 (Grade Equivalent 4.0 – 8.9)

Seven strands (also known as domains) comprise Florida’s ABE mathematic standards across four EFLs. Each of the four EFLs of the ABE Mathematics course has a limited number of standards. This allows mathematical instruction at each EFL 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: ABE Mathematics Strands/Domains across EFLs and Grade Equivalents

ABE Mathematics Strands, EFL and Grade Equivalents
Strands | Basic | Intermediate
| EFL 1 GE 0 – 1.9 | EFL 2 GE 2.0 – 3.9 | EFL 3 GE 4.0 – 5.9 | EFL 4 GE 6.0 – 8.9
Number Sense and Operations | ✓ | ✓ | ✓ | ✓
Fractions | | ✓ | ✓ |
Algebraic Reasoning | ✓ | ✓ | ✓ | ✓
Function* | | | | ✓^*
Measurement | ✓ | ✓ | ✓ |
Geometric Reasoning | ✓ | ✓ | ✓ | ✓
Data and Probability | ✓ | ✓ | ✓ | ✓
* In the Function domain, the suggested instruction should begin at the mid-point of the EFL. 

ABE MATHEMATICS (MA) STANDARDS
Mathematics Standards EFL 1 (Basic)
Beginning ABE Literacy, GE 0.0 – 1.9 
 
EFL 1 emphasizes understanding place value. Mathematics instruction begins with basic literacy skills. The primary focus of level 1 is counting, cardinality, number sense and base-ten operations. Students at this level are developing their understanding of whole number relationships, developing an understanding of measurement of physical objects, money and time, two-digit place value and understanding the relationship between addition and subtraction.   
 
This level begins building a foundation for algebra by introducing the concept of an equation, a variable and the meaning of the equal sign, all within the context of addition and subtraction within 20.  
 
Lastly, instruction provides some attention to categorizing, composing and decomposing two- and three- dimensional geometric figures as a basis for understanding the properties of congruence, similarity and symmetry. 
 
ABE Mathematics Standards EFL 2 (Basic) 
Beginning Basic Education, GE: 2.0 – 3.9  
 
EFL 2 emphasizes understanding place value for whole numbers to 1000; adding and subtracting multi-digit whole numbers, including using a standard algorithm and building towards fluency and algebraic reasoning in addition and subtraction to 3 digits; understanding and exploring strategies for multiplication and division within 100 and connecting to area of rectangles. These skills are a crucial foundation for fractions and prepare students for work with rational numbers, ratios, rates and proportions in subsequent levels.  
 
In the areas of measurement and geometry, priorities are using standard units to measure objects, time and perimeter of geometric figures.  Students develop the foundation for area, volume, congruence and symmetry by working with rectangular arrays and areas. Additionally, students extend geometric reasoning to lines and the attributes of quadrilaterals. 
 
ABE Mathematics Standards EFL 3 (Intermediate) 
Low Intermediate Basic Education, GE: 4.0 – 5.9  
 
In EFL 3, the focus is providing a conceptual foundation for learning functions. The emphasis on standards for numbers and operations continues; however, attention to algebra and geometry increase considerably.  
 
Fluency with multi-digit whole numbers, using the standard algorithm, as well as calculations with fractions and decimals, are critical at this level. This extends to working with the concept of ratio and rates, addition and subtraction of fractions and decimals with procedural fluency and understanding why the procedures for multiplying and dividing decimals and fractions make sense.   
 
Students at level 3 generate patterns in numbers and shapes and focus on reading, writing and interpreting expressions and equations. In addition, developing an understanding of the coordinate plane and plotting pairs of numbers in the first quadrant, classifying and measuring angles and developing and finding volumes of right rectangular prisms take precedence.  
 
Measurement and data instruction adds the understanding of measures of center, spread and display of collected data with line plots. Students also interpret mean, median, mode and range. 
 
ABE Mathematics Standards EFL 4 
High Intermediate Basic Education, GE: 6.0 – 8.9    
 
Like preceding levels, EFL 4 also emphasizes number sense and operations, but here the attention is on fluency in all four operations with rational numbers – both negative and positive.  Students must understand and translate between fractions, decimals and percents.  The foundation for understanding of irrational numbers is built here, including calculation with square and cube roots, solving simple quadratic equations and representing numbers in scientific notation. 
 
Another area of concentration is algebra and functions: formulating and reasoning about expressions and equations, creating equivalent expressions using Law of Exponents and solving linear equations and inequalities as well as systems of linear equations; grasping the concept of a function; and using functions to describe quantitative relationships.  
 
Building on the geometric analysis in level 3, the focus turns to analyzing two- and three-dimensional figures (including circles and cylinders), using distance, angle, similarity and congruence and understanding basic right triangle trigonometry.  Extending geometric reasoning to plotting points on the coordinate plane, area and volume of geometric figures and applying the Pythagorean Theorem. 
 
EFL 4 is where understanding and applying ratios, rates and proportional reasoning are developed and applied to solve problems and a bridge between rational number operations and algebraic relationships is created. Students also develop an understanding of proportional relationships in two variables. 
 
Having worked with measurement data in previous levels, students learn to understand summary statistics and distributions and develop statistical thinking, including representing and comparing categorical and numerical data and creating and reasoning about linear relationships including modeling an association in bivariate data with a linear equation. Students will also develop an understanding of probability. 

ABE MATHEMATICS (MA)
Standards and Benchmark Skills
ABE Educational Functioning Levels 1 through 4

Number Sense and Operations
MA.L1.NSO (GE: 0.0 – 1.9)

MA.L1.NSO.1 Recite number names sequentially within 100 and extend counting sequences. Develop an understanding for the place value of two-digit numbers.

MA.L1.NSO.1.1 Recite the number names to 100 by ones and by tens. 
MA.L1.NSO.1.2 Starting at a given number, count forward and backwards within 120 by ones. Skip count by 2s to 20 and by 5s to 100.
MA.L1.NSO.1.3 Read numbers from 0 to 100 written in standard form, expanded form and word form. Write numbers from 0 to 100 using standard form and expanded form.
MA.L1.NSO.1.4 Compose and decompose two-digit numbers in multiple ways using tens and ones. Demonstrate each composition or decomposition with objects, drawings and expressions or equations.
MA.L1.NSO.1.5 Plot, order and compare whole numbers up to 100 using the number line and terms less than, equal to or greater than.

MA.L1.NSO.2 Develop an understanding of addition and subtraction operations with one and two-digit whole numbers.

MA.L1.NSO.2.1 Explore addition of two whole numbers from 0 to 10 and related subtraction facts.
MA.L1.NSO.2.2 Recall addition facts with sums to 10 and related subtraction facts with automaticity.
MA.L1.NSO.2.3 Add two whole numbers with sums from 0 to 20 and subtract using related facts with procedural reliability.
MA.L1.NSO.2.4 Identify the number that is one more, one less, ten more and ten less than a given two-digit number.
MA.L1.NSO.2.5 Explore the addition of a two-digit number and a one-digit number with sums to 100.

Number Sense and Operations
MA.L2.NSO (GE: 2.0 – 3.9)

MA.L2.NSO.1 Understand the place value of four-digit whole numbers.

MA.L2.NSO.1.1 Read and write numbers from 0 to 10,000 using standard form, expanded form and word form.
MA.L2.NSO.1.2 Compose and decompose four-digit numbers in multiple ways using thousands, hundreds, tens and ones. Demonstrate each composition or decomposition using objects, drawings and expressions or equations.
MA.L2.NSO.1.3 Plot, order and compare whole numbers up to 10,000.
MA.L2.NSO.1.4 Round whole numbers from 0 to 1,000 to the nearest 10 or 100.

MA.L2.NSO.2 Add and subtract multi-digit whole numbers. Build an understanding of multiplication and division operations.

MA.L2.NSO.2.1 Recall addition facts with sums to 20 and related subtraction facts with automaticity.
MA.L2.NSO.2.2 Add and subtract multi-digit whole numbers, including using a standard algorithm with procedural fluency.
MA.L2.NSO.2.3 Identify the number that is ten more, ten less, one hundred more and one hundred less than a given three-digit number.
MA.L2.NSO.2.4 Explore multiplication of two whole numbers with products from 0 to 144 and related division facts.
MA.L2.NSO.2.5 Explore the addition of two whole numbers with sums up to 1,000. Explore the subtraction of a whole number from a whole number, each no larger than 1,000.
MA.L2.NSO.2.6 Multiply a one-digit whole number by a multiple of 10, up to 90 or a multiple of 100, up to 900, with procedural reliability.
MA.L2.NSO.2.7 Multiply two whole numbers from 0 to 12 and divide using related facts with procedural reliability.

Number Sense and Operations
MA.L3.NSO (GE: 4.0 – 5.9)

MA.L3.NSO.1a Understand the place value of multi-digit numbers.

MA.L3.NSO.1a.1 Express how the value of a digit in a multi-digit whole-number changes if the digit moves one place to the left or right.
MA.L3.NSO.1a.2 Read and write multi-digit whole numbers from 0 to 1,000,000 using standard form, expanded form and word form.
MA.L3.NSO.1a.3 Plot, order and compare multi-digit whole numbers up to 1,000,000.
MA.L3.NSO.1a.4 Round whole numbers from 0 to 10,000 to the nearest 10,100 or 1,000.
MA.L3.NSO.1a.5 Plot, order and compare decimals up to the hundredths.

MA.L3.NSO.1b Understand the place value of multi-digit numbers with decimals to the thousandths place.

MA.L3.NSO.1b.1 Express how the value of a digit in a multi-digit number with decimals to the thousandths changes if the digit moves one or more places to the left or right.
MA.L3.NSO.1b.2 Read and write multi-digit numbers with decimals to the thousandths using standard form, word form and expanded form.
MA.L3.NSO.1b.3 Compose and decompose multi-digit numbers with decimals to the thousandths in multiple ways using the values of the digits in each place. Demonstrate the compositions or decompositions using objects, drawings and expressions or equations.

MA.L3.NSO.1c Rewrite numbers in equivalent forms. | MA.L3.NSO.1c.1 Know and apply the Laws of Exponents to evaluate numerical expressions and generate equivalent numerical expressions, limited to whole-number exponents.

MA.L3.NSO.2a Build understanding of operations with multi-digit numbers including decimals.

MA.L3.NSO.2a.1 Recall multiplication facts with factors up to 12 and related division facts with automaticity. 
MA.L3.NSO.2a.2 Multiply two whole numbers, up to three digits by up to two digits, with procedural reliability.
MA.L3.NSO.2a.3 Multiply two whole numbers, each up to two digits, including using a standard algorithm with procedural fluency. 
MA.L3.NSO.2a.4 Divide a whole number up to four digits by a one-digit whole number with procedural reliability. Represent remainders as fractional parts of the divisor.
MA.L3.NSO.2a.5 Explore the multiplication and division of multi-digit whole numbers using estimation, rounding and place value. 
MA.L3.NSO.2a.6 Identify the number that is one-tenth more, one-tenth less, one-hundredth more and one-hundredth less than a given number. 
MA.L3.NSO.2a.7 Explore the addition and subtraction of multi-digit numbers with decimals to the hundredths.

MA.L3.NSO.2b Add, subtract, multiply and divide multi-digit numbers.

MA.L3.NSO.2b.1 Multiply multi-digit whole numbers, including using a standard algorithm with procedural fluency.
MA.L3.NSO.2b.2 Divide multi-digit whole numbers, up to five digits by two digits, including using a standard algorithm with procedural fluency. Represent remainders as fractions.
MA.L3.NSO.2b.3 Add and subtract multi-digit numbers with decimals to the thousandths, including using a standard algorithm with procedural fluency.
MA.L3.NSO.2b.4 Explore the multiplication and division of multi-digit numbers with decimals to the hundredths using estimation, rounding and place value. 
MA.L3.NSO.2b.5 Multiply and divide a multi-digit number with decimals to the tenths by one tenth and one-hundredth with procedural reliability.

MA.L3.NSO.3 Apply properties of operations to rewrite numbers in equivalent forms.

MA.L3.NSO.3.1 Given a mathematical or real-world context, find the greatest common factor and least common multiple of two whole numbers.
MA.L3.NSO.3.2 Rewrite the sum of two composite whole numbers having a common factor as a common factor multiplied by the sum of two whole numbers.
MA.L3.NSO.3.3 Express composite whole numbers as a product of prime factors with natural number exponents.

Number Sense and Operations
MA.L4.NSO (GE: 6.0 – 8.9)

MA.L4.NSO.1a Extend knowledge of numbers to negative numbers and develop an understanding of absolute value.

MA.L4.NSO.1a.1 Extend previous understanding of numbers to define rational numbers. Plot, order and compare rational numbers.
MA.L4.NSO.1a.2 Given a mathematical or real-world context, represent quantities that have opposite directions using rational numbers. Compare them on a number line and explain the meaning of zero within its context. 
MA.L4.NSO.1a.3 Given a mathematical or real-world context, interpret the absolute value of a number as the distance from zero on a number line. Find the absolute value of rational numbers.
MA.L4.NSO.1a.4 Solve mathematical and real-world problems involving absolute value, including the comparison of absolute value.

MA.L4.NSO.1b Rewrite rational numbers in different but equivalent forms including fractions, mixed numbers, repeating decimals and percentages to solve mathematical and real-world problems. | MA.L4.NSO.1b.1 Rewrite rational numbers in different but equivalent forms including fractions, mixed numbers, repeating decimals and percentages to solve mathematical and real-world problems

MA.L4.NSO.1c Solve problems involving rational numbers, including numbers in scientific notation and extend the understanding of rational numbers to irrational numbers.

MA.L4.NSO.1c.1 Extend previous understanding of rational numbers to define irrational numbers within the real number system. Locate an approximate value of a numerical expression involving irrational numbers on a number line.
MA.L4.NSO.1c.2 Plot, order and compare rational and irrational numbers, represented in various forms.
MA.L4.NSO.1c.3 Extend previous understanding of the Laws of Exponents to include integer exponents. Apply the Laws of Exponents to evaluate numerical expressions and generate equivalent numerical expressions, limited to integer exponents and rational number bases, with procedural fluency with variables on both sides. 
MA.L4.NSO.1c.4 Add, subtract, multiply and divide numbers expressed in scientific notation with procedural fluency.
MA.L4.NSO.1c.5 Solve real-world problems involving operations with numbers expressed in scientific notation.
MA.L4.NSO.1c.6 Solve multi-step mathematical and real-world problems involving the order of operations with rational numbers, including exponents and radicals.

MA.L4.NSO.2 Add, subtract, multiply and divide rational numbers.

MA.L4.NSO.2.1 Solve mathematical problems using multi-step order of operations with rational numbers including grouping symbols, whole-number exponents and absolute value. 
MA.L4.NSO.2.2 Add, subtract, multiply and divide rational numbers with procedural fluency.
MA.L4.NSO.2.3 Solve real-world problems involving any of the four operations with rational numbers.

MA.L4.NSO.3 Apply properties of operations to rewrite numbers in equivalent forms.

MA.L4.NSO.3.1 Evaluate positive rational numbers and integers with natural number exponents.
MA.L4.NSO.3.2 Rewrite positive rational numbers in different but equivalent forms including fractions, terminating decimals and percentages.

Fractions 
MA.L1.FR (GE: 0.0 – 1.9)

Not a focus standard at this level

Fractions 
MA.L2.FR (GE: 2.0 – 3.9)

MA.L2.FR.1 Understand fractions as numbers and represent fractions.

MA.L2.FR.1.1 Partition circles and rectangles into two, three or four equal-sized parts. Name the parts using appropriate language and describe the whole as two halves, three thirds or four fourths. 
MA.L2.FR.1.2 Partition rectangles into two, three or four equal-sized parts in two different ways showing that equal-sized parts of the same whole may have different shapes.
MA.L2.FR.1.3 Represent and interpret unit fractions in the form 1 / 𝑛 as the quantity formed by one part when a whole is partitioned into 𝑛 equal parts. 
MA.L2.FR.1.4 Represent and interpret fractions, including fractions greater than one, in the form of 𝑚 / 𝑛 as the result of adding the unit fraction 1 / 𝑛 to itself 𝑚 times. 
MA.L2.FR.1.5 Read and write fractions, including fractions greater than one, using standard form, numeral-word form and word form.

MA.L2.FR.2 Order and compare fractions and identify equivalent fractions.

MA.L2.FR.2.1 Plot, order and compare fractional numbers with the same numerator or the same denominator.
MA.L2.FR.2.2 Identify equivalent fractions and explain why they are equivalent.

Fractions 
MA.L3.FR (GE: 4.0 – 5.9)

MA.L3.FR.1a Develop an understanding of the relationship between different fractions and the relationship between fractions and decimals.

MA.L3.FR.1a.1 Model and express a fraction, including mixed numbers and fractions greater than one, with the denominator 10 as an equivalent fraction with the denominator 100.
MA.L3.FR.1a.2 Use decimal notation to represent fractions with denominators of 10 or 100, including mixed numbers and fractions greater than 1 and use fractional notation with denominators of 10 or 100 to represent decimals.
MA.L3.FR.1a.3 Identify and generate equivalent fractions, including fractions greater than one. Describe how the numerator and denominator are affected when the equivalent fraction is created.
MA.L3.FR.1a.4 Plot, order and compare fractions, including mixed numbers and fractions greater than one, with different numerators and different denominators.

MA.L3.FR.1b Interpret a fraction as an answer to a division problem. | MA.L3.FR.1b.1 Given a mathematical or real-world problem, represent the division of two whole numbers as a fraction.

MA.L3.FR.2a Build a foundation of addition, subtraction and multiplication operations with fractions.

MA.L3.FR.2a.1 Decompose a fraction, including mixed numbers and fractions greater than one, into a sum of fractions with the same denominator in multiple ways. Demonstrate each decomposition with objects, drawings and equations.
MA.L3.FR.2a.2 Add and subtract fractions with like denominators, including mixed numbers and fractions greater than one, with procedural reliability.
MA.L3.FR.2a.3 Explore the addition of a fraction with denominator of 10 to a fraction with denominator of 100 using equivalent fractions.
MA.L3.FR.2a.4 Extend previous understanding of multiplication to explore the multiplication of a fraction by a whole number or a whole number by a fraction.

MA.L3.FR.2b Perform operations with fractions.

MA.L3.FR.2b.1 Extend previous understanding of multiplication to multiply a fraction by a fraction, including mixed numbers and fractions greater than 1, with procedural reliability.
MA.L3.FR.2b.2 When multiplying a given number by a fraction less than 1 or a fraction greater than 1, predict and explain the relative size of the product to the given number without calculating.
MA.L3.FR.2b.3 Extend previous understanding of division to explore the division of a unit fraction by a whole number and a whole number by a unit fraction.

Fractions 
MA.L4.FR (GE: 6.0 – 8.9)

Not a focus standard at this level

Algebraic Reasoning
MA.L1.AR (GE: 0.0 – 1.9)

MA.L1.AR.1a Solve addition problems with sums between 0 and 20 and subtraction problems using related facts.

MA.L1.AR.1a.1 Apply properties of addition to find a sum of three or more whole numbers.
MA.L1.AR.1a.2 Solve addition and subtraction real-world problems using objects, drawings or equations to represent the problem.

MA.L1.AR.1b Solve addition problems with sums between 0 - 100 and related subtraction problems. | MA.L1.AR.1ab.1 Solve one- and two-step addition and subtraction real-world problems.
MA.L1.AR.2a Develop an understanding of the equal sign. | MA.L1.AR.2a.1 Explain why addition or subtraction equations are true using objects or drawings.

MA.L1.AR.2b Develop an understanding of the relationship between addition and subtraction.

MA.L1.AR.2b.1 Restate a subtraction problem as a missing addend problem using the relationship between addition and subtraction.
MA.L1.AR.2b.2 Determine and explain if equations involving addition or subtraction are true or false.
MA.L1.AR.2b.3 Determine the unknown whole number in an addition or subtraction equation, relating three whole numbers, with the unknown in any position.

Algebraic Reasoning
MA.L2.AR (GE: 2.0 – 3.9)

MA.L2.AR.1a Solve addition problems with sums between 0 and 100 and related subtraction problems. | MA.L2.AR.1a.1 Solve one- and two-step addition and subtraction real-world problems, limited to sums up to 100 and related differences.

MA.L2.AR.1b Solve multiplication and division problems.

MA.L2.AR.1b.1 Apply the distributive property to multiply a one-digit number and two-digit number. Apply properties of multiplication to find a product of one-digit whole numbers.
MA.3.AR.1.b.2 Solve one- and two-step real-world problems involving any of four operations with whole numbers.

MA.L2.AR.2a Demonstrate an understanding of equality and addition and subtraction.

MA.L2.AR.2a.1 Determine and explain whether equations involving addition and subtraction are true or false.
MA.L2.AR.2a.2 Determine the unknown whole number in an addition or subtraction equation, relating three or four whole numbers, with the unknown in any position.

MA.L2.AR.2b Develop an understanding of equality and multiplication and division.

MA.L2.AR.2b.1 Restate a division problem as a missing factor problem using the relationship between multiplication and division.
MA.L2.AR.2b.2 Determine and explain whether an equation involving multiplication or division is true or false.
MA.L2.AR.2b.3 Determine the unknown whole number in a multiplication or division equation, relating three whole numbers, with the unknown in any position.

MA.L2.AR.3 Develop an understanding of multiplication.

MA.L2.AR.3.1 Represent an even number using two equal groups or two equal addends. Represent an odd number using two equal groups with one left over or two equal addends plus 1.
MA.L2.AR.3.2 Use repeated addition to find the total number of objects in a collection of equal groups. Represent the total number of objects using rectangular arrays and equations.

Algebraic Reasoning
MA.L3.AR (GE: 4.0 – 5.9)

MA.L3.AR.1 Represent and solve problems involving the four operations with whole numbers and fractions.

MA.L3.AR.1.1 Solve real-world problems involving addition and subtraction of fractions with like denominators, including mixed numbers and fractions greater than one.
MA.L3.AR.1.2 Solve real-world problems involving multiplication of a fraction by a whole number or a whole number by a fraction.
MA.L3.AR.1.3 Solve multi-step real-world problems involving any combination of the four operations with whole numbers, including problems in which remainders must be interpreted within the context.
MA.L3.AR.1.4 Solve real-world problems involving the addition, subtraction or multiplication of fractions, including mixed numbers and fractions greater than 1. 
MA.L3.AR.1.5 Solve real-world problems involving division of a unit fraction by a whole number and a whole number by a unit fraction.

MA.L3.AR.2 Demonstrate an understanding of equality, operations with whole numbers, the order of operations and equivalent numerical expressions.

MA.L3.AR.2.1 Determine and explain whether an equation involving any of the four operations with whole numbers is true or false.
MA.L3.AR.2.2 Given a mathematical or real-world context, write an equation involving multiplication or division to determine the unknown whole number with the unknown in any position.
MA.L3.AR.2.3 Translate written real-world and mathematical descriptions into numerical expressions and numerical expressions into written mathematical descriptions.
MA.L3.AR.2.4 Evaluate multi-step numerical expressions using order of operations. 
MA.L3.AR.2.5 Determine and explain whether an equation involving any of the four operations is true or false.
MA.L3.AR.2.6 Given a mathematical or real-world context, write an equation involving any of the four operations to determine the unknown whole number with the unknown in any position.

MA.L3.AR.3a Recognize numerical patterns, including patterns that follow a given rule.

MA.L3.AR.3a.1 Determine factor pairs for a whole number from 0 to 144. Determine whether a whole number from 0 to 144 is prime, composite or neither. 
MA.L3.AR.3a.2 Generate, describe and extend a numerical pattern that follows a given rule.

MA.L3.AR.3b Analyze patterns and relationships between inputs and outputs.

MA.L3.AR.3b.1 Given a numerical pattern, identify and write a rule that can describe the pattern as an expression.
MA.L3.AR.3b.2 Given a rule for a numerical pattern, use a two-column table to record the inputs and outputs.

Algebraic Reasoning
MA.L4.AR (GE: 6.0 – 8.9)

MA.L4.AR.1a Apply previous understanding of arithmetic expressions to algebraic expressions.

MA.L4.AR.1a.1 Given a mathematical or real-world context, translate written descriptions into algebraic expressions and translate algebraic expressions into written descriptions.
MA.L4.AR.1a.2 Translate a real-world written description into an algebraic inequality in the form of 𝑥 > 𝑎, 𝑥 < 𝑎, 𝑥 ≥ 𝑎 or 𝑥 ≤ 𝑎. Represent the inequality on a number line.
MA.L4.AR.1a.3 Evaluate algebraic expressions using substitution and order of operations.
MA.L4.AR.1a.4 Apply the properties of operations to generate equivalent algebraic expressions with integer coefficients.

MA.L4.AR.1b Rewrite algebraic expressions in equivalent forms.

MA.L4.AR.1b.1 Apply properties of operations to add and subtract linear expressions with rational coefficients. 
MA.L4.AR.1b.2 Determine whether two linear expressions are equivalent.

MA.L4.AR.1c Generate equivalent algebraic expressions.

MA.L4.AR.1c.1 Apply the Laws of Exponents to generate equivalent algebraic expressions, limited to integer exponents and monomial bases.
MA.L4.AR.1c.2 Apply properties of operations to multiply two linear expressions with rational coefficients.
MA.L4.AR.1c.3 Rewrite the sum of two algebraic expressions having a common monomial factor as a common factor multiplied by the sum of two algebraic expressions.

MA.L4.AR.2a Develop an understanding for solving equations and inequalities. Write and solve one-step equations in one variable.

MA.L4.AR.2a.1 Given an equation or inequality and a specified set of integer values, determine which values make the equation or inequality true or false.
MA.L4.AR.2a.2 Write and solve one-step equations in one variable within a mathematical or real-world context using addition and subtraction, where all terms and solutions are integers.
MA.L4.AR.2a.3 Write and solve one-step equations in one variable within a mathematical or real-world context using multiplication and division, where all terms and solutions are integers.
MA.L4.AR.2a.4 Determine the unknown decimal or fraction in an equation involving any of the four operations, relating three numbers, with the unknown in any position.

MA.L4.AR.2b Write and solve equations and inequalities in one variable.

MA.L4.AR.2b.1 Write and solve one-step inequalities in one variable within a mathematical context and represent solutions algebraically or graphically.
MA.L4.AR.2b.2 Write and solve two-step equations in one variable within a mathematical or real-world context, where all terms are rational numbers.

MA.L4.AR.2c Solve multi-step one-variable equations and inequalities.

MA.L4.AR.2c.1 Solve multi-step linear equations in one variable, with rational number coefficients. Include equations with variables on both sides.
MA.L4.AR.2c.2 Solve two-step linear inequalities in one variable and represent solutions algebraically and graphically.
MA.L4.AR.2c.3 Given an equation in the form of 𝑥^2 = 𝑝 and 𝑥^3 = 𝑞, where 𝑝 is a whole number and 𝑞 is an integer, determine the real solutions.

MA.L4.AR.3a Understand ratio and unit rate concepts and use them to solve problems.

MA.L4.AR.3a.1 Given a real-world context, write and interpret ratios to show the relative sizes of two quantities using appropriate notation:  𝑎 / 𝑏, 𝑎 to 𝑏, or 𝑎: 𝑏 where 𝑏 ≠ 0.
MA.L4.AR.3a.2 Given a real-world context, determine a rate for a ratio of quantities with different units. Calculate and interpret the corresponding unit rate.
MA.L4.AR.3a.3 Extend previous understanding of fractions and numerical patterns to generate or complete a two- or three-column table to display equivalent part-to-part ratios and part-to-part-to-whole ratios.
MA.L4.AR.3a.4 Apply ratio relationships to solve mathematical and real-world problems involving percentages using the relationship between two quantities.
MA.L4.AR.3a.5 Solve mathematical and real-world problems involving ratios, rates and unit rates, including comparisons, mixtures, ratios of lengths and conversions within the same measurement system.

MA.L4.AR.3b Use percentages and proportional reasoning to solve problems

MA.L4.AR.3b.1 Apply previous understanding of percentages and ratios to solve multi-step real world percent problems.
MA.L4.AR.3b.2 Apply previous understanding of ratios to solve real-world problems involving proportions.
MA.L4.AR.3b.3 Solve mathematical and real-world problems involving the conversion of units across different measurement systems.

MA.L4.AR.3c Extend understanding of proportional relationships to two-variable linear equations.

MA.L4.AR.3c.1 Determine if a linear relationship is also a proportional relationship.
MA.L4.AR.3c.2 Given a table, graph or written description of a linear relationship, determine the slope.
MA.L4.AR.3c.3 Given a table, graph or written description of a linear relationship, write an equation in slope-intercept form.
MA.L4.AR.3c.4 Given a mathematical or real-world context, graph a two-variable linear equation from a written description, a table or an equation in slope-intercept form.
MA.L4.AR.3c.5 Given a real-world context, determine and interpret the slope and 𝑦-intercept of a two-variable linear equation from a written description, a table, a graph or an equation in slope-intercept form.

MA.L4.AR.4 Develop an understanding of two-variable systems of equations.

MA.L4.AR.4.1 Given a system of two linear equations and a specified set of possible solutions, determine which ordered pairs satisfy the system of linear equations.
MA.L4.AR.4.2 Given a system of two linear equations represented graphically on the same coordinate plane, determine whether there is one solution, no solution or infinitely many solutions.
MA.L4.AR.4.3 Given a mathematical or real-world context, solve systems of two linear equations by graphing.

Functions
MA.L4.F (GE: 6.0 – 8.9)
Note:  Suggested instruction level begins at 7.0 – 8.9

MA.L4.F.1 Define, evaluate and compare functions.

MA.L4.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.L4.F.1.2 Given a function defined by a graph or an equation, determine whether the function is a linear function. Given an input-output table, determine whether it could represent a linear function.
MA.L4.F.1.3 Analyze a real-world written description or graphical representation of a functional relationship between two quantities and identify where the function is increasing, decreasing or constant.

Measurement 
MA.L1.M (GE: 0.0 – 1.9)

MA.L1.M.1 Compare and measure the length of objects.

MA.L1.M.1.1 Express the length of an object, up to 20 units long, as a whole number of lengths by laying non-standard objects end to end with no gaps or overlaps.
MA.L1.M.1.2 Estimate the length of an object to the nearest inch. Measure the length of an object to the nearest inch or centimeter.
MA.L1.M.1.3 Compare and order the length of up to three objects using direct and indirect comparison.

Measurement 
MA.L2.M (GE: 2.0 – 3.9)

MA.L2.M.1 Measure attributes of objects and solve problems involving measurement.

MA.L2.M.1.1 Select and use appropriate tools to measure the length of an object, the volume of liquid within a beaker and temperature.
MA.L2.M.1.2 Solve real-world problems involving any of the four operations with whole number lengths, masses, weights, temperatures or liquid volumes.

MA.L2.M.2 Tell time and solve problems involving time and money.

MA.L2.M.2.1 Find the value of combinations of pennies, nickels and dimes up to one dollar and the value of combinations of one, five and ten-dollar bills up to $100. Use the ¢ and $ symbols appropriately.
MA.L2.M.2.2 Solve one- and two-step addition and subtraction real-world problems involving either dollar bills within $100 or coins within 100¢ using $ and ¢ symbols appropriately.
MA.L2.M.2.3 Using analog and digital clocks tell and write time to the nearest minute using a.m. and p.m. appropriately. Express portions of an hour using the fractional terms half an hour, half-past, quarter of an hour, quarter after and quarter til.
MA.L2.M.2.4 Solve one- and two-step real-world problems involving elapsed time.

Measurement 
MA.L3.M (GE: 4.0 – 5.9)

MA.L3.M.1 Measure the length of objects and solve multi-step problems involving measurement and conversions between units.

MA.L3.M.1.1 Select and use appropriate tools to measure attributes of objects.
MA.L3.M.1.2 Convert within a single system of measurement using the units: yards, feet, inches; kilometers, meters, centimeters, millimeters; pounds, ounces; kilograms, grams; gallons, quarts, pints, cups; liter, milliliter; and hours, minutes, seconds.
MA.L3.M.1.3 Solve multi-step real-world problems that involve converting measurement units to equivalent measurements within a single system of measurement.

MA.L3.M.2 Solve problems involving time and money.

MA.L3.M.2.1 Solve two-step real-world problems involving distances and intervals of time using any combination of the four operations.
MA.L3.M.2.2 Solve one- and two-step addition and subtraction real-world problems involving money using decimal notation.
MA.L3.M.2.3 Solve multi-step real-world problems involving money using decimal notation.

Measurement 
MA.L4.M (GE: 6.0 – 8.9)

Not a focus standard at this level

Geometric Reasoning
MA.L1.GR (GE: 0.0 – 1.9)

MA.L1.GR.1 Identify and analyze two- and three-dimensional figures based on their defining attributes.

MA.L1.GR.1.1 Identify, compare and sort two- and three-dimensional figures based on their attributes. Figures are limited to circles, semi-circles, triangles, rectangles, squares, trapezoids, hexagons, spheres, cubes, rectangular prisms, cones and cylinders.
MA.L1.GR.1.2 Sketch two-dimensional figures when given defining attributes. Figures are limited to triangles, rectangles, squares and hexagons.
MA.L1.GR.1.3 Compose and decompose two- and three-dimensional figures. Figures are limited to semi-circles, triangles, rectangles, squares, trapezoids, hexagons, cubes, rectangular prisms, cones and cylinders.
MA.L1.GR.1.4 Given a real-world object, identify parts that are modeled by two- and three-dimensional figures. Figures are limited to semi-circles, triangles, rectangles, squares and hexagons, spheres, cubes, rectangular prisms, cones and cylinders.

Geometric Reasoning 
MA.L2.GR (GE: 2.0 – 3.9)

MA.L2.GR.1 Describe and identify relationships between lines and classify quadrilaterals.

MA.L2.GR.1.1 Describe and draw points, lines, line segments, rays, intersecting lines, perpendicular lines and parallel lines. Identify these in two-dimensional figures.
MA.L2.GR.1.2 Informally explore angles as an attribute of two-dimensional figures. Figures are limited to triangles, rectangles, squares, pentagons, hexagons and octagons.
MA.L2.GR.1.3 Categorize two-dimensional figures based on the number and length of sides, number of vertices, whether they are closed or not and whether the edges are curved or straight.
MA.L2.GR.1.4 Identify and draw quadrilaterals based on their defining attributes. Quadrilaterals include parallelograms, rhombi, rectangles, squares and trapezoids. Draw line(s) of symmetry in a two-dimensional figure and identify line symmetric two-dimensional figures. Identify and draw quadrilaterals based on their defining attributes. Quadrilaterals include parallelograms, rhombi, rectangles, squares and trapezoids.
MA.L2.GR.1.5 Draw line(s) of symmetry in a two-dimensional figure and identify line symmetric two-dimensional figures.

MA.L2.GR.2 Solve problems involving the perimeter and area of rectangles.

MA.L2.GR.2.1 Explore perimeter as an attribute of a figure by placing unit segments along the boundary without gaps or overlaps. Find perimeters of rectangles by counting unit segments.
MA.L2.GR.2.2 Find the perimeter of a polygon with whole-number side lengths. Polygons are limited to triangles, rectangles, squares and pentagons.
MA.L2.GR.2.3 Explore area as an attribute of a two-dimensional figure by covering the figure with unit squares without gaps or overlaps. Find areas of rectangles by counting unit squares. 
MA.L2.GR.2.4 Find the area of a rectangle with whole-number side lengths using a visual model and a multiplication formula.
MA.L2.GR.2.5 Solve mathematical and real-world problems involving the perimeter and the area of rectangles with whole-number side lengths using a visual model and a formula.
MA.L2.GR.2.6 Solve mathematical and real-world problems involving the perimeter and area of composite figures composed of non-overlapping rectangles with whole number side lengths.

Geometric Reasoning 
MA.L3.GR (GE: 4.0 – 5.9)

MA.L3.GR.1a Draw, classify and measure angles.

MA.L3.GR.1a.1 Identify and classify angles as acute, right, obtuse, straight or reflex.
MA.L3.GR.1a.2 Estimate angle measures. Using a protractor, measure angles in whole-number degrees and draw angles of specified measure in whole-number degrees. Demonstrate that angle measure is additive.
MA.L3.GR.1a.3 Solve real-world and mathematical problems involving unknown whole number angle measures. Write an equation to represent the unknown.

MA.L3.GR.1b Classify two-dimensional figures and three-dimensional figures based on defining attributes.

MA.L3.GR.1b.1 Classify triangles or quadrilaterals into different categories based on shared defining attributes. Explain why a triangle or quadrilateral would or would not belong to a category. 
MA.L3.GR.1b.2 Identify and classify three-dimensional figures into categories based on their defining attributes. Figures are limited to right pyramids, right prisms, right circular cylinders, right circular cones and spheres.

MA.L3.GR.2 Solve problems involving the perimeter and area of rectangles.

MA.L3.GR.2.1 Solve perimeter and area mathematical and real-world problems, including problems with unknown sides, for rectangles with whole-number side lengths.
MA.L3.GR.2.2 Solve problems involving rectangles with the same perimeter and different areas or with the same area and different perimeters.
MA.L3.GR.2.3 Find the perimeter and area of a rectangle with fractional or decimal side lengths using visual models and formulas.

MA.L3.GR.3 Solve problems involving the volume of right rectangular prisms.

MA.L3.GR.3.1 Explore volume as an attribute of three-dimensional figures by packing them with unit cubes without gaps. Find the volume of a right rectangular prism with whole-number side lengths by counting unit cubes.
MA.L3.GR.3.2 Find the volume of a right rectangular prism with whole-number side lengths using a visual model and a formula.
MA.L3.GR.3.3 Solve real-world problems involving the volume of right rectangular prisms, including problems with an unknown edge length, with whole-number edge lengths using a visual model or a formula. Write an equation with a variable for the unknown to represent the problem.

MA.L3.GR.4 Plot points and represent problems on the coordinate plane.

MA.L3.GR.4.1 Identify the origin and axes in the coordinate system. Plot and label ordered pairs in the first quadrant of the coordinate plane.
MA.L3.GR.4.2 Represent mathematical and real-world problems by plotting points in the first quadrant of the coordinate plane and interpret coordinate values of points in the context of the situation.
MA.L3.GR.4.3 Solve mathematical and real-world problems by plotting points on a coordinate plane, including finding the perimeter or area of a rectangle.

Geometric Reasoning 
MA.L4.GR (GE: 6.0 – 8.9)

MA.L4.GR.1a Model and solve problems involving two-dimensional figures including applying previous understandings of the coordinate plane.

MA.L4.GR.1a.1 Extend previous understanding of the coordinate plane to plot rational number ordered pairs in all four quadrants and on both axes. Identify the 𝑥- or 𝑦-axis as the line of reflection when two ordered pairs have an opposite 𝑥- or 𝑦-coordinate.
MA.L4.GR.1a.2 Find distances between ordered pairs, limited to the same 𝑥-coordinate or the same 𝑦-coordinate, represented on the coordinate plane.
MA.L4.GR.1a.3 Derive a formula for the area of a right triangle using a rectangle. Apply a formula to find the area of a triangle.
MA.L4.GR.1a.4 Solve mathematical and real-world problems involving the area of quadrilaterals and composite figures by decomposing them into triangles or rectangles.

MA.L4.GR.1b Solve problems involving two-dimensional figures, including circles.

MA.L4.GR.1b.1 Apply formulas to find the areas of trapezoids, parallelograms and rhombi.
MA.L4.GR.1b.2 Solve mathematical or real-world problems involving the area of polygons or composite figures by decomposing them into triangles or quadrilaterals. 
MA.L4.GR.1b.3 Explore the proportional relationship between circumferences and diameters of circles. Apply a formula for the circumference of a circle to solve mathematical and real-world problems.
MA.L4.GR.1b.4 Explore and apply a formula to find the area of a circle to solve mathematical and real-world problems.
MA.L4.GR.1b.5 Solve mathematical and real-world problems involving dimensions and areas of geometric figures, including scale drawings and scale factors.

MA.L4.GR.1c Develop an understanding of the Pythagorean Theorem and angle relationships involving triangles.

MA.L4.GR.1c.1 Apply the Pythagorean Theorem to solve mathematical and real-world problems involving unknown side lengths in right triangles.
MA.L4.GR.1c.2 Apply the Pythagorean Theorem to solve mathematical and real-world problems involving the distance between two points in a coordinate plane.
MA.L4.GR.1c.3 Use the Triangle Inequality Theorem to determine if a triangle can be formed from a given set of sides. Use the converse of the Pythagorean Theorem to determine if a right triangle can be formed from a given set of sides.
MA.L4.GR.1c.4 Solve mathematical problems involving the relationships between supplementary, complementary, vertical or adjacent angles.
MA.L4.GR.1c.5 Solve problems involving the relationships of interior and exterior angles of a triangle.
MA.L4.GR.1c.6 Develop and use formulas for the sums of the interior angles of regular polygons by decomposing them into triangles.

MA.L4.GR.2a Model and solve problems involving three dimensional figures.

MA.L4.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.L4.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.L4.GR.2b Solve problems involving three-dimensional figures, including right circular cylinders.

MA.L4.GR.2b.1 Given a mathematical or real-world context, find the surface area of a right circular cylinder using the figure’s net.
MA.L4.GR.2b.2 Solve real-world problems involving surface area of right circular cylinders.
MA.L4.GR.2b.3 Solve mathematical and real-world problems involving volume of right circular cylinders.

MA.L4.GR.2c Understand similarity and congruence using models and transformations.

MA.L4.GR.2c.1 Given a preimage and image generated by a single transformation, identify the transformation that describes the relationship.
MA.L4.GR.2c.2 Given a preimage and image generated by a single dilation, identify the scale factor that describes the relationship.
MA.L4.GR.2c.3 Describe and apply the effect of a single transformation on two-dimensional figures using coordinates and the coordinate plane.
MA.L4.GR.2c.4 Solve mathematical and real-world problems involving proportional relationships between similar triangles.

Data and Probability
MA.L1.DP (GE: 0.0 – 1.9)

MA.L1.DP.1 Collect, represent and interpret data using pictographs and tally marks.

MA.L1.DP.1.1 Collect data into categories and represent the results using tally marks or pictographs.
MA.L1.DP.1.2 Interpret data represented with tally marks or pictographs by calculating the total number of data points and comparing the totals of different categories.

Data and Probability
MA.L2.DP (GE: 2.0 – 3.9)

MA.L2.DP.1 Collect, represent and interpret numerical and categorical data.

MA.L2.DP.1.1 Collect and represent numerical and categorical data with whole-number values using tables, scaled pictographs, scaled bar graphs or line plots. Use appropriate titles, labels and units.
MA.L2.DP.1.2 Interpret data with whole-number values represented with tables, scaled pictographs, circle graphs, scaled bar graphs or line plots by solving one- and two-step problems.

Data and Probability
MA.L3.DP (GE: 4.0 – 5.9)

MA.L3.DP.1 Collect and represent data and find the mean, mode, median or range of a data set.

MA.L3.DP.1.1 Develop an understanding of statistics and determine measures of center and measures of variability. 
MA.L3.DP.1.2 Recognize and formulate a statistical question that would generate numerical data.
MA.L3.DP.1 3 Discuss a set of data collected to answer a statistical questions as a distribution which can be described by its center, spread and overall shape
MA.L3.DP.1.4 Collect and represent numerical data, including fractional and decimal values, using tables, stem-and-leaf plots, line plots or line graphs
MA.L3.DP.1.5 Create box plots and histograms to represent sets of numerical data within real world contexts.
MA.L3.DP.1.6 Given a real-world scenario, solve problems involving numerical data and determine and describe how changes in data values impact measures of center and variation.

Data and Probability
MA.L4.DP (GE: 6.0 – 8.9)

MA.L4.DP.1a Summarize statistical distributions graphically and numerically.

MA.L4.DP.1a.1 Given a numerical data set within a real-world context, find and interpret mean, median, mode and range.
MA.L4.DP.1a.2 Given a box plot within a real-world context, determine the minimum, the lower quartile, the median, the upper quartile and the maximum. Use this summary of the data to describe the spread and distribution of the data. 
MA.L4.DP.1a.3 Given a histogram or line plot within a real-world context, qualitatively describe and interpret the spread and distribution of the data, including any symmetry, skewness, gaps, clusters, outliers and the range.

MA.L4.DP.1b Represent and interpret numerical and categorical data.

MA.L4.DP.1b.1 Interpret data and find the mean, mode, median or range of a data set.
MA.L4.DP.1b.2 Interpret numerical data, with whole-number values, represented with tables or line plots by determining the mean, mode, median or range.
MA.L4.DP.1b.3 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.L4.DP.1b.4 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.L4.DP.1b.5 Given categorical data from a random sample, use proportional relationships to make predictions about a population.
MA.L4.DP.1b.6 Use proportional reasoning to construct, display and interpret data in circle graphs.
MA.L4.DP.1b.6 Given a real-world numerical or categorical data set, choose and create an appropriate graphical representation.

MA.L4.DP.1c Represent and investigate numerical bivariate data.

MA.L4.DP.1c.1 Given a set of real-world bivariate numerical data, construct a scatter plot or a line graph as appropriate for the context.
MA.L4.DP.1c.2 Given a scatter plot within a real-world context, describe patterns of association. 
MA.L4.DP.1c.3 Given a scatter plot with a linear association, informally fit a straight line.

MA.L4.DP.2a Develop an understanding of probability. Find and compare experimental and theoretical probabilities.

MA.L4.DP.2a.1 Determine the sample space for a simple experiment.
MA.L4.DP.2a.2 Given the probability of a chance event, interpret the likelihood of it occurring. Compare the probabilities of chance events.
MA.L4.DP.2a.3 Find the theoretical probability of an event related to a simple experiment.
MA.L4.DP.2a.4 Use a simulation of a simple experiment to find experimental probabilities and compare them to theoretical probabilities.

MA.L4.DP.2b Represent and find probabilities of repeated experiments.

MA.L4.DP.2b.1 Determine the sample space for a repeated experiment.
MA.L4.DP.2b.2 Find the theoretical probability of an event related to a repeated experiment.
MA.L4.DP.2b.3 Solve real-world problems involving probabilities related to single or repeated experiments, including making predictions based on theoretical probability.

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