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Access Point #: MAFS.912.F-LE.1.AP.1b Archived Access Point

In a linear situation using graphs or numbers, predict the change in rate based on a given change in one variable (e.g., If I have been adding sugar at a rate of 1T per cup of water, what happens to my rate if I switch to 2T of sugar for every cup of water?).

Clarifications:

Essential Understandings

Concrete:

  • Model rate of change using tools or manipulatives.
  • Model increasing/decreasing rate of change in a problem using tools or manipulatives.
  • Model rate of change using a graph.
  • Model increasing/decreasing rate of change in a problem using a graph.
  • Match the change in the variable to the change in the rate given the situation.
Representation:
  • Identify the rate of change in a problem.
  • Compare and contrast two rates of change on a graph.
  • Compare and contrast two rates of change in a display.
  • Understand the following concepts and vocabulary: rate of change, variable, increase, decrease, linear.

Access Point Standards

Visit the specific benchmark webpage to find related instructional resources.

  • MAFS.912.F-LE.1.1: Distinguish between situations that can be modeled with linear functions and with exponential functions. ★
    1. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
    2. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
    3. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

Access Point Information

Number: MAFS.912.F-LE.1.AP.1b
Category: Access Points
Date Adopted or Revised: 06/14
Cluster: Construct and compare linear, quadratic, and exponential models and solve problems. (Algebra 1 - Supporting Cluster) (Algebra 2 - Supporting Cluster): 

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Access Point Courses

  • Algebra 1 (#1200310) In Algebra 1, instructional time will emphasize five areas: (1) performing operations with polynomials and radicals, and extending the Laws of Exponents to include rational exponents; (2) extending understanding of functions to linear, quadratic and exponential functions and using them to model and analyze real-world relationships; (3) solving quadratic equations in one variable and systems of linear equations and inequalities in two variables; (4) building functions, identifying their key features and representing them in various ways and (5) representing and interpreting categorical and numerical data with one and two variables. All clarifications stated, whether general or specific to Algebra I, are expectations for instruction of that benchmark. Curricular content for all subjects must integrate critical-thinking, problem-solving, and workforce-literacy skills; communication, reading, and writing skills; mathematics skills; collaboration skills; contextual and applied-learning skills; technology-literacy skills; information and media-literacy skills; and civic-engagement skills.
  • Algebra 1 Honors (#1200320) In Algebra 1 Honors, instructional time will emphasize five areas: (1) performing operations with polynomials and radicals, and extending the Laws of Exponents to include rational exponents; (2) extending understanding of functions to linear, quadratic and exponential functions and using them to model and analyze real-world relationships; (3) solving quadratic equations in one variable and systems of linear equations and inequalities in two variables; (4) building functions, identifying their key features and representing them in various ways and (5) representing and interpreting categorical and numerical data with one and two variables. All clarifications stated, whether general or specific to Algebra I Honors, are expectations for instruction of that benchmark. Curricular content for all subjects must integrate critical-thinking, problem-solving, and workforce-literacy skills; communication, reading, and writing skills; mathematics skills; collaboration skills; contextual and applied-learning skills; technology-literacy skills; information and media-literacy skills; and civic-engagement skills.
  • Algebra 1-A (#1200370) In Algebra 1-A, instructional time will emphasize four areas: (1) extending understanding of functions to linear functions and using them to model and analyze real-world relationships; (2) solving linear equations and inequalities in one variable and systems of linear equations and inequalities in two variables; (3) building linear functions, identifying their key features and representing them in various ways and (4) representing and interpreting categorical and numerical data with one and two variables. All clarifications stated, whether general or specific to Algebra I-A, are expectations for instruction of that benchmark. Please note that all clarifications that address Algebra 1 also should be addressed within Algebra 1-A. Curricular content for all subjects must integrate critical-thinking, problem-solving, and workforce-literacy skills; communication, reading, and writing skills; mathematics skills; collaboration skills; contextual and applied-learning skills; technology-literacy skills; information and media-literacy skills; and civic-engagement skills.
  • Foundational Skills in Mathematics 9-12 (#1200400) This course supports students who need additional instruction in foundational mathematics skills as it relates to core instruction. Instruction will use explicit, systematic, and sequential approaches to mathematics instruction addressing all strands including number sense & operations, algebraic reasoning, functions, geometric reasoning and data analysis & probability. Teachers will use the listed benchmarks that correspond to each students’ needs. Effective instruction matches instruction to the need of the students in the group and provides multiple opportunities to practice the skill and receive feedback. The additional time allotted for this course is in addition to core instruction. The intervention includes materials and strategies designed to supplement core instruction.
  • Liberal Arts Mathematics 2 (#1207310)
  • Access Informal Geometry (#7912060)
  • Access Mathematics for Liberal Arts (#7912070) Access Courses: Access courses are for students with the most significant cognitive disabilities. Access courses are designed to provide students access to grade-level general curriculum. Access points are alternate academic achievement standards included in access courses that target the salient content of Florida’s standards. Access points are intentionally designed to academically challenge students with the most significant cognitive disabilities. 
  • Access Algebra 1A (#7912080) Access Courses: Access courses are for students with the most significant cognitive disabilities. Access courses are designed to provide students access to grade-level general curriculum. Access points are alternate academic achievement standards included in access courses that target the salient content of Florida’s standards. Access points are intentionally designed to academically challenge students with the most significant cognitive disabilities. 
  • Access Algebra 1B (#7912090) Access Courses: Access courses are for students with the most significant cognitive disabilities. Access courses are designed to provide students access to grade-level general curriculum. Access points are alternate academic achievement standards included in access courses that target the salient content of Florida’s standards. Access points are intentionally designed to academically challenge students with the most significant cognitive disabilities. 
  • Bioscience 1 Honors (#2000500)
  • Bioscience 2 Honors (#2000510)
  • Algebra 1 for Credit Recovery (#1200315) Credit Recovery courses are credit bearing courses with specific content requirements defined by state academic standards (SAS). Students enrolled in a Credit Recovery course must have previously attempted the corresponding course (and/or End-of-Course assessment) since the course requirements for the Credit Recovery course is exactly the same as the previously attempted corresponding course. For example, Geometry (1206310) and Geometry for Credit Recovery (1206315) have identical content requirements. It is important to note that Credit Recovery courses are not bound by Section 1003.436(1) (a), Florida Statutes, requiring a minimum of 135 hours of bona fide instruction (120 hours in a school/district implementing block scheduling) in a designed course of study that contains student performance standards, since the students have previously attempted successful completion of the corresponding course. Additionally, Credit Recovery courses should ONLY be used for credit recovery, grade forgiveness, or remediation for students needing to prepare for an End-of-Course assessment retake. In Algebra 1, instructional time will emphasize five areas: (1) performing operations with polynomials and radicals, and extending the Laws of Exponents to include rational exponents; (2) extending understanding of functions to linear, quadratic and exponential functions and using them to model and analyze real-world relationships; (3) solving quadratic equations in one variable and systems of linear equations and inequalities in two variables; (4) building functions, identifying their key features and representing them in various ways and (5) representing and interpreting categorical and numerical data with one and two variables. All clarifications stated, whether general or specific to Algebra I, are expectations for instruction of that benchmark. Curricular content for all subjects must integrate critical-thinking, problem-solving, and workforce-literacy skills; communication, reading, and writing skills; mathematics skills; collaboration skills; contextual and applied-learning skills; technology-literacy skills; information and media-literacy skills; and civic-engagement skills.
  • Algebra 1-A for Credit Recovery (#1200375) In Algebra 1-A, instructional time will emphasize four areas: (1) extending understanding of functions to linear functions and using them to model and analyze real-world relationships; (2) solving linear equations and inequalities in one variable and systems of linear equations and inequalities in two variables; (3) building linear functions, identifying their key features and representing them in various ways and (4) representing and interpreting categorical and numerical data with one and two variables. All clarifications stated, whether general or specific to Algebra I-A, are expectations for instruction of that benchmark. Please note that all clarifications that address Algebra 1 also should be addressed within Algebra 1-A. Curricular content for all subjects must integrate critical-thinking, problem-solving, and workforce-literacy skills; communication, reading, and writing skills; mathematics skills; collaboration skills; contextual and applied-learning skills; technology-literacy skills; information and media-literacy skills; and civic-engagement skills. Special notes: Credit Recovery courses are credit bearing courses with specific content requirements defined by state academic standards (SAS). Students enrolled in a Credit Recovery course must have previously attempted the corresponding course (and/or End-of-Course assessment) since the course requirements for the Credit Recovery course are exactly the same as the previously attempted corresponding course. For example, Geometry (1206310) and Geometry for Credit Recovery (1206315) have identical content requirements. It is important to note that Credit Recovery courses are not bound by Section 1003.436(1)(a), Florida Statutes, requiring a minimum of 135 hours of bona fide instruction (120 hours in a school/district implementing block scheduling) in a designed course of study that contains student performance standards, since the students have previously attempted successful completion of the corresponding course. Additionally, Credit Recovery courses should ONLY be used for credit recovery, grade forgiveness, or remediation for students needing to prepare for an End-of-Course assessment retake.
  • Access Geometry (#7912065) Access Courses: Access courses are for students with the most significant cognitive disabilities. Access courses are designed to provide students access to grade-level general curriculum. Access points are alternate academic achievement standards included in access courses that target the salient content of Florida’s standards. Access points are intentionally designed to academically challenge students with the most significant cognitive disabilities. 
  • Access Algebra 1 (#7912075) Access Courses: Access courses are for students with the most significant cognitive disabilities. Access courses are designed to provide students access to grade-level general curriculum. Access points are alternate academic achievement standards included in access courses that target the salient content of Florida’s standards. Access points are intentionally designed to academically challenge students with the most significant cognitive disabilities. 
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