# FOR TEACHERS BY TEACHERS

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```					                                                                                                                FOR TEACHERS BY TEACHERS
MATH CURRICULUM GUIDE

STANDARD 1: Number Sense: Students develop number sense and use numbers and number relationships in problem-solving situations and communicate the reasoning used in solving these problems.

Benchmark 1.1 Demonstrate meanings for real numbers, absolute value, and scientific notation using physical materials and technology in problem-solving situations.

Enduring Understanding                                                                 Assessment           Key        Suggested Instructional                                        Differentiation              Quarter
State Frameworks                                              Essential Questions           Essential Skills                                                                            Resources
Conceptual Vocabulary                                                                   Methods           Strategy           Practices                                            Adaptations/Extensions           Taught

1.1a Work problems                                                                           Write fractional           CHOOSE FROM:           McREL     McREL                       CHOOSE FROM: Graphic          CHOOSE FROM THE
involving rational                                                                           exponents as roots and     Oral, performance-               homework and practice       organizers, text books,       FOLLOWING LIST: Whole
exponents and roots                                                                          roots as fractional        based, written                   graphic organizers          State's released items,       group, small group, one-on-
exponents                  (pen/pencil, paper,                                          AVID strategies, horizontal   one, cooperative learning,
journal, report,)                                            team planning, Internet.      peer mentoring, tiered
Exponents and roots are       What does a non-integer                                 portfolio, projects                                                                        activities, stations, compacting,
interchangeable               exponent mean?                                                                                                                                     agendas, complex instructions,
orbital studies, entry points,
problem-based learning, choice
boards, 4mat . Website: ASCD
Express

1.1b Formalize                                                                               Determine to which         CHOOSE FROM:          McREL      McREL                       CHOOSE FROM: Graphic          CHOOSE FROM THE
knowledge of subsets of                                                                      subsets of the complex     Oral, performance-               graphic organizers          organizers, text books,       FOLLOWING LIST: Whole
number systems (whole -                                                                      numbers a number           based, written                                               State's released items,       group, small group, one-on-
integer - rational - irrational                                                              belongs                    (pen/pencil, paper,                                          AVID strategies, horizontal   one, cooperative learning,
- real - complex)                                                                                                       journal, report,)                                            team planning, Internet.      peer mentoring, tiered
When is one set preferable                              portfolio, projects                                                                        activities, stations, compacting,
There are different sets of
to another to represent                                                                                                                            agendas, complex instructions,
numbers
numbers?                                                                                                                                           orbital studies, entry points,
problem-based learning, choice
boards, 4mat . Website: ASCD
Express

Benchmark 1.2 Developing, testing, and explaining conjectures about the properties of number systems and sets of numbers

1.2a Determine when an                                                                       In a given situation,      CHOOSE FROM:          HOTS       HOTS                        CHOOSE FROM: Graphic          CHOOSE FROM THE
expression is undefined                                                                      interpret the meaning at   Oral, performance-               analyzing                   organizers, text books,       FOLLOWING LIST: Whole
the points where the       based, written                                               State's released items,       group, small group, one-on-
expression is undefined    (pen/pencil, paper,                                          AVID strategies, horizontal   one, cooperative learning,
journal, report,)                                            team planning, Internet.      peer mentoring, tiered
There is real-world meaning   Why is an expression                                    portfolio, projects                                                                        activities, stations, compacting,
behind why an expression is   undefined at certain                                                                                                                               agendas, complex instructions,
undefined                     points?                                                                                                                                            orbital studies, entry points,
problem-based learning, choice
boards, 4mat . Website: ASCD
Express

Revision 4-26-2006/jkw                                                                                                                                                                                                                            1
FOR TEACHERS BY TEACHERS
MATH CURRICULUM GUIDE

STANDARD 1: Number Sense: Students develop number sense and use numbers and number relationships in problem-solving situations and communicate the reasoning used in solving these problems.

Benchmark 1.2 Develop, test, and explain conjectures about the properties of number systems and sets of numbers

Enduring Understanding                                                                 Assessment            Key        Suggested Instructional                                        Differentiation              Quarter
State Frameworks                                           Essential Questions            Essential Skills                                                                           Resources
Conceptual Vocabulary                                                                   Methods            Strategy           Practices                                            Adaptations/Extensions           Taught

1.2b Investigate limits by                                                                Finding limits of series CHOOSE FROM:           HOTS       HOTS                        CHOOSE FROM: Graphic          CHOOSE FROM THE
examining infinite                                                                        and expressions for the Oral, performance-                 generating                  organizers, text books,       FOLLOWING LIST: Whole
sequences and series                                                                      nth term of a sequence based, written                                                  State's released items,       group, small group, one-on-
(arithmetic and geometric)                                                                                         (pen/pencil, paper,                                           AVID strategies, horizontal   one, cooperative learning,
journal, report,)                                             team planning, Internet.      peer mentoring, tiered
Some series converge, while   What is the limit of a given
portfolio, projects                                                                         activities, stations, compacting,
others do not.                series?
agendas, complex instructions,
Sequences can be written as   What is the nth term of a
orbital studies, entry points,
algebraic expressions.        sequence?
problem-based learning, choice
boards, 4mat . Website: ASCD
Express

Benchmark 1.3 Use number sense to estimate and justify the reasonableness of solutions to problems involving real numbers.

STANDARD 7: Students communicate the reasoning used in problem-solving situations

Benchmark A: Communicate the use of number sense, including estimations and mental math, needed to solve problems and determine the reasonableness of the solution.

State Frameworks            Enduring Understanding         Essential Questions            Essential Skills         Assessment          Key          Suggested Instructional          Resources                     Differentiation              Quarter
Conceptual Vocabulary                                                                   Methods            Strategy           Practices                                            Adaptations/Extensions           Taught

7A.1 Students generate                                                                    Translating math into    CHOOSE FROM:           McREL      McREL                       CHOOSE FROM: Graphic          CHOOSE FROM THE
and solve problems of                                                                     real world situations    Oral, performance-                Organizing information      organizers, text books,       FOLLOWING LIST: Whole
appropriate complexity                                                                                             based, written                    Problem writing             Mastery Math materials (Al    group, Small group, one-on-
created from real-world                                                                                            (pen/pencil, paper,                                           Ludwig) , Algebra pizzazz,    one, Cooperative learning,
problems.                                                  How is math a universal                                 journal, report,)                                             States released items,        Peer mentoring (Learning
Mathematics is a tool for     language?                                               portfolio, projects,                                          AVID strategies,              buddies), tiered activities,
communication.                How would you learn math                                                                                              Foldables, Horizontal         stations, compacting, agendas,
without a math teacher?                                                                                               planning internet.            complex instructions orbital
studies, Entry points, Problem
based learning, choice boards,
4mat . Website: ASCD Express

Revision 4-26-2006/jkw                                                                                                                                                                                                                         2
FOR TEACHERS BY TEACHERS
MATH CURRICULUM GUIDE

STANDARD 7: Students communicate the reasoning used in problem-solving situations

Benchmark A: Communicate the use of number sense, including estimations and mental math, needed to solve problems and determine the reasonableness of the solution.

State Frameworks            Enduring Understanding          Essential Questions              Essential Skills        Assessment          Key          Suggested Instructional              Resources                   Differentiation            Quarter
Conceptual Vocabulary                                                                     Methods            Strategy           Practices                                              Adaptations/Extensions         Taught

7A.2 Identify the essential                                                                  Extracting important     CHOOSE FROM:           HOTS       HOTS                            CHOOSE FROM: Graphic         CHOOSE FROM THE
components of                                                                                information              Oral, performance-                Knowledge                       organizers, text books,      FOLLOWING LIST: Whole
mathematical and real-                                                                                                based, written                                                    Mastery Math materials (Al   group, Small group, one-on-
world problems                                                                                                        (pen/pencil, paper,    SIOP       SIOP                            Ludwig) , Algebra pizzazz,   one, Cooperative learning,
journal, report,)                 GIST--Finding Main Idea         States released items,       Peer mentoring (Learning
It is essential to be able to   How do you read
portfolio, projects,              Deleting unimportant            AVID strategies,             buddies), tiered activities,
communicate the reasoning       mathematical stuff?
information                     Foldables, Horizontal        stations, compacting, agendas,
used to solve problems.         What's your problem?
planning internet.           complex instructions orbital
studies, Entry points, Problem
based learning, choice boards,
4mat . Website: ASCD Express

7A.3 Choose and apply a                                                                      Problem solving          CHOOSE FROM:           McREL      McREL:                          CHOOSE FROM: Graphic         CHOOSE FROM THE
strategy to solve                                                                            strategies               Oral, performance-                Graphic organizers              organizers, text books,      FOLLOWING LIST: Whole
mathematical and real-                                                                                                based, written                                                    Mastery Math materials (Al   group, Small group, one-on-
world problems                                                                                                        (pen/pencil, paper,                                               Ludwig) , Algebra pizzazz,   one, Cooperative learning,
journal, report,)                                                 States released items,       Peer mentoring (Learning
It is essential to be able to                                                           portfolio, projects,                                              AVID strategies,             buddies), tiered activities,
communicate the reasoning       What's in your toolbox?                                                                                                   Foldables, Horizontal        stations, compacting, agendas,
used to solve problems.                                                                                                                                   planning internet.           complex instructions orbital
studies, Entry points, Problem
based learning, choice boards,
4mat . Website: ASCD Express

7A.4 Evaluate the                                                                            Significant figures      CHOOSE FROM:           McREL      McREL                           CHOOSE FROM: Graphic         CHOOSE FROM THE
solutions of mathematical                                                                    Estimating               Oral, performance-                Precision & Accuracy Practice   organizers, text books,      FOLLOWING LIST: Whole
and real world problems                                                                      Mental Math              based, written                                                    Mastery Math materials (Al   group, Small group, one-on-
for reasonableness.                                                                                                   (pen/pencil, paper,                                               Ludwig) , Algebra pizzazz,   one, Cooperative learning,
journal, report,)                                                 States released items,       Peer mentoring (Learning
It is essential to be able to
How close is close                                      portfolio, projects,                                              AVID strategies,             buddies), tiered activities,
communicate the reasoning
enough?                                                                                                                   Foldables, Horizontal        stations, compacting, agendas,
used to solve problems.
planning internet.           complex instructions orbital
studies, Entry points, Problem
based learning, choice boards,
4mat . Website: ASCD Express

7A.5 Explain the strategy                                                                    Explain processes for    CHOOSE FROM:           McREL      McREL                           CHOOSE FROM: Graphic         CHOOSE FROM THE
used and the solution to                                                                     solutions                Oral, performance-                Practice explaining answers     organizers, text books,      FOLLOWING LIST: Whole
mathematical and real-                                                                                                based, written                    Journal writing                 Mastery Math materials (Al   group, Small group, one-on-
world problems through                                        How would you                                           (pen/pencil, paper,                                               Ludwig) , Algebra pizzazz,   one, Cooperative learning,
Mathematics is a tool for
written and oral                                              communicate the solution                                journal, report,)                                                 States released items,       Peer mentoring (Learning
communication.
communication.                                                to a problem to an alien?                               portfolio, projects,                                              AVID strategies,             buddies), tiered activities,
It is essential to be able to
How can you convince a                                                                                                    Foldables, Horizontal        stations, compacting, agendas,
communicate the reasoning
total stranger (who dislikes                                                                                              planning internet.           complex instructions orbital
used to solve problems.
you) that you are right?                                                                                                                               studies, Entry points, Problem
based learning, choice boards,
4mat . Website: ASCD Express

Revision 4-26-2006/jkw                                                                                                                                                                                                                           3
FOR TEACHERS BY TEACHERS
MATH CURRICULUM GUIDE

STANDARD 2: Algebra: Students use algebraic methods to explore, model, and describe patterns and functions involving numbers, shapes, data, and graphs in problem-solving situations and communicate the reasoning used in
solving these problems.

Benchmark 2.1 Model real world phenomena (for example: distance-verses-time relationships, compound interest, amortization tables, mortality rates-using functions, equations, inequalities, and matrices)

Enduring Understanding                                                                   Assessment           Key         Suggested Instructional                                           Differentiation              Quarter
State Frameworks                                            Essential Questions            Essential Skills                                                                               Resources
Conceptual Vocabulary                                                                     Methods           Strategy            Practices                                               Adaptations/Extensions           Taught

2.1a Model real-world                                                                      Use real-world data to    CHOOSE FROM:          SIOP       SIOP                            CHOOSE FROM: Graphic          CHOOSE FROM THE
phenomena using                                                                            create exponential        Oral, performance-               non-linguistic representation   organizers, text books,       FOLLOWING LIST: Whole
exponential and                                                                            functions and use         based, written                                                   State's released items,       group, small group, one-on-
logarithmic relationships                                                                  logarithms to help        (pen/pencil, paper,                                              AVID strategies, horizontal   one, cooperative learning,
manipulate those          journal, report,)                                                team planning, Internet.      peer mentoring, tiered
Seeing exponential growth        How can you apply
functions                 portfolio, projects                                                                            activities, stations, compacting,
and decay as percent             exponential and logarithmic
agendas, complex instructions,
increase/decrease in real-       functions to real-world
orbital studies, entry points,
world situations                 situations?
problem-based learning, choice
boards, 4mat . Website: ASCD
Express

2.1b Represent and solve                                                                   Solving linear systems    CHOOSE FROM:          SIOP       SIOP                            CHOOSE FROM: Graphic          CHOOSE FROM THE
problems using linear                                                                      and using the solutions   Oral, performance-               non-linguistic representation   organizers, text books,       FOLLOWING LIST: Whole
programming.                                                                               to find an optimization   based, written                                                   State's released items,       group, small group, one-on-
point                     (pen/pencil, paper,                                              AVID strategies, horizontal   one, cooperative learning,
journal, report,)                                                team planning, Internet.      peer mentoring, tiered
How can you use linear
Linear inequalities are useful                                                           portfolio, projects                                                                            activities, stations, compacting,
in developing economic                                                                                                                                                                  agendas, complex instructions,
maximize profits or
models for business                                                                                                                                                                     orbital studies, entry points,
minimize costs?
problem-based learning, choice
boards, 4mat . Website: ASCD
Express

Benchmark 2.2 Represent functional relationships using written explanations, tables, and graphs and describing the connections among these relationships.

2.2a Write expressions                                                                     Accurately define         CHOOSE FROM:          HOTS       McREL                           CHOOSE FROM: Graphic          CHOOSE FROM THE
that require planning                                                                      variables and             Oral, performance-               generating                      organizers, text books,       FOLLOWING LIST: Whole
and/or manipulating to                                                                     understand what type of   based, written                                                   State's released items,       group, small group, one-on-
accurately model a                                                                         model is appropriate      (pen/pencil, paper,                                              AVID strategies, horizontal   one, cooperative learning,
situation                                                                                                            journal, report,)                                                team planning, Internet.      peer mentoring, tiered
Translating real-world           How do we express tables,                               portfolio, projects                                                                            activities, stations, compacting,
situations into mathematical     graphs and data from real-                                                                                                                             agendas, complex instructions,
models for a variety of types    world situations using                                                                                                                                 orbital studies, entry points,
of functions                     expressions or equations?                                                                                                                              problem-based learning, choice
boards, 4mat . Website: ASCD
Express

Revision 4-26-2006/jkw                                                                                                                                                                                                                             4
FOR TEACHERS BY TEACHERS
MATH CURRICULUM GUIDE

STANDARD 2: Algebra: Students use algebraic methods to explore, model, and describe patterns and functions involving numbers, shapes, data, and graphs in problem-solving situations and communicate the reasoning used in
solving these problems.

Benchmark 2.2 Represent functional relationships using written explanations, tables, and graphs and describing the connections among these relationships.

Enduring Understanding                                                               Assessment           Key         Suggested Instructional                                           Differentiation              Quarter
State Frameworks                                          Essential Questions         Essential Skills                                                                               Resources
Conceptual Vocabulary                                                                 Methods           Strategy            Practices                                               Adaptations/Extensions           Taught

2.2b Represent quadratic                                                               Accurately define         CHOOSE FROM:          McREL      McREL                           CHOOSE FROM: Graphic          CHOOSE FROM THE
(parabolic and circular)                                                               variables and             Oral, performance-               non-linguistic representation   organizers, text books,       FOLLOWING LIST: Whole
and absolute value                                                                     understand what type of   based, written                                                   State's released items,       group, small group, one-on-
equations and inequalities                                                             model is appropriate      (pen/pencil, paper,                                              AVID strategies, horizontal   one, cooperative learning,
for common algebra                                                                                               journal, report,)     HOTS       HOTS                            team planning, Internet.      peer mentoring, tiered
settings                   Translating real-world           How do you define the                                portfolio, projects              application                                                   activities, stations, compacting,
situations into mathematical     variables and determine                                                                                                                             agendas, complex instructions,
models for parabolic, circular   what type of model is                                                                                                                               orbital studies, entry points,
and absolute value functions     appropriate?                                                                                                                                        problem-based learning, choice
boards, 4mat . Website: ASCD
Express

Benchmark 2.3 Solve problems involving functional relations using graphing calculators and/or computers, as well as, appropriate paper-and-pencil techniques.

2.3a Use the inverse                                                                   Solving linear and non- CHOOSE FROM:            HOTS       HOTS                            CHOOSE FROM: Graphic          CHOOSE FROM THE
relationships for the four                                                             linear equations        Oral, performance-                 application                     organizers, text books,       FOLLOWING LIST: Whole
basic operations,                                                                                              based, written                                                     State's released items,       group, small group, one-on-
exponentiation, and root                                                                                       (pen/pencil, paper,                                                AVID strategies, horizontal   one, cooperative learning,
extractions to determine                                                                                       journal, report,)                                                  team planning, Internet.      peer mentoring, tiered
unknown quantities                                                                                             portfolio, projects                                                                              activities, stations, compacting,
How do you undo a series                                                                                                                            agendas, complex instructions,
Operations can be undone
of operations?                                                                                                                                      orbital studies, entry points,
problem-based learning, choice
boards, 4mat . Website: ASCD
Express

Revision 4-26-2006/jkw                                                                                                                                                                                                                         5
FOR TEACHERS BY TEACHERS
MATH CURRICULUM GUIDE

STANDARD 2: Algebra: Students use algebraic methods to explore, model, and describe patterns and functions involving numbers, shapes, data, and graphs in problem-solving situations and communicate the reasoning used in
solving these problems.

Benchmark 2.3 Solve problems involving functional relations using graphing calculators and/or computers, as well as, appropriate paper-and-pencil techniques.

Enduring Understanding                                                             Assessment           Key        Suggested Instructional                                        Differentiation              Quarter
State Frameworks                                       Essential Questions          Essential Skills                                                                           Resources
Conceptual Vocabulary                                                               Methods           Strategy           Practices                                            Adaptations/Extensions           Taught

2.3b Apply the rules of                                                             Raising positive and      CHOOSE FROM:          HOTS       HOTS                        CHOOSE FROM: Graphic          CHOOSE FROM THE
exponents and roots to                                                              negative numbers to       Oral, performance-               application                 organizers, text books,       FOLLOWING LIST: Whole
draw conclusions or solve                                                           even and odd powers       based, written                                               State's released items,       group, small group, one-on-
problems that involve                                                                                         (pen/pencil, paper,                                          AVID strategies, horizontal   one, cooperative learning,
positive/negative integer                                                                                     journal, report,)                                            team planning, Internet.      peer mentoring, tiered
When you raise negative
bases, even/odd            There are patterns to be                                                           portfolio, projects                                                                        activities, stations, compacting,
exponents, and simplifying recognized when numbers are numbers to odd powers or                                                                                                                          agendas, complex instructions,
roots                                                  even powers, what                                                                                                                                 orbital studies, entry points,
raised to powers
happens to the function?                                                                                                                          problem-based learning, choice
boards, 4mat . Website: ASCD
Express

2.3c Solve logarithmic                                                              Using logs to undo        CHOOSE FROM:          HOTS       HOTS                        CHOOSE FROM: Graphic          CHOOSE FROM THE
and exponential equations                                                           exponents and vice        Oral, performance-               analyze                     organizers, text books,       FOLLOWING LIST: Whole
versa                     based, written                                               State's released items,       group, small group, one-on-
(pen/pencil, paper,                                          AVID strategies, horizontal   one, cooperative learning,
journal, report,)                                            team planning, Internet.      peer mentoring, tiered
portfolio, projects                                                                        activities, stations, compacting,
Logs and exponents are      How are logarithms and
agendas, complex instructions,
inverse operations          exponents related?
orbital studies, entry points,
problem-based learning, choice
boards, 4mat . Website: ASCD
Express

2.3d Apply properties of                                                            Multiplying complex       CHOOSE FROM:          HOTS       HOTS                        CHOOSE FROM: Graphic          CHOOSE FROM THE
and perform basic                                                                   numbers and               Oral, performance-               application                 organizers, text books,       FOLLOWING LIST: Whole
operations on complex                                                               simplifying powers of I   based, written                                               State's released items,       group, small group, one-on-
numbers                                                                                                       (pen/pencil, paper,                                          AVID strategies, horizontal   one, cooperative learning,
journal, report,)                                            team planning, Internet.      peer mentoring, tiered
How do you represent the                              portfolio, projects                                                                        activities, stations, compacting,
The concept of the square                                                                                                                                                    agendas, complex instructions,
square root of a negative
root of a negative number                                                                                                                                                    orbital studies, entry points,
number?
problem-based learning, choice
boards, 4mat . Website: ASCD
Express

Revision 4-26-2006/jkw                                                                                                                                                                                                                   6
FOR TEACHERS BY TEACHERS
MATH CURRICULUM GUIDE

STANDARD 2: Algebra: Students use algebraic methods to explore, model, and describe patterns and functions involving numbers, shapes, data, and graphs in problem-solving situations and communicate the reasoning used in
solving these problems.

Benchmark 2.3 Solve problems involving functional relations using graphing calculators and/or computers, as well as, appropriate paper-and-pencil techniques.

Enduring Understanding                                                                   Assessment           Key        Suggested Instructional                                        Differentiation              Quarter
State Frameworks                                           Essential Questions            Essential Skills                                                                           Resources
Conceptual Vocabulary                                                                     Methods           Strategy           Practices                                            Adaptations/Extensions           Taught

2.3e Add, subtract,                                                                       Perform basic             CHOOSE FROM:          HOTS       HOTS                        CHOOSE FROM: Graphic          CHOOSE FROM THE
multiply, and divide                                                                      operations on             Oral, performance-               knowledge                   organizers, text books,       FOLLOWING LIST: Whole
polynomials                                                                               polynomials               based, written                                               State's released items,       group, small group, one-on-
(pen/pencil, paper,                                          AVID strategies, horizontal   one, cooperative learning,
journal, report,)                                            team planning, Internet.      peer mentoring, tiered
How are polynomial                                      portfolio, projects                                                                        activities, stations, compacting,
Basic operations can be
operations different from                                                                                                                          agendas, complex instructions,
applied to polynomials                                                                                                                                                            orbital studies, entry points,
integer operations?
problem-based learning, choice
boards, 4mat . Website: ASCD
Express

2.3f Solve quadratic                                                                      Choosing and using        CHOOSE FROM:          HOTS       HOTS                        CHOOSE FROM: Graphic          CHOOSE FROM THE
(parabolic and circular)                                                                  appropriate techniques    Oral, performance-               application                 organizers, text books,       FOLLOWING LIST: Whole
and absolute value                                                                        for solving quadratics,   based, written                                               State's released items,       group, small group, one-on-
equations and inequalities                                                                and absolute value        (pen/pencil, paper,                                          AVID strategies, horizontal   one, cooperative learning,
for common algebra                                          What is an appropriate        functions                 journal, report,)                                            team planning, Internet.      peer mentoring, tiered
settings                   There are multiple techniques    strategy for solving a                                  portfolio, projects                                                                        activities, stations, compacting,
for solving non-linear           quadratic equation/                                                                                                                                agendas, complex instructions,
equations                        inequality or an absolute                                                                                                                          orbital studies, entry points,
value equation/inequality?                                                                                                                         problem-based learning, choice
boards, 4mat . Website: ASCD
Express

2.3g Find solutions to                                                                    Choosing and using        CHOOSE FROM:          SIOP       SIOP                        CHOOSE FROM: Graphic          CHOOSE FROM THE
systems of 3 or more                                                                      appropriate techniques    Oral, performance-               practice and application    organizers, text books,       FOLLOWING LIST: Whole
linear equations using a                                                                  for solving systems of    based, written                                               State's released items,       group, small group, one-on-
variety of methods                                                                        linear equations          (pen/pencil, paper,                                          AVID strategies, horizontal   one, cooperative learning,
including inverse matrices                                                                                          journal, report,)                                            team planning, Internet.      peer mentoring, tiered
What methods can be                                     portfolio, projects                                                                        activities, stations, compacting,
Systems of equations are not                                                                                                                                                      agendas, complex instructions,
used for solving systems of
restricted to two variables                                                                                                                                                       orbital studies, entry points,
linear equations?
problem-based learning, choice
boards, 4mat . Website: ASCD
Express

Revision 4-26-2006/jkw                                                                                                                                                                                                                         7
FOR TEACHERS BY TEACHERS
MATH CURRICULUM GUIDE

STANDARD 2: Algebra: Students use algebraic methods to explore, model, and describe patterns and functions involving numbers, shapes, data, and graphs in problem-solving situations and communicate the reasoning used in
solving these problems.

Benchmark 2.3 Solve problems involving functional relations using graphing calculators and/or computers, as well as, appropriate paper-and-pencil techniques.

Enduring Understanding                                                              Assessment           Key        Suggested Instructional                                        Differentiation              Quarter
State Frameworks                                         Essential Questions          Essential Skills                                                                          Resources
Conceptual Vocabulary                                                                Methods           Strategy           Practices                                            Adaptations/Extensions           Taught

2.3h Perform function                                                                 Perform function         CHOOSE FROM:          SIOP       SIOP                        CHOOSE FROM: Graphic          CHOOSE FROM THE
operations including                                                                  operations               Oral, performance-               practice and application    organizers, text books,       FOLLOWING LIST: Whole
composition of functions                                                                                       based, written                                               State's released items,       group, small group, one-on-
(pen/pencil, paper,                                          AVID strategies, horizontal   one, cooperative learning,
journal, report,)                                            team planning, Internet.      peer mentoring, tiered
Functions can be combined to                                                        portfolio, projects                                                                        activities, stations, compacting,
What is the meaning of a
create new functions that                                                                                                                                                      agendas, complex instructions,
composite function?
have meaning                                                                                                                                                                   orbital studies, entry points,
problem-based learning, choice
boards, 4mat . Website: ASCD
Express

Benchmark 2.4 Analyze and explain the behaviors, transformation, and general properties of types of equations and functions( for example: linear, quadratic, and exponential)

2.4a Understand how the                                                               Explaining how change CHOOSE FROM:             McREL/     McREL/HOTS                  CHOOSE FROM: Graphic          CHOOSE FROM THE
base affects exponential                                                              of base affects the rate Oral, performance-    HOTS       generating                  organizers, text books,       FOLLOWING LIST: Whole
growth and decay in                                                                   of growth or decay       based, written                                               State's released items,       group, small group, one-on-
applied settings                                                                                               (pen/pencil, paper,                                          AVID strategies, horizontal   one, cooperative learning,
journal, report,)                                            team planning, Internet.      peer mentoring, tiered
Understand how the base        How does the base affect                             portfolio, projects                                                                        activities, stations, compacting,
affects exponential growth and the rate of growth or                                                                                                                           agendas, complex instructions,
decay in applied settings      decay?                                                                                                                                          orbital studies, entry points,
problem-based learning, choice
boards, 4mat . Website: ASCD
Express

2.4b Solve, identify, and                                                             Finding roots and       CHOOSE FROM:           HOTS       HOTS                        CHOOSE FROM: Graphic          CHOOSE FROM THE
discuss characteristics and                                                           interpreting meaning of Oral, performance-                analyze                     organizers, text books,       FOLLOWING LIST: Whole
types of solutions to a                                                               roots                   based, written                                                State's released items,       group, small group, one-on-
variety of polynomial                                                                                         (pen/pencil, paper,                                           AVID strategies, horizontal   one, cooperative learning,
equations                                                                                                     journal, report,)                                             team planning, Internet.      peer mentoring, tiered
Understand how the degree of
How does the degree of a                           portfolio, projects                                                                         activities, stations, compacting,
the function affects the shape
polynomial affect its                                                                                                                          agendas, complex instructions,
of the graph and possible
characteristics?                                                                                                                               orbital studies, entry points,
number of roots
problem-based learning, choice
boards, 4mat . Website: ASCD
Express

Revision 4-26-2006/jkw                                                                                                                                                                                                                    8
FOR TEACHERS BY TEACHERS
MATH CURRICULUM GUIDE

STANDARD 2: Algebra: Students use algebraic methods to explore, model, and describe patterns and functions involving numbers, shapes, data, and graphs in problem-solving situations and communicate the reasoning used in
solving these problems.

Benchmark 2.5 Interpret algebraic equations and inequalities geometrically and describing geometric relationships algebraically

Enduring Understanding                                                         Assessment            Key        Suggested Instructional                                        Differentiation              Quarter
State Frameworks                                      Essential Questions         Essential Skills                                                                          Resources
Conceptual Vocabulary                                                           Methods            Strategy           Practices                                            Adaptations/Extensions           Taught

2.5a Find the midpoint                                                            Find the midpoint or    CHOOSE FROM:           HOTS       HOTS                        CHOOSE FROM: Graphic          CHOOSE FROM THE
and length of a line                                                              length of any line      Oral, performance-                knowledge                   organizers, text books,       FOLLOWING LIST: Whole
segment                                                                           segment                 based, written                                                State's released items,       group, small group, one-on-
(pen/pencil, paper,                                           AVID strategies, horizontal   one, cooperative learning,
journal, report,)                                             team planning, Internet.      peer mentoring, tiered
portfolio, projects                                                                         activities, stations, compacting,
Every line segment has a     What is the meaning of                                                                                                                         agendas, complex instructions,
midpoint                     'midpoint'?                                                                                                                                    orbital studies, entry points,
problem-based learning, choice
boards, 4mat . Website: ASCD
Express

STANDARD 7: Students communicate the reasoning used in problem-solving situations

Benchmark B Communicate the use of patterns and functions needed to model real-world situations and solve appropriate problems.

State Frameworks           Enduring Understanding     Essential Questions         Essential Skills        Assessment          Key          Suggested Instructional          Resources                     Differentiation              Quarter
Conceptual Vocabulary                                                           Methods            Strategy           Practices                                            Adaptations/Extensions           Taught

7B.1 Students generate                                                            Translating math into   CHOOSE FROM:           McREL      McREL                       CHOOSE FROM: Graphic          CHOOSE FROM THE
and solve problems of                                                             real world situations   Oral, performance-                Summarizing--Organizing     organizers, text books,       FOLLOWING LIST: Whole
appropriate complexity                                                                                    based, written                    information                 Mastery Math materials (Al    group, Small group, one-on-
created from real-world                                                                                   (pen/pencil, paper,               Problem writing             Ludwig) , Algebra pizzazz,    one, Cooperative learning,
problems.                                              How is math a universal                            journal, report,)                                             States released items,        Peer mentoring (Learning
Mathematics is a tool for    language?                                          portfolio, projects,                                          AVID strategies,              buddies), tiered activities,
communication.               How would you learn math                                                                                         Foldables, Horizontal         stations, compacting, agendas,
without a math teacher?                                                                                          planning internet.            complex instructions orbital
studies, Entry points, Problem
based learning, choice boards,
4mat . Website: ASCD Express

Revision 4-26-2006/jkw                                                                                                                                                                                                                9
FOR TEACHERS BY TEACHERS
MATH CURRICULUM GUIDE

STANDARD 7: Students communicate the reasoning used in problem-solving situations

Benchmark B Communicate the use of patterns and functions needed to model real-world situations and solve appropriate problems.

State Frameworks            Enduring Understanding          Essential Questions         Essential Skills        Assessment          Key          Suggested Instructional              Resources                   Differentiation            Quarter
Conceptual Vocabulary                                                                Methods            Strategy           Practices                                              Adaptations/Extensions         Taught

7B.2 Identify the essential                                                             Extracting important     CHOOSE FROM:           HOTS       HOTS                            CHOOSE FROM: Graphic         CHOOSE FROM THE
components of                                                                           information              Oral, performance-                Knowledge                       organizers, text books,      FOLLOWING LIST: Whole
mathematical and real-                                                                                           based, written                                                    Mastery Math materials (Al   group, Small group, one-on-
world problems                                                                                                   (pen/pencil, paper,    SIOP       SIOP                            Ludwig) , Algebra pizzazz,   one, Cooperative learning,
journal, report,)                 Finding Main Idea               States released items,       Peer mentoring (Learning
It is essential to be able to   How do you read                                    portfolio, projects,                                              AVID strategies,             buddies), tiered activities,
Deleting unimportant
communicate the reasoning       mathematical stuff?                                                                                                  Foldables, Horizontal        stations, compacting, agendas,
information
used to solve problems.         What's your problem?                                                                                                 planning internet.           complex instructions orbital
studies, Entry points, Problem
based learning, choice boards,
4mat . Website: ASCD Express

7B.3 Choose and apply a                                                                 Problem solving          CHOOSE FROM:           McREL      McREL:                          CHOOSE FROM: Graphic         CHOOSE FROM THE
strategy to solve                                                                       strategies               Oral, performance-                Graphic organizers              organizers, text books,      FOLLOWING LIST: Whole
mathematical and real-                                                                                           based, written                                                    Mastery Math materials (Al   group, Small group, one-on-
world problems                                                                                                   (pen/pencil, paper,                                               Ludwig) , Algebra pizzazz,   one, Cooperative learning,
journal, report,)                                                 States released items,       Peer mentoring (Learning
It is essential to be able to                                                      portfolio, projects,                                              AVID strategies,             buddies), tiered activities,
communicate the reasoning       What's in your toolbox?                                                                                              Foldables, Horizontal        stations, compacting, agendas,
used to solve problems.                                                                                                                              planning internet.           complex instructions orbital
studies, Entry points, Problem
based learning, choice boards,
4mat . Website: ASCD Express

7B.4 Evaluate the                                                                       Significant figures      CHOOSE FROM:           McREL      McREL                           CHOOSE FROM: Graphic         CHOOSE FROM THE
solutions of mathematical                                                               Estimating               Oral, performance-                Precision & Accuracy Practice   organizers, text books,      FOLLOWING LIST: Whole
and real world problems                                                                 Mental Math              based, written                                                    Mastery Math materials (Al   group, Small group, one-on-
for reasonableness.                                                                                              (pen/pencil, paper,                                               Ludwig) , Algebra pizzazz,   one, Cooperative learning,
journal, report,)                                                 States released items,       Peer mentoring (Learning
It is essential to be able to                                                      portfolio, projects,                                              AVID strategies,             buddies), tiered activities,
How close is close
communicate the reasoning                                                                                                                            Foldables, Horizontal        stations, compacting, agendas,
enough?
used to solve problems.                                                                                                                              planning internet.           complex instructions orbital
studies, Entry points, Problem
based learning, choice boards,
4mat . Website: ASCD Express

Revision 4-26-2006/jkw                                                                                                                                                                                                                      10
FOR TEACHERS BY TEACHERS
MATH CURRICULUM GUIDE

STANDARD 7: Students communicate the reasoning used in problem-solving situations

Benchmark B Communicate the use of patterns and functions needed to model real-world situations and solve appropriate problems.

State Frameworks            Enduring Understanding           Essential Questions             Essential Skills        Assessment          Key          Suggested Instructional            Resources                     Differentiation              Quarter
Conceptual Vocabulary                                                                     Methods            Strategy           Practices                                              Adaptations/Extensions           Taught

7B.5 Explain the strategy                                                                    Explain processes for   CHOOSE FROM:           McREL      McREL                         CHOOSE FROM: Graphic          CHOOSE FROM THE
used and the solution to                                                                     solutions               Oral, performance-                Practice explaining answers   organizers, text books,       FOLLOWING LIST: Whole
mathematical and real-                                                                                               based, written                    Journal writing               Mastery Math materials (Al    group, Small group, one-on-
world problems through                                        How would you                                          (pen/pencil, paper,                                             Ludwig) , Algebra pizzazz,    one, Cooperative learning,
written and oral             Mathematics is a tool for                                                               journal, report,)                                               States released items,        Peer mentoring (Learning
communicate the solution
communication.               communication.                                                                          portfolio, projects,                                            AVID strategies,              buddies), tiered activities,
to a problem to an alien?
It is essential to be able to                                                                                                                          Foldables, Horizontal         stations, compacting, agendas,
How can you convince a
communicate the reasoning                                                                                                                               planning internet.            complex instructions orbital
total stranger (who dislikes
used to solve problems.                                                                                                                                                               studies, Entry points, Problem
you) that you are right?
based learning, choice boards,
4mat . Website: ASCD Express

STANDARD 3: Data Analysis: Students use data collection and analysis, statistics, and probability in problem-solving situations and communicate the reasoning and processes used in solving these problems.

Benchmark 3.3 Fit curves to scatter plots using informal methods or appropriate technology to determine the strengths of the relationship between two data sets and to make predictions

Enduring Understanding                                                                   Assessment            Key        Suggested Instructional                                          Differentiation              Quarter
State Frameworks                                             Essential Questions             Essential Skills                                                                            Resources
Conceptual Vocabulary                                                                     Methods            Strategy           Practices                                              Adaptations/Extensions           Taught

3.3a Decide which type of                                                                    Choosing an             CHOOSE FROM:           SIOP       SIOP                          CHOOSE FROM: Graphic          CHOOSE FROM THE
non-linear model fits non-                                                                   appropriate model for   Oral, performance-                modeling                      organizers, text books,       FOLLOWING LIST: Whole
linear data most                                                                             data                    based, written                                                  State's released items,       group, small group, one-on-
appropriately                                                                                                        (pen/pencil, paper,                                             AVID strategies, horizontal   one, cooperative learning,
journal, report,)                                               team planning, Internet.      peer mentoring, tiered
portfolio, projects                                                                           activities, stations, compacting,
All data can be modeled by       What is an appropriate                                                                                                                               agendas, complex instructions,
some type of equation            model for these data?                                                                                                                                orbital studies, entry points,
problem-based learning, choice
boards, 4mat . Website: ASCD
Express

Revision 4-26-2006/jkw                                                                                                                                                                                                                             11
FOR TEACHERS BY TEACHERS
MATH CURRICULUM GUIDE

STANDARD 3: Data Analysis: Students use data collection and analysis, statistics, and probability in problem-solving situations and communicate the reasoning and processes used in solving these problems.

Benchmark 3.5 Use experimental and theoretical probability to represent and solve problems involving uncertainty (for example, the chance of playing professional sports if a student is a successful high school athlete.

Enduring Understanding                                                             Assessment           Key         Suggested Instructional                                          Differentiation              Quarter
State Frameworks                                         Essential Questions         Essential Skills                                                                             Resources
Conceptual Vocabulary                                                               Methods           Strategy            Practices                                              Adaptations/Extensions           Taught

3.5a Exhibit knowledge of                                                            Making diagrams to       CHOOSE FROM:          McREL      McREL/SIOP                     CHOOSE FROM: Graphic          CHOOSE FROM THE
conditional and joint                                                                analyze probabilities;   Oral, performance-    SIOP       graphic organizer              organizers, text books,       FOLLOWING LIST: Whole
probability                                                                          knowing when to add or   based, written                                                  State's released items,       group, small group, one-on-
multiply probabilities   (pen/pencil, paper,                                             AVID strategies, horizontal   one, cooperative learning,
journal, report,)                                               team planning, Internet.      peer mentoring, tiered
portfolio, projects                                                                           activities, stations, compacting,
The probability of an event   What is the sample space                                                                                                                          agendas, complex instructions,
depends on the situation      of this compound event?                                                                                                                           orbital studies, entry points,
problem-based learning, choice
boards, 4mat . Website: ASCD
Express

Benchmark 3.6 Solve real-world problems with informal use of combinations and permutations (for example, determine the number of possible meals at a restaurant featuring a given number of side dishes)

3.6a Solve real-world                                                                Calculating numbers of   CHOOSE FROM:          McREL      McREL                          CHOOSE FROM: Graphic          CHOOSE FROM THE
problems with formal use                                                             possible arrangements    Oral, performance-               similarities and differences   organizers, text books,       FOLLOWING LIST: Whole
of combinations and                                                                  or combinations for      based, written                                                  State's released items,       group, small group, one-on-
permutations.                                                                        given situations         (pen/pencil, paper,                                             AVID strategies, horizontal   one, cooperative learning,
journal, report,)                                               team planning, Internet.      peer mentoring, tiered
There are techniques for
What is the difference                               portfolio, projects                                                                           activities, stations, compacting,
simplifying the counting
between combinations and                                                                                                                           agendas, complex instructions,
process for numbers of
permutations?                                                                                                                                      orbital studies, entry points,
arrangements or combinations
problem-based learning, choice
boards, 4mat . Website: ASCD
Express

3.6b Use Venn diagrams                                                               Arranging data in a      CHOOSE FROM:          McREL/SI McREL/SIOP graphic               CHOOSE FROM: Graphic          CHOOSE FROM THE
in counting                                                                          Venn diagram             Oral, performance-    OP       organizer                        organizers, text books,       FOLLOWING LIST: Whole
based, written                                                  State's released items,       group, small group, one-on-
(pen/pencil, paper,                                             AVID strategies, horizontal   one, cooperative learning,
journal, report,)                                               team planning, Internet.      peer mentoring, tiered
portfolio, projects                                                                           activities, stations, compacting,
Venn diagrams can be used to What is the purpose of a
agendas, complex instructions,
display information          Venn diagram?
orbital studies, entry points,
problem-based learning, choice
boards, 4mat . Website: ASCD
Express

Revision 4-26-2006/jkw                                                                                                                                                                                                                      12
FOR TEACHERS BY TEACHERS
MATH CURRICULUM GUIDE

STANDARD 7: Students communicate the reasoning used in problem-solving situations

Benchmark C: Communicate the use of probability and statistics needed to represent and solve problems involving uncertainty.

State Frameworks            Enduring Understanding          Essential Questions         Essential Skills        Assessment          Key          Suggested Instructional          Resources                   Differentiation            Quarter
Conceptual Vocabulary                                                                Methods            Strategy           Practices                                          Adaptations/Extensions         Taught

7C.1 Students generate                                                                   Translating math into   CHOOSE FROM:           McREL      McREL                       CHOOSE FROM: Graphic         CHOOSE FROM THE
and solve problems of                                                                    real world situations   Oral, performance-                Summarizing--Organizing     organizers, text books,      FOLLOWING LIST: Whole
appropriate complexity                                                                                           based, written                    information                 Mastery Math materials (Al   group, Small group, one-on-
created from real-world                                                                                          (pen/pencil, paper,               Problem writing             Ludwig) , Algebra pizzazz,   one, Cooperative learning,
problems.                                                     How is math a universal                            journal, report,)                                             States released items,       Peer mentoring (Learning
Mathematics is a tool for       language?                                          portfolio, projects,                                          AVID strategies,             buddies), tiered activities,
communication.                  How would you learn math                                                                                         Foldables, Horizontal        stations, compacting, agendas,
without a math teacher?                                                                                          planning internet.           complex instructions orbital
studies, Entry points, Problem
based learning, choice boards,
4mat . Website: ASCD Express

7C.2 Identify the essential                                                              Extracting important    CHOOSE FROM:           HOTS       HOTS                        CHOOSE FROM: Graphic         CHOOSE FROM THE
components of                                                                            information             Oral, performance-                Knowledge                   organizers, text books,      FOLLOWING LIST: Whole
mathematical and real-                                                                                           based, written                                                Mastery Math materials (Al   group, Small group, one-on-
world problems                                                                                                   (pen/pencil, paper,    SIOP       SIOP                        Ludwig) , Algebra pizzazz,   one, Cooperative learning,
journal, report,)                 Finding Main Idea           States released items,       Peer mentoring (Learning
It is essential to be able to   How do you read
portfolio, projects,              Deleting unimportant        AVID strategies,             buddies), tiered activities,
communicate the reasoning       mathematical stuff?
information                 Foldables, Horizontal        stations, compacting, agendas,
used to solve problems.         What's your problem?
planning internet.           complex instructions orbital
studies, Entry points, Problem
based learning, choice boards,
4mat . Website: ASCD Express

7C.3 Choose and apply a                                                                  Problem solving         CHOOSE FROM:           McREL      McREL:                      CHOOSE FROM: Graphic         CHOOSE FROM THE
strategy to solve                                                                        strategies              Oral, performance-                Graphic organizers          organizers, text books,      FOLLOWING LIST: Whole
mathematical and real-                                                                                           based, written                                                Mastery Math materials (Al   group, Small group, one-on-
world problems                                                                                                   (pen/pencil, paper,                                           Ludwig) , Algebra pizzazz,   one, Cooperative learning,
journal, report,)                                             States released items,       Peer mentoring (Learning
It is essential to be able to                                                      portfolio, projects,                                          AVID strategies,             buddies), tiered activities,
communicate the reasoning       What's in your toolbox?                                                                                          Foldables, Horizontal        stations, compacting, agendas,
used to solve problems.                                                                                                                          planning internet.           complex instructions orbital
studies, Entry points, Problem
based learning, choice boards,
4mat . Website: ASCD Express

Revision 4-26-2006/jkw                                                                                                                                                                                                                  13
FOR TEACHERS BY TEACHERS
MATH CURRICULUM GUIDE

STANDARD 7: Students communicate the reasoning used in problem-solving situations

Benchmark C: Communicate the use of probability and statistics needed to represent and solve problems involving uncertainty.

State Frameworks           Enduring Understanding          Essential Questions              Essential Skills        Assessment          Key          Suggested Instructional              Resources                   Differentiation            Quarter
Conceptual Vocabulary                                                                     Methods            Strategy           Practices                                              Adaptations/Extensions         Taught

7C.4 Evaluate the                                                                          Significant figures      CHOOSE FROM:           McREL      McREL                           CHOOSE FROM: Graphic         CHOOSE FROM THE
solutions of mathematical                                                                  Estimating               Oral, performance-                Precision & Accuracy Practice   organizers, text books,      FOLLOWING LIST: Whole
and real world problems                                                                    Mental Math              based, written                                                    Mastery Math materials (Al   group, Small group, one-on-
for reasonableness.                                                                                                 (pen/pencil, paper,                                               Ludwig) , Algebra pizzazz,   one, Cooperative learning,
journal, report,)                                                 States released items,       Peer mentoring (Learning
It is essential to be able to                                                           portfolio, projects,                                              AVID strategies,             buddies), tiered activities,
How close is close
communicate the reasoning                                                                                                                                 Foldables, Horizontal        stations, compacting, agendas,
enough?
used to solve problems.                                                                                                                                   planning internet.           complex instructions orbital
studies, Entry points, Problem
based learning, choice boards,
4mat . Website: ASCD Express

7C.5 Explain the strategy                                                                  Explain processes for    CHOOSE FROM:           McREL      McREL                           CHOOSE FROM: Graphic         CHOOSE FROM THE
used and the solution to                                                                   solutions                Oral, performance-                Practice explaining answers     organizers, text books,      FOLLOWING LIST: Whole
mathematical and real-                                                                                              based, written                    Journal writing                 Mastery Math materials (Al   group, Small group, one-on-
world problems through                                      How would you                                           (pen/pencil, paper,                                               Ludwig) , Algebra pizzazz,   one, Cooperative learning,
Mathematics is a tool for
written and oral                                            communicate the solution                                journal, report,)                                                 States released items,       Peer mentoring (Learning
communication.
communication.                                              to a problem to an alien?                               portfolio, projects,                                              AVID strategies,             buddies), tiered activities,
It is essential to be able to
How can you convince a                                                                                                    Foldables, Horizontal        stations, compacting, agendas,
communicate the reasoning
total stranger (who dislikes                                                                                              planning internet.           complex instructions orbital
used to solve problems.
you) that you are right?                                                                                                                               studies, Entry points, Problem
based learning, choice boards,
4mat . Website: ASCD Express

Revision 4-26-2006/jkw                                                                                                                                                                                                                          14
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MATH CURRICULUM GUIDE

STANDARD 4: Geometry: Students use geometric concepts, properties, and relationships in problem-solving situations and communicate the reasoning used in solving these problems.

Benchmark 4.1 Find and analyze relationships among geometric figures using transformations (For example: reflections, translations, rotations, dilations) in coordinate systems

Enduring Understanding                                                               Assessment           Key        Suggested Instructional                                        Differentiation              Quarter
State Frameworks                                             Essential Questions          Essential Skills                                                                         Resources
Conceptual Vocabulary                                                                 Methods           Strategy           Practices                                            Adaptations/Extensions           Taught

4.1a Find and analyze                                                                     Performing              CHOOSE FROM:          HOTS       HOTS                        CHOOSE FROM: Graphic          CHOOSE FROM THE
relationships among                                                                       transformations of      Oral, performance-               analyze                     organizers, text books,       FOLLOWING LIST: Whole
parabolas and circles                                                                     parabolas and circles   based, written                                               State's released items,       group, small group, one-on-
using transformations.                                                                                            (pen/pencil, paper,   McREL      McREL                       AVID strategies, horizontal   one, cooperative learning,
journal, report,)                compare and contrast        team planning, Internet.      peer mentoring, tiered
Transformation of a parent      How does a transformation                           portfolio, projects                                                                        activities, stations, compacting,
function can yield any function affect the graph and the                                                                                                                       agendas, complex instructions,
in its family                   equation of a function?                                                                                                                        orbital studies, entry points,
problem-based learning, choice
boards, 4mat . Website: ASCD
Express

Benchmark 4.2 Derive and use methods to measure perimeter, area, and volume of regular geometric figures.

4.2a Use relationships                                                                    Calculate arc lengths   CHOOSE FROM:          HOTS       HOTS                        CHOOSE FROM: Graphic          CHOOSE FROM THE
among angles, arcs, and                                                                                           Oral, performance-               knowledge                   organizers, text books,       FOLLOWING LIST: Whole
distances around a circle                                                                                         based, written                                               State's released items,       group, small group, one-on-
(pen/pencil, paper,   SIOP       SIOP                        AVID strategies, horizontal   one, cooperative learning,
journal, report,)                practice and application    team planning, Internet.      peer mentoring, tiered
portfolio, projects                                                                        activities, stations, compacting,
How is arc length related                                                                                                                       agendas, complex instructions,
Arcs are portions of circles
to a central angle?                                                                                                                             orbital studies, entry points,
problem-based learning, choice
boards, 4mat . Website: ASCD
Express

4.2b Use scale factors to                                                                 Calculating scale       CHOOSE FROM:          HOTS       HOTS                        CHOOSE FROM: Graphic          CHOOSE FROM THE
determine the magnitude                                                                   changes in two and      Oral, performance-               application                 organizers, text books,       FOLLOWING LIST: Whole
of a size change in 2 and 3                                                               three dimensions        based, written                                               State's released items,       group, small group, one-on-
dimensions                                                                                                        (pen/pencil, paper,                                          AVID strategies, horizontal   one, cooperative learning,
journal, report,)                                            team planning, Internet.      peer mentoring, tiered
Scale factors in two and three If a parameter is changed,                           portfolio, projects                                                                        activities, stations, compacting,
dimensions are different than how does it affect area or                                                                                                                       agendas, complex instructions,
one dimensional changes        volume?                                                                                                                                         orbital studies, entry points,
problem-based learning, choice
boards, 4mat . Website: ASCD
Express

Revision 4-26-2006/jkw                                                                                                                                                                                                                       15
FOR TEACHERS BY TEACHERS
MATH CURRICULUM GUIDE

STANDARD 4: Geometry: Students use geometric concepts, properties, and relationships in problem-solving situations and communicate the reasoning used in solving these problems.

Benchmark 4.3 Make and test conjectures about geometric shapes and their properties, incorporating technology where appropriate

Enduring Understanding                                                                   Assessment           Key        Suggested Instructional                                        Differentiation              Quarter
State Frameworks                                            Essential Questions          Essential Skills                                                                            Resources
Conceptual Vocabulary                                                                     Methods           Strategy           Practices                                            Adaptations/Extensions           Taught

4.3a Solve problems                                                                      Apply knowledge of       CHOOSE FROM:            HOTS       HOTS                        CHOOSE FROM: Graphic          CHOOSE FROM THE
involving inscribed and                                                                  geometric conjectures Oral, performance-                    application                 organizers, text books,       FOLLOWING LIST: Whole
circumscribed figures and                                                                and linear relationships based, written                                                 State's released items,       group, small group, one-on-
tangents of circles                                                                                               (pen/pencil, paper,                                            AVID strategies, horizontal   one, cooperative learning,
How do we apply                                      journal, report,)                                              team planning, Internet.      peer mentoring, tiered
geometric conjectures to                             portfolio, projects                                                                          activities, stations, compacting,
Geometry and Algebra are                                                                                                                                                           agendas, complex instructions,
problems with inscribed
related                                                                                                                                                                            orbital studies, entry points,
and circumscribed figures
and tangents of circles?                                                                                                                          problem-based learning, choice
boards, 4mat . Website: ASCD
Express

4.3b Solve multi-step                                                                    Apply knowledge of         CHOOSE FROM:          HOTS       HOTS                        CHOOSE FROM: Graphic          CHOOSE FROM THE
geometry problems that                                                                   geometric conjectures      Oral, performance-               application                 organizers, text books,       FOLLOWING LIST: Whole
involve integrating                                                                      and linear relationships   based, written                                               State's released items,       group, small group, one-on-
concepts, planning,                                                                      in real-world situations   (pen/pencil, paper,                                          AVID strategies, horizontal   one, cooperative learning,
visualization, and/or                                                                                               journal, report,)                                            team planning, Internet.      peer mentoring, tiered
making connections with     Geometry has applications in                                                            portfolio, projects                                                                        activities, stations, compacting,
other content areas                                          How does geometry relate                                                                                                                          agendas, complex instructions,
to the real-world?                                                                                                                                orbital studies, entry points,
world phenomena
problem-based learning, choice
boards, 4mat . Website: ASCD
Express

Benchmark 4.4 Use trigonometric ratios in problem-solving situations (for example: finding the height of a building from a given point, if the distance to and building and the angle of elevation are known)

4.4a Exhibit knowledge of                                                                Finding and using          CHOOSE FROM:          SIOP       SIOP                        CHOOSE FROM: Graphic          CHOOSE FROM THE
unit circle trigonometry                                                                 trigonometric ratios       Oral, performance-               practice and application    organizers, text books,       FOLLOWING LIST: Whole
(embed properties of                                                                     related to points          based, written                                               State's released items,       group, small group, one-on-
special right triangles,                                                                 anywhere on a circle       (pen/pencil, paper,                                          AVID strategies, horizontal   one, cooperative learning,
Pythagorean Theorem)                                                                                                journal, report,)                                            team planning, Internet.      peer mentoring, tiered
portfolio, projects                                                                        activities, stations, compacting,
Trigonometry is not limited to   How does trigonometry
agendas, complex instructions,
right triangles                  relate to circles?
orbital studies, entry points,
problem-based learning, choice
boards, 4mat . Website: ASCD
Express

Revision 4-26-2006/jkw                                                                                                                                                                                                                         16
FOR TEACHERS BY TEACHERS
MATH CURRICULUM GUIDE

STANDARD 7: Students communicate the reasoning used in problem-solving situations

Benchmark D: Communicate the use of geometric concepts needed to model real-world situations and solve appropriate problems.

State Frameworks            Enduring Understanding          Essential Questions         Essential Skills        Assessment          Key          Suggested Instructional          Resources                   Differentiation            Quarter
Conceptual Vocabulary                                                                Methods            Strategy           Practices                                          Adaptations/Extensions         Taught

7D.1 Students generate                                                                   Translating math into   CHOOSE FROM:           McREL      McREL                       CHOOSE FROM: Graphic         CHOOSE FROM THE
and solve problems of                                                                    real world situations   Oral, performance-                Summarizing--Organizing     organizers, text books,      FOLLOWING LIST: Whole
appropriate complexity                                                                                           based, written                    information                 Mastery Math materials (Al   group, Small group, one-on-
created from real-world                                                                                          (pen/pencil, paper,               Problem writing             Ludwig) , Algebra pizzazz,   one, Cooperative learning,
problems.                                                     How is math a universal                            journal, report,)                                             States released items,       Peer mentoring (Learning
Mathematics is a tool for       language?                                          portfolio, projects,                                          AVID strategies,             buddies), tiered activities,
communication.                  How would you learn math                                                                                         Foldables, Horizontal        stations, compacting, agendas,
without a math teacher?                                                                                          planning internet.           complex instructions orbital
studies, Entry points, Problem
based learning, choice boards,
4mat . Website: ASCD Express

7D.2 Identify the essential                                                              Extracting important    CHOOSE FROM:           HOTS       HOTS                        CHOOSE FROM: Graphic         CHOOSE FROM THE
components of                                                                            information             Oral, performance-                Knowledge                   organizers, text books,      FOLLOWING LIST: Whole
mathematical and real-                                                                                           based, written                                                Mastery Math materials (Al   group, Small group, one-on-
world problems                                                                                                   (pen/pencil, paper,    SIOP       SIOP                        Ludwig) , Algebra pizzazz,   one, Cooperative learning,
journal, report,)                 Finding Main Idea           States released items,       Peer mentoring (Learning
It is essential to be able to   How do you read                                    portfolio, projects,              Deleting unimportant        AVID strategies,             buddies), tiered activities,
communicate the reasoning       mathematical stuff?                                                                  information                 Foldables, Horizontal        stations, compacting, agendas,
used to solve problems.         What's your problem?                                                                                             planning internet.           complex instructions orbital
studies, Entry points, Problem
based learning, choice boards,
4mat . Website: ASCD Express

7D.3 Choose and apply a                                                                  Problem solving         CHOOSE FROM:           McREL      McREL:                      CHOOSE FROM: Graphic         CHOOSE FROM THE
strategy to solve                                                                        strategies              Oral, performance-                Graphic organizers          organizers, text books,      FOLLOWING LIST: Whole
mathematical and real-                                                                                           based, written                                                Mastery Math materials (Al   group, Small group, one-on-
world problems                                                                                                   (pen/pencil, paper,                                           Ludwig) , Algebra pizzazz,   one, Cooperative learning,
journal, report,)                                             States released items,       Peer mentoring (Learning
It is essential to be able to                                                      portfolio, projects,                                          AVID strategies,             buddies), tiered activities,
communicate the reasoning       What's in your toolbox?                                                                                          Foldables, Horizontal        stations, compacting, agendas,
used to solve problems.                                                                                                                          planning internet.           complex instructions orbital
studies, Entry points, Problem
based learning, choice boards,
4mat . Website: ASCD Express

Revision 4-26-2006/jkw                                                                                                                                                                                                                  17
FOR TEACHERS BY TEACHERS
MATH CURRICULUM GUIDE

STANDARD 7: Students communicate the reasoning used in problem-solving situations

Benchmark D: Communicate the use of geometric concepts needed to model real-world situations and solve appropriate problems.

State Frameworks            Enduring Understanding          Essential Questions              Essential Skills        Assessment          Key          Suggested Instructional              Resources                     Differentiation              Quarter
Conceptual Vocabulary                                                                     Methods            Strategy           Practices                                                Adaptations/Extensions           Taught

7D.4 Evaluate the                                                                           Significant figures      CHOOSE FROM:           McREL      McREL                           CHOOSE FROM: Graphic          CHOOSE FROM THE
solutions of mathematical                                                                   Estimating               Oral, performance-                Precision & Accuracy Practice   organizers, text books,       FOLLOWING LIST: Whole
and real world problems                                                                     Mental Math              based, written                                                    Mastery Math materials (Al    group, Small group, one-on-
for reasonableness.                                                                                                  (pen/pencil, paper,                                               Ludwig) , Algebra pizzazz,    one, Cooperative learning,
journal, report,)                                                 States released items,        Peer mentoring (Learning
It is essential to be able to                                                            portfolio, projects,                                              AVID strategies,              buddies), tiered activities,
How close is close
communicate the reasoning                                                                                                                                  Foldables, Horizontal         stations, compacting, agendas,
enough?
used to solve problems.                                                                                                                                    planning internet.            complex instructions orbital
studies, Entry points, Problem
based learning, choice boards,
4mat . Website: ASCD Express

7D.5 Explain the strategy                                                                   Explain processes for    CHOOSE FROM:           McREL      McREL                           CHOOSE FROM: Graphic          CHOOSE FROM THE
used and the solution to                                                                    solutions                Oral, performance-                Practice explaining answers     organizers, text books,       FOLLOWING LIST: Whole
mathematical and real-                                                                                               based, written                    Journal writing                 Mastery Math materials (Al    group, Small group, one-on-
world problems through                                       How would you                                           (pen/pencil, paper,                                               Ludwig) , Algebra pizzazz,    one, Cooperative learning,
written and oral            Mathematics is a tool for                                                                journal, report,)                                                 States released items,        Peer mentoring (Learning
communicate the solution
communication.              communication. It is essential                                                           portfolio, projects,                                              AVID strategies,              buddies), tiered activities,
to a problem to an alien?
to be able to communicate the                                                                                                                              Foldables, Horizontal         stations, compacting, agendas,
How can you convince a
reasoning used to solve                                                                                                                                    planning internet.            complex instructions orbital
total stranger (who dislikes
problems.                                                                                                                                                                                studies, Entry points, Problem
you) that you are right?
based learning, choice boards,
4mat . Website: ASCD Express

STANDARD 5: Measurement: Students use a variety of tools and techniques to measure, apply the results in problem-solving situations, and communicate the reasoning involved in solving these problems.

Benchmark 5.1 Measure quantities indirectly using techniques of algebra, geometry, or trigonometry

Enduring Understanding                                                                   Assessment            Key        Suggested Instructional                                            Differentiation              Quarter
State Frameworks                                            Essential Questions              Essential Skills                                                                              Resources
Conceptual Vocabulary                                                                     Methods            Strategy           Practices                                                Adaptations/Extensions           Taught

5.1a Use appropriate                                                                        Using trigonometry or CHOOSE FROM:              HOTS       HOTS                            CHOOSE FROM: Graphic          CHOOSE FROM THE
measurements to solve                                                                       similarity to make    Oral, performance-                   application                     organizers, text books,       FOLLOWING LIST: Whole
problems indirectly (for                                                                    indirect measurements based, written                                                       State's released items,       group, small group, one-on-
example, find lengths                                                                                             (pen/pencil, paper,                                                  AVID strategies, horizontal   one, cooperative learning,
using law of sines.                                                                                               journal, report,)                                                    team planning, Internet.      peer mentoring, tiered
portfolio, projects                                                                                activities, stations, compacting,
Measurements can be made        What is an indirect
agendas, complex instructions,
indirectly                       measurement?
orbital studies, entry points,
problem-based learning, choice
boards, 4mat . Website: ASCD
Express

Revision 4-26-2006/jkw                                                                                                                                                                                                                              18
FOR TEACHERS BY TEACHERS
MATH CURRICULUM GUIDE

STANDARD 5: Measurement: Students use a variety of tools and techniques to measure, apply the results in problem-solving situations, and communicate the reasoning involved in solving these problems.

Benchmark 5.2 Select and use appropriate tools and techniques to measure quantities in order to achieve specified degrees of precision, accuracy, and error (or tolerance) of measurements.

Enduring Understanding                                                          Assessment           Key        Suggested Instructional                                        Differentiation              Quarter
State Frameworks                                          Essential Questions        Essential Skills                                                                       Resources
Conceptual Vocabulary                                                            Methods           Strategy           Practices                                            Adaptations/Extensions           Taught

5.2a Select and use                                                                  Making accurate       CHOOSE FROM:          SIOP       SIOP                        CHOOSE FROM: Graphic          CHOOSE FROM THE
appropriate tools and                                                                measurements          Oral, performance-               practice and application    organizers, text books,       FOLLOWING LIST: Whole
techniques to measure                                                                                      based, written                                               State's released items,       group, small group, one-on-
quantities in order to                                                                                     (pen/pencil, paper,                                          AVID strategies, horizontal   one, cooperative learning,
achieve specified degrees                                                                                  journal, report,)                                            team planning, Internet.      peer mentoring, tiered
of precision, accuracy and                                                                                 portfolio, projects                                                                        activities, stations, compacting,
error of measurements.     There are different tools and   What unit of measure is                                                                                                                    agendas, complex instructions,
units of measure                appropriate?                                                                                                                               orbital studies, entry points,
problem-based learning, choice
boards, 4mat . Website: ASCD
Express

Benchmark 5.3 Determine the degree of accuracy of a measurement (for example: by understanding and using significant digits)

Revision 4-26-2006/jkw                                                                                                                                                                                                                19
FOR TEACHERS BY TEACHERS
MATH CURRICULUM GUIDE

STANDARD 7: Students communicate the reasoning used in problem-solving situations

Benchmark E: Communicate the use of appropriate measurement techniques needed to solve problems and report the degree of accuracy required.

State Frameworks            Enduring Understanding          Essential Questions         Essential Skills        Assessment          Key          Suggested Instructional          Resources                   Differentiation            Quarter
Conceptual Vocabulary                                                                Methods            Strategy           Practices                                          Adaptations/Extensions         Taught

7E.1 Generate and solve                                                                  Translating math into   CHOOSE FROM:           McREL      McREL                       CHOOSE FROM: Graphic         CHOOSE FROM THE
problems of appropriate                                                                  real world situations   Oral, performance-                Summarizing--Organizing     organizers, text books,      FOLLOWING LIST: Whole
complexity created from                                                                                          based, written                    information                 Mastery Math materials (Al   group, Small group, one-on-
real-world problems.                                                                                             (pen/pencil, paper,               Problem writing             Ludwig) , Algebra pizzazz,   one, Cooperative learning,
How is math a universal                            journal, report,)                                             States released items,       Peer mentoring (Learning
Mathematics is a tool for       language?                                          portfolio, projects,                                          AVID strategies,             buddies), tiered activities,
communication.                  How would you learn math                                                                                         Foldables, Horizontal        stations, compacting, agendas,
without a math teacher?                                                                                          planning internet.           complex instructions orbital
studies, Entry points, Problem
based learning, choice boards,
4mat . Website: ASCD Express

7E.2 Identify the essential                                                              Extracting important    CHOOSE FROM:           HOTS       HOTS                        CHOOSE FROM: Graphic         CHOOSE FROM THE
components of                                                                            information             Oral, performance-                Knowledge                   organizers, text books,      FOLLOWING LIST: Whole
mathematical and real-                                                                                           based, written                                                Mastery Math materials (Al   group, Small group, one-on-
world problems                                                                                                   (pen/pencil, paper,    SIOP       SIOP                        Ludwig) , Algebra pizzazz,   one, Cooperative learning,
journal, report,)                 Finding Main Idea           States released items,       Peer mentoring (Learning
It is essential to be able to   How do you read                                    portfolio, projects,              Deleting unimportant        AVID strategies,             buddies), tiered activities,
communicate the reasoning       mathematical stuff?                                                                  information                 Foldables, Horizontal        stations, compacting, agendas,
used to solve problems.         What's your problem?                                                                                             planning internet.           complex instructions orbital
studies, Entry points, Problem
based learning, choice boards,
4mat . Website: ASCD Express

7E.3 Choose and apply a                                                                  Problem solving         CHOOSE FROM:           McREL      McREL:                      CHOOSE FROM: Graphic         CHOOSE FROM THE
strategy to solve                                                                        strategies              Oral, performance-                Graphic organizers          organizers, text books,      FOLLOWING LIST: Whole
mathematical and real-                                                                                           based, written                                                Mastery Math materials (Al   group, Small group, one-on-
world problems                                                                                                   (pen/pencil, paper,                                           Ludwig) , Algebra pizzazz,   one, Cooperative learning,
journal, report,)                                             States released items,       Peer mentoring (Learning
It is essential to be able to                                                      portfolio, projects,                                          AVID strategies,             buddies), tiered activities,
communicate the reasoning       What's in your toolbox?                                                                                          Foldables, Horizontal        stations, compacting, agendas,
used to solve problems.                                                                                                                          planning internet.           complex instructions orbital
studies, Entry points, Problem
based learning, choice boards,
4mat . Website: ASCD Express

Revision 4-26-2006/jkw                                                                                                                                                                                                                  20
FOR TEACHERS BY TEACHERS
MATH CURRICULUM GUIDE

STANDARD 7: Students communicate the reasoning used in problem-solving situations

Benchmark E: Communicate the use of appropriate measurement techniques needed to solve problems and report the degree of accuracy required.

State Frameworks           Enduring Understanding          Essential Questions              Essential Skills        Assessment          Key          Suggested Instructional              Resources                   Differentiation            Quarter
Conceptual Vocabulary                                                                     Methods            Strategy           Practices                                              Adaptations/Extensions         Taught

7E.4 Evaluate the                                                                          Significant figures      CHOOSE FROM:           McREL      McREL                           CHOOSE FROM: Graphic         CHOOSE FROM THE
solutions of mathematical                                                                  Estimating               Oral, performance-                Precision & Accuracy Practice   organizers, text books,      FOLLOWING LIST: Whole
and real world problems                                                                    Mental Math              based, written                                                    Mastery Math materials (Al   group, Small group, one-on-
for reasonableness.                                                                                                 (pen/pencil, paper,                                               Ludwig) , Algebra pizzazz,   one, Cooperative learning,
journal, report,)                                                 States released items,       Peer mentoring (Learning
It is essential to be able to                                                           portfolio, projects,                                              AVID strategies,             buddies), tiered activities,
How close is close
communicate the reasoning                                                                                                                                 Foldables, Horizontal        stations, compacting, agendas,
enough?
used to solve problems.                                                                                                                                   planning internet.           complex instructions orbital
studies, Entry points, Problem
based learning, choice boards,
4mat . Website: ASCD Express

7E.5 Explain the strategy                                                                  Explain processes for    CHOOSE FROM:           McREL      McREL                           CHOOSE FROM: Graphic         CHOOSE FROM THE
used and the solution to                                                                   solutions                Oral, performance-                Practice explaining answers     organizers, text books,      FOLLOWING LIST: Whole
mathematical and real-                                                                                              based, written                    Journal writing                 Mastery Math materials (Al   group, Small group, one-on-
world problems through                                      How would you                                           (pen/pencil, paper,                                               Ludwig) , Algebra pizzazz,   one, Cooperative learning,
written and oral            Mathematics is a tool for                                                               journal, report,)                                                 States released items,       Peer mentoring (Learning
communicate the solution
communication.              communication.                                                                          portfolio, projects,                                              AVID strategies,             buddies), tiered activities,
to a problem to an alien?
It is essential to be able to                                                                                                                             Foldables, Horizontal        stations, compacting, agendas,
How can you convince a
communicate the reasoning                                                                                                                                 planning internet.           complex instructions orbital
total stranger (who dislikes
used to solve problems.                                                                                                                                                                studies, Entry points, Problem
you) that you are right?
based learning, choice boards,
4mat . Website: ASCD Express

Revision 4-26-2006/jkw                                                                                                                                                                                                                          21
FOR TEACHERS BY TEACHERS
MATH CURRICULUM GUIDE

STANDARD 6: Computation: Students link concepts and procedures as they develop and use computational techniques, including estimation, mental arithmetic, paper-and-pencil, calculators, and computers, in problem-solving
situations and communicate the reasoning involved in solving these problems.

Benchmark 6.1 Use ratios, proportions, and percents in problem-solving situations

Enduring Understanding                                                             Assessment          Key        Suggested Instructional                                        Differentiation              Quarter
State Frameworks                                             Essential Questions      Essential Skills                                                                         Resources
Conceptual Vocabulary                                                               Methods          Strategy           Practices                                            Adaptations/Extensions           Taught

6.1a Solve word                                                                       Use ratios, proportions CHOOSE FROM:          HOTS       HOTS                        CHOOSE FROM: Graphic          CHOOSE FROM THE
problems containing                                                                   and percents in applied Oral, performance-               analyzing                   organizers, text books,       FOLLOWING LIST: Whole
several rates, proportions,                                                           situations              based, written                                               State's released items,       group, small group, one-on-
or percentages                                                                                                (pen/pencil, paper,                                          AVID strategies, horizontal   one, cooperative learning,
How can you solve                                journal, report,)                                            team planning, Internet.      peer mentoring, tiered
problems involving                               portfolio, projects                                                                        activities, stations, compacting,
Rates, proportions and
percentages are related and
combined grades, or                                                                                                                         orbital studies, entry points,
have real-world applications
traveling at different                                                                                                                      problem-based learning, choice
speeds, etc.?                                                                                                                               boards, 4mat . Website: ASCD
Express

Benchmark 6.2 Select and use appropriate methods for computing with real numbers in problem-solving situations from among mental arithmetic, estimation, paper-and-pencil, calculator, and computer methods, and determining
whether the results are reasonable.
6.2a Apply appropriate                                                                Fraction Operations,    CHOOSE FROM:          HOTS       HOTS                        CHOOSE FROM: Graphic          CHOOSE FROM THE
computational methods to                                                              Inverse Operations,     Oral, performance-               application                 organizers, text books,       FOLLOWING LIST: Whole
solve multi-step problems                                                             Order of Operations     based, written                                               State's released items,       group, small group, one-on-
involving rational numbers.                                                                                   (pen/pencil, paper,                                          AVID strategies, horizontal   one, cooperative learning,
journal, report,)                                            team planning, Internet.      peer mentoring, tiered
Mathematics incorporates                                                        portfolio, projects                                                                        activities, stations, compacting,
What are the steps for
multiple problem solving                                                                                                                                                   agendas, complex instructions,
solving this problem?
strategies                                                                                                                                                                 orbital studies, entry points,
problem-based learning, choice
boards, 4mat . Website: ASCD
Express

Revision 4-26-2006/jkw                                                                                                                                                                                                                  22
FOR TEACHERS BY TEACHERS
MATH CURRICULUM GUIDE

STANDARD 7: Students communicate the reasoning used in problem-solving situations

Benchmark F: Communicate the use of appropriate computational techniques needed to solve problems and determine whether the results are reasonable.

State Frameworks            Enduring Understanding          Essential Questions         Essential Skills      Assessment          Key          Suggested Instructional          Resources                   Differentiation            Quarter
Conceptual Vocabulary                                                              Methods            Strategy           Practices                                          Adaptations/Extensions         Taught

7F.1 Students generate        Mathematics is a tool for       How is math a universal  Translating math into   CHOOSE FROM:           McREL      McREL                       CHOOSE FROM: Graphic         CHOOSE FROM THE
and solve problems of         communication.                  language?                real world situations   Oral, performance-                Summarizing--Organizing     organizers, text books,      FOLLOWING LIST: Whole
appropriate complexity                                        How would you learn math                         based, written                    information                 Mastery Math materials (Al   group, Small group, one-on-
created from real-world                                       without a math teacher?                          (pen/pencil, paper,               Problem writing             Ludwig) , Algebra pizzazz,   one, Cooperative learning,
problems.                                                                                                      journal, report,)                                             States released items,       Peer mentoring (Learning
portfolio, projects,                                          AVID strategies,             buddies), tiered activities,
Foldables, Horizontal        stations, compacting, agendas,
planning internet.           complex instructions orbital
studies, Entry points, Problem
based learning, choice boards,
4mat . Website: ASCD Express

7F.2 Identify the essential   It is essential to be able to   How do you read           Extracting important   CHOOSE FROM:           HOTS       HOTS                        CHOOSE FROM: Graphic         CHOOSE FROM THE
components of                 communicate the reasoning       mathematical stuff?       information            Oral, performance-                Knowledge                   organizers, text books,      FOLLOWING LIST: Whole
mathematical and real-        used to solve problems.         What's your problem?                             based, written                                                Mastery Math materials (Al   group, Small group, one-on-
world problems                                                                                                 (pen/pencil, paper,    SIOP       SIOP                        Ludwig) , Algebra pizzazz,   one, Cooperative learning,
journal, report,)                 Finding Main Idea           States released items,       Peer mentoring (Learning
portfolio, projects,              Deleting unimportant        AVID strategies,             buddies), tiered activities,
information                 Foldables, Horizontal        stations, compacting, agendas,
planning internet.           complex instructions orbital
studies, Entry points, Problem
based learning, choice boards,
4mat . Website: ASCD Express

7F.3 Choose and apply a       It is essential to be able to   What's in your toolbox?   Problem solving        CHOOSE FROM:           McREL      McREL:                      CHOOSE FROM: Graphic         CHOOSE FROM THE
strategy to solve             communicate the reasoning                                 strategies             Oral, performance-                Graphic organizers          organizers, text books,      FOLLOWING LIST: Whole
mathematical and real-        used to solve problems.                                                          based, written                                                Mastery Math materials (Al   group, Small group, one-on-
world problems                                                                                                 (pen/pencil, paper,                                           Ludwig) , Algebra pizzazz,   one, Cooperative learning,
journal, report,)                                             States released items,       Peer mentoring (Learning
portfolio, projects,                                          AVID strategies,             buddies), tiered activities,
Foldables, Horizontal        stations, compacting, agendas,
planning internet.           complex instructions orbital
studies, Entry points, Problem
based learning, choice boards,
4mat . Website: ASCD Express

Revision 4-26-2006/jkw                                                                                                                                                                                                                23
FOR TEACHERS BY TEACHERS
MATH CURRICULUM GUIDE

STANDARD 7: Students communicate the reasoning used in problem-solving situations

Benchmark F: Communicate the use of appropriate computational techniques needed to solve problems and determine whether the results are reasonable.

State Frameworks           Enduring Understanding           Essential Questions           Essential Skills        Assessment          Key          Suggested Instructional              Resources                   Differentiation            Quarter
Conceptual Vocabulary                                                                   Methods            Strategy           Practices                                              Adaptations/Extensions         Taught

7F.4Evaluate the solutions It is essential to be able to     How close is close          Significant figures      CHOOSE FROM:           McREL      McREL                           CHOOSE FROM: Graphic         CHOOSE FROM THE
of mathematical and real communicate the reasoning           enough?                     Estimating               Oral, performance-                Precision & Accuracy Practice   organizers, text books,      FOLLOWING LIST: Whole
world problems for         used to solve problems.                                       Mental Math              based, written                                                    Mastery Math materials (Al   group, Small group, one-on-
reasonableness.                                                                                                   (pen/pencil, paper,                                               Ludwig) , Algebra pizzazz,   one, Cooperative learning,
journal, report,)                                                 States released items,       Peer mentoring (Learning
portfolio, projects,                                              AVID strategies,             buddies), tiered activities,
Foldables, Horizontal        stations, compacting, agendas,
planning internet.           complex instructions orbital
studies, Entry points, Problem
based learning, choice boards,
4mat . Website: ASCD Express

7F.5 Explain the strategy   Mathematics is a tool for        How would you                Explain processes for   CHOOSE FROM:           McREL      McREL                           CHOOSE FROM: Graphic         CHOOSE FROM THE
used and the solution to    communication. It is essential   communicate the solution solutions                   Oral, performance-                Practice explaining answers     organizers, text books,      FOLLOWING LIST: Whole
mathematical and real-      to be able to communicate the    to a problem to an alien?                            based, written                    Journal writing                 Mastery Math materials (Al   group, Small group, one-on-
world problems through      reasoning used to solve          How can you convince a                               (pen/pencil, paper,                                               Ludwig) , Algebra pizzazz,   one, Cooperative learning,
written and oral            problems.                        total stranger (who dislikes                         journal, report,)                                                 States released items,       Peer mentoring (Learning
communication.                                               you) that you are right?                             portfolio, projects,                                              AVID strategies,             buddies), tiered activities,
Foldables, Horizontal        stations, compacting, agendas,
planning internet.           complex instructions orbital
studies, Entry points, Problem
based learning, choice boards,
4mat . Website: ASCD Express

Revision 4-26-2006/jkw                                                                                                                                                                                                                        24

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