Mathematics for College Algebra B.E.S.T. Instructional Guide for Mathematics
The B.E.S.T. Instructional Guide for Mathematics (B1G-M) is intended to assist educators with
planning for student learning and instruction aligned to Florida’s Benchmarks for Excellent
Student Thinking (B.E.S.T.) Standards. This guide is designed to aid high-quality instruction
through the identification of components that support the learning and teaching of the B.E.S.T.
Mathematics Standards and Benchmarks. The B1G-M includes an analysis of information related
to the B.E.S.T. Standards for Mathematics within this specific mathematics course, the
instructional emphasis and aligned resources. This document is posted on the B.E.S.T. Standards
for Mathematics webpage of the Florida Department of Education’s website and will continue to
undergo edits as needed.
Structural Framework and Intentional Design of the B.E.S.T. Standards for Mathematics
Florida’s B.E.S.T. Standards for Mathematics were built on the following.
• The coding scheme for the standards and benchmarks was changed to be consistent with
other content areas. The new coding scheme is structured as follows:
Content.GradeLevel.Strand.Standard.Benchmark.
• Strands were streamlined to be more consistent throughout.
• The standards and benchmarks were written to be clear and concise to ensure that they
are easily understood by all stakeholders.
• The benchmarks were written to allow teachers to meet students’ individual skills,
knowledge and ability.
• The benchmarks were written to allow students the flexibility to solve problems using a
method or strategy that is accurate, generalizable and efficient depending on the content
(i.e., the numbers, expressions or equations).
• The benchmarks were written to allow for student discovery (i.e., exploring) of strategies
rather than the teaching, naming and assessing of each strategy individually.
• The benchmarks were written to support multiple pathways for success in career and
college for students.
• The benchmarks should not be taught in isolation but should be combined purposefully.
• The benchmarks may be addressed at multiple points throughout the year, with the
intention of gaining mastery by the end of the year.
• Appropriate progression of content within and across strands was developed for each
grade level and across grade levels.
• There is an intentional balance of conceptual understanding and procedural fluency with
the application of accurate real-world context intertwined within mathematical concepts
for relevance.
• The use of other content areas, like science and the arts, within real-world problems
should be accurate, relevant, authentic and reflect grade-level appropriateness.
, Components of the B.E.S.T. Instructional Guide for Mathematics
The following table is an example of the layout for each benchmark and includes the defining
attributes for each component. It is important to note that instruction should not be limited to the
possible connecting benchmarks, related terms, strategies or examples provided. To do so would
strip the intention of an educator meeting students’ individual skills, knowledge and abilities.
Benchmark
focal point for instruction within lesson or task
This section includes the benchmark as identified in the B.E.S.T. Standards for Mathematics.
The benchmark, also referred to as the Benchmark of Focus, is the focal point for student
learning and instruction. The benchmark, and its related example(s) and clarification(s), can also
be found in the course description. The 9-12 benchmarks may be included in multiple courses;
select the example(s) or clarification(s) as appropriate for the identified course.
Connecting Benchmarks/Horizontal Alignment Terms from the K-12 Glossary
in other standards within the grade level or course
This section includes a list of connecting This section includes terms from
benchmarks that relate horizontally to the Appendix C: K-12 Glossary, found
Benchmark of Focus. Horizontal alignment is within the B.E.S.T. Standards for
the intentional progression of content within a Mathematics document, which are
grade level or course linking skills within and relevant to the identified Benchmark
across strands. Connecting benchmarks are of Focus. The terms included in this
benchmarks that either make a mathematical section should not be viewed as a
connection or include prerequisite skills. The comprehensive vocabulary list, but
information included in this section is not a instead should be considered during
comprehensive list, and educators are instruction or act as a reference for
encouraged to find other connecting educators.
benchmarks. Additionally, this list will not
include benchmarks from the same standard
since benchmarks within the same standard
already have an inherent connection.
Vertical Alignment
across grade levels or courses :
This section includes a list of related benchmarks that connect vertically to the Benchmark of
Focus. Vertical alignment is the intentional progression of content from one year to the next,
spanning across multiple grade levels. Benchmarks listed in this section make mathematical
connections from prior grade levels or courses in future grade levels or courses within and
across strands. If the Benchmark of Focus is a new concept or skill, it may not have any
previous benchmarks listed. Likewise, if the Benchmark of Focus is a mathematical skill or
concept that is finalized in learning and does not have any direct connection to future grade
levels or courses, it may not have any future benchmarks listed. The information included in
this section is not a comprehensive list, and educators are encouraged to find other benchmarks
within a vertical progression.
2 | Page
, Purpose and Instructional Strategies
This section includes further narrative for instruction of the benchmark and vertical alignment.
Additionally, this section may also include the following:
• explanations and details for the benchmark;
• vocabulary not provided within Appendix C;
• possible instructional strategies and teaching methods; and
• strategies to embed potentially related Mathematical Thinking and Reasoning Standards
(MTRs).
Common Misconceptions or Errors
This section will include common student misconceptions or errors and may include strategies
to address the identified misconception or error. Recognition of these misconceptions and errors
enables educators to identify them in the classroom and make efforts to correct the
misconception or error. This corrective effort in the classroom can also be a form of formative
assessment within instruction.
Instructional Tasks
demonstrate the depth of the benchmark and the connection to the related benchmarks
This section will include example instructional tasks, which may be open-ended and are
intended to demonstrate the depth of the benchmark. Some instructional tasks include
integration of the Mathematical Thinking and Reasoning Standards (MTRs) and related
benchmark(s). Enrichment tasks may be included to make connections to benchmarks in later
grade levels or courses. Tasks may require extended time, additional materials and
collaboration.
Instructional Items
demonstrate the focus of the benchmark
This section will include example instructional items which may be used as evidence to
demonstrate the students’ understanding of the benchmark. Items may highlight one or more
parts of the benchmark.
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.
3 | Page
, Mathematical Thinking and Reasoning Standards
MTRs: Because Math Matters
Florida students are expected to engage with mathematics through the Mathematical Thinking
and Reasoning Standards (MTRs) by utilizing their language as a self-monitoring tool in the
classroom, promoting deeper learning and understanding of mathematics. The MTRs are
standards which should be used as a lens when planning for student learning and instruction of
the B.E.S.T. Standards for Mathematics.
Structural Framework and Intentional Design of the Mathematical Thinking and Reasoning
Standards
The Mathematical Thinking and Reasoning Standards (MTRs) are built on the following.
• The MTRs have the same coding scheme as the standards and benchmarks; however,
they are written at the standard level because there are no benchmarks.
• In order to fulfill Florida’s unique coding scheme, the 5th place (benchmark) will always
be a “1” for the MTRs.
• The B.E.S.T. Standards for Mathematics should be taught through the lens of the MTRs.
• At least one of the MTRs should be authentically and appropriately embedded throughout
every lesson based on the expectation of the benchmark(s).
• The bulleted language of the MTRs were written for students to use as self-monitoring
tools during daily instruction.
• The clarifications of the MTRs were written for teachers to use as a guide to inform their
instructional practices.
• The MTRs ensure that students stay engaged, persevere in tasks, share their thinking,
balance conceptual understanding and procedures, assess their solutions, make
connections to previous learning and extended knowledge, and apply mathematical
concepts to real-world applications.
• The MTRs should not stand alone as a separate focus for instruction, but should be
combined purposefully.
• The MTRs will be addressed at multiple points throughout the year, with the intention of
gaining mastery of mathematical skills by the end of the year and building upon these
skills as they continue in their K-12 education.
4 | Page
The B.E.S.T. Instructional Guide for Mathematics (B1G-M) is intended to assist educators with
planning for student learning and instruction aligned to Florida’s Benchmarks for Excellent
Student Thinking (B.E.S.T.) Standards. This guide is designed to aid high-quality instruction
through the identification of components that support the learning and teaching of the B.E.S.T.
Mathematics Standards and Benchmarks. The B1G-M includes an analysis of information related
to the B.E.S.T. Standards for Mathematics within this specific mathematics course, the
instructional emphasis and aligned resources. This document is posted on the B.E.S.T. Standards
for Mathematics webpage of the Florida Department of Education’s website and will continue to
undergo edits as needed.
Structural Framework and Intentional Design of the B.E.S.T. Standards for Mathematics
Florida’s B.E.S.T. Standards for Mathematics were built on the following.
• The coding scheme for the standards and benchmarks was changed to be consistent with
other content areas. The new coding scheme is structured as follows:
Content.GradeLevel.Strand.Standard.Benchmark.
• Strands were streamlined to be more consistent throughout.
• The standards and benchmarks were written to be clear and concise to ensure that they
are easily understood by all stakeholders.
• The benchmarks were written to allow teachers to meet students’ individual skills,
knowledge and ability.
• The benchmarks were written to allow students the flexibility to solve problems using a
method or strategy that is accurate, generalizable and efficient depending on the content
(i.e., the numbers, expressions or equations).
• The benchmarks were written to allow for student discovery (i.e., exploring) of strategies
rather than the teaching, naming and assessing of each strategy individually.
• The benchmarks were written to support multiple pathways for success in career and
college for students.
• The benchmarks should not be taught in isolation but should be combined purposefully.
• The benchmarks may be addressed at multiple points throughout the year, with the
intention of gaining mastery by the end of the year.
• Appropriate progression of content within and across strands was developed for each
grade level and across grade levels.
• There is an intentional balance of conceptual understanding and procedural fluency with
the application of accurate real-world context intertwined within mathematical concepts
for relevance.
• The use of other content areas, like science and the arts, within real-world problems
should be accurate, relevant, authentic and reflect grade-level appropriateness.
, Components of the B.E.S.T. Instructional Guide for Mathematics
The following table is an example of the layout for each benchmark and includes the defining
attributes for each component. It is important to note that instruction should not be limited to the
possible connecting benchmarks, related terms, strategies or examples provided. To do so would
strip the intention of an educator meeting students’ individual skills, knowledge and abilities.
Benchmark
focal point for instruction within lesson or task
This section includes the benchmark as identified in the B.E.S.T. Standards for Mathematics.
The benchmark, also referred to as the Benchmark of Focus, is the focal point for student
learning and instruction. The benchmark, and its related example(s) and clarification(s), can also
be found in the course description. The 9-12 benchmarks may be included in multiple courses;
select the example(s) or clarification(s) as appropriate for the identified course.
Connecting Benchmarks/Horizontal Alignment Terms from the K-12 Glossary
in other standards within the grade level or course
This section includes a list of connecting This section includes terms from
benchmarks that relate horizontally to the Appendix C: K-12 Glossary, found
Benchmark of Focus. Horizontal alignment is within the B.E.S.T. Standards for
the intentional progression of content within a Mathematics document, which are
grade level or course linking skills within and relevant to the identified Benchmark
across strands. Connecting benchmarks are of Focus. The terms included in this
benchmarks that either make a mathematical section should not be viewed as a
connection or include prerequisite skills. The comprehensive vocabulary list, but
information included in this section is not a instead should be considered during
comprehensive list, and educators are instruction or act as a reference for
encouraged to find other connecting educators.
benchmarks. Additionally, this list will not
include benchmarks from the same standard
since benchmarks within the same standard
already have an inherent connection.
Vertical Alignment
across grade levels or courses :
This section includes a list of related benchmarks that connect vertically to the Benchmark of
Focus. Vertical alignment is the intentional progression of content from one year to the next,
spanning across multiple grade levels. Benchmarks listed in this section make mathematical
connections from prior grade levels or courses in future grade levels or courses within and
across strands. If the Benchmark of Focus is a new concept or skill, it may not have any
previous benchmarks listed. Likewise, if the Benchmark of Focus is a mathematical skill or
concept that is finalized in learning and does not have any direct connection to future grade
levels or courses, it may not have any future benchmarks listed. The information included in
this section is not a comprehensive list, and educators are encouraged to find other benchmarks
within a vertical progression.
2 | Page
, Purpose and Instructional Strategies
This section includes further narrative for instruction of the benchmark and vertical alignment.
Additionally, this section may also include the following:
• explanations and details for the benchmark;
• vocabulary not provided within Appendix C;
• possible instructional strategies and teaching methods; and
• strategies to embed potentially related Mathematical Thinking and Reasoning Standards
(MTRs).
Common Misconceptions or Errors
This section will include common student misconceptions or errors and may include strategies
to address the identified misconception or error. Recognition of these misconceptions and errors
enables educators to identify them in the classroom and make efforts to correct the
misconception or error. This corrective effort in the classroom can also be a form of formative
assessment within instruction.
Instructional Tasks
demonstrate the depth of the benchmark and the connection to the related benchmarks
This section will include example instructional tasks, which may be open-ended and are
intended to demonstrate the depth of the benchmark. Some instructional tasks include
integration of the Mathematical Thinking and Reasoning Standards (MTRs) and related
benchmark(s). Enrichment tasks may be included to make connections to benchmarks in later
grade levels or courses. Tasks may require extended time, additional materials and
collaboration.
Instructional Items
demonstrate the focus of the benchmark
This section will include example instructional items which may be used as evidence to
demonstrate the students’ understanding of the benchmark. Items may highlight one or more
parts of the benchmark.
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.
3 | Page
, Mathematical Thinking and Reasoning Standards
MTRs: Because Math Matters
Florida students are expected to engage with mathematics through the Mathematical Thinking
and Reasoning Standards (MTRs) by utilizing their language as a self-monitoring tool in the
classroom, promoting deeper learning and understanding of mathematics. The MTRs are
standards which should be used as a lens when planning for student learning and instruction of
the B.E.S.T. Standards for Mathematics.
Structural Framework and Intentional Design of the Mathematical Thinking and Reasoning
Standards
The Mathematical Thinking and Reasoning Standards (MTRs) are built on the following.
• The MTRs have the same coding scheme as the standards and benchmarks; however,
they are written at the standard level because there are no benchmarks.
• In order to fulfill Florida’s unique coding scheme, the 5th place (benchmark) will always
be a “1” for the MTRs.
• The B.E.S.T. Standards for Mathematics should be taught through the lens of the MTRs.
• At least one of the MTRs should be authentically and appropriately embedded throughout
every lesson based on the expectation of the benchmark(s).
• The bulleted language of the MTRs were written for students to use as self-monitoring
tools during daily instruction.
• The clarifications of the MTRs were written for teachers to use as a guide to inform their
instructional practices.
• The MTRs ensure that students stay engaged, persevere in tasks, share their thinking,
balance conceptual understanding and procedures, assess their solutions, make
connections to previous learning and extended knowledge, and apply mathematical
concepts to real-world applications.
• The MTRs should not stand alone as a separate focus for instruction, but should be
combined purposefully.
• The MTRs will be addressed at multiple points throughout the year, with the intention of
gaining mastery of mathematical skills by the end of the year and building upon these
skills as they continue in their K-12 education.
4 | Page
