AlgI Texas S&S Fall2015 - Agile Mind

14 Pages·2014·0.19 MB·English

Agile
 Mind
 Algebra
 I
 Scope
 and
 Sequence,
 2015-­‐2016

Texas
 Essential
 Knowledge
 and
 Skills
 for
 Mathematics

In
 the
 three
 years
 prior
 to
 Algebra
 I,
 students
 have
 already
 begun
 their
 study
 of
 algebraic
 concepts.
 They
 have
 investigated
 variables
 and
 expressions,
 solved

equations,
 constructed
 and
 analyzed
 tables,
 used
 equations
 and
 graphs
 to
 describe
 relationships
 between
 quantities,
 and
 studied
 linear
 equations
 and

systems
 of
 linear
 equations.

The
 Algebra
 I
 course
 outlined
 in
 this
 scope
 and
 sequence
 document
 begins
 with
 connections
 back
 to
 that
 earlier
 work,
 efficiently
 reviewing
 algebraic

concepts
 that
 students
 have
 already
 studied
 while
 at
 the
 same
 time
 moving
 students
 forward
 into
 the
 new
 ideas
 described
 in
 the
 high
 school
 standards.

Students
 contrast
 exponential
 and
 linear
 functions
 as
 they
 explore
 exponential
 models
 using
 the
 familiar
 tools
 of
 tables,
 graphs,
 and
 symbols.
 Finally,
 they

apply
 these
 same
 tools
 to
 a
 study
 of
 quadratic
 functions.
 Throughout,
 the
 connection
 between
 functions
 and
 equations
 is
 made
 explicit
 to
 give
 students
 more

ways
 to
 model
 and
 make
 sense
 of
 problems.

Throughout
 this
 Algebra
 I
 course,
 students
 use
 mathematical
 processes
 to
 acquire
 and
 demonstrate
 mathematical
 understanding.
 The
 student
 is
 expected
 to:

(A)

 apply
 mathematics
 to
 problems
 arising
 in
 everyday
 life,
 society,
 and
 the
  (D)

 communicate
 mathematical
 ideas,
 reasoning,
 and
 their
 implications

workplace;

  using
 multiple
 representations,
 including
 symbols,
 diagrams,
 graphs,
 and

language
 as
 appropriate;

(B)

 use
 a
 problem-­‐solving
 model
 that
 incorporates
 analyzing
 given
  (E)

 create
 and
 use
 representations
 to
 organize,
 record,
 and
 communicate

information,
 formulating
 a
 plan
 or
 strategy,
 determining
 a
 solution,
  mathematical
 ideas;

justifying
 the
 solution,
 and
 evaluating
 the
 problem-­‐solving
 process
 and
 the

(F)

 analyze
 mathematical
 relationships
 to
 connect
 and
 communicate

reasonableness
 of
 the
 solution;

mathematical
 ideas;
 and

(C)

 select
 tools,
 including
 real
 objects,
 manipulatives,
 paper
 and
 pencil,
 and
  (G)

 display,
 explain,
 and
 justify
 mathematical
 ideas
 and
 arguments
 using

technology
 as
 appropriate,
 and
 techniques,
 including
 mental
 math,
  precise
 mathematical
 language
 in
 written
 or
 oral
 communication.

estimation,
 and
 number
 sense
 as
 appropriate,
 to
 solve
 problems;

These
 processes
 should
 become
 the
 natural
 way
 in
 which
 students
 come
 to
 understand
 and
 do
 mathematics.
 While,
 depending
 on
 the
 content
 to
 be

understood
 or
 on
 the
 problem
 to
 be
 solved,
 any
 process
 might
 be
 seen
 or
 applied,
 some
 processes
 may
 prove
 more
 useful
 than
 others.
 Opportunities
 for

highlighting
 certain
 processes
 are
 indicated
 in
 different
 topics
 in
 this
 document,
 but
 this
 highlighting
 should
 not
 be
 interpreted
 to
 mean
 that
 other
 processes

are
 absent
 from
 those
 topics.

Copyright
 2014
 Agile
 Mind,
 Inc.
 ®
  Page
 1
 of
 14

The
 Charles
 A.
 Dana
 Center
 at
 The
 University
 of
 Texas
 at
 Austin

  July
 11,
 2014
Agile
 Mind
 Algebra
 I
 Scope
 and
 Sequence,
 2015-­‐2016

Texas
 Essential
 Knowledge
 and
 Skills
 for
 Mathematics

Agile
 Mind
 Topics
  Time
  Topic
 Descriptions
  Texas
 Essential
 Knowledge
 and
 Skills
 for
 Mathematics

allotment

(1
 block
 =

45

minutes)

Representing
 relationships
 mathematically

(2)
 Linear
 functions,
 equations,
 and
 inequalities.

 The
 student

1:
 Constructing
 graphs
  4
 blocks
  This
 topic
 introduces
 the
 principles
 for
 creating
 neutral,

applies
 mathematical
 process
 standards
 when
 using
 properties
 of

well-­‐designed
 graphs.
 Choosing
 appropriate
 values
 for

linear
 functions
 to
 write
 and
 represent
 in
 multiple
 ways,
 with
 and

both
 axes
 to
 present
 meaningful
 displays
 of
 data
 is

without
 technology,
 linear
 equations,
 inequalities,
 and
 systems
 of

highlighted.
 Students
 also
 review
 the
 distinction
 between

equations.

 The
 student
 is
 expected
 to:

independent
 and
 dependent
 variables
 in
 a
 functional

relationship,
 learn
 conventions
 related
 to
 this
 distinction,
  (A)

 determine
 the
 domain
 and
 range
 of
 a
 linear
 function
 in

and
 are
 formally
 introduced
 to
 the
 concept
 of
 the
  mathematical
 problems;
 determine
 reasonable
 domain
 and
 range

domain
 and
 range
 of
 a
 function.

 Students
 also
  values
 for
 real-­‐world
 situations,
 both
 continuous
 and
 discrete;
 and

distinguish
 between
 discrete
 and
 continuous
 data.
  represent
 domain
 and
 range
 using
 inequalities;

(12)
 Number
 and
 algebraic
 methods.
 The
 student
 applies
 the

mathematical
 process
 standards
 and
 algebraic
 methods
 to
 write,

solve,
 analyze,
 and
 evaluate
 equations,
 relations,
 and
 functions.

The
 student
 is
 expected
 to:
(A)

 decide
 whether
 relations
 represented
 verbally,
 tabularly,

graphically,
 and
 symbolically
 define
 a
 function;

(2)
 Linear
 functions,
 equations,
 and
 inequalities.

 The
 student

2:
 Multiple
  6
 blocks
  This
 topic
 connects
 the
 various
 representations
 of
 a

applies
 mathematical
 process
 standards
 when
 using
 properties
 of

representations
 in
 the
  problem—words,
 concrete
 elements,
 numbers,
 graphs,

linear
 functions
 to
 write
 and
 represent
 in
 multiple
 ways,
 with
 and

real
 world
  and
 algebraic
 expression-­‐-­‐as
 students
 explore
 linear

without
 technology,
 linear
 equations,
 inequalities,
 and
 systems
 of

relationships.
 Students
 also
 learn
 how
 the
 same
 situation

equations.

 The
 student
 is
 expected
 to:

can
 be
 represented
 by
 different
 but
 equivalent
 algebraic

expressions.
  (A)

 determine
 the
 domain
 and
 range
 of
 a
 linear
 function
 in

mathematical
 problems;
 determine
 reasonable
 domain
 and
 range

values
 for
 real-­‐world
 situations,
 both
 continuous
 and
 discrete;
 and

represent
 domain
 and
 range
 using
 inequalities;

(12)
 Number
 and
 algebraic
 methods.
 The
 student
 applies
 the

mathematical
 process
 standards
 and
 algebraic
 methods
 to
 write,

solve,
 analyze,
 and
 evaluate
 equations,
 relations,
 and
 functions.

The
 student
 is
 expected
 to:
Copyright
 2014
 Agile
 Mind,
 Inc.
 ®
  Page
 2
 of
 14

The
 Charles
 A.
 Dana
 Center
 at
 The
 University
 of
 Texas
 at
 Austin

  July
 11,
 2014
Agile
 Mind
 Algebra
 I
 Scope
 and
 Sequence,
 2015-­‐2016

Texas
 Essential
 Knowledge
 and
 Skills
 for
 Mathematics

(A)

 decide
 whether
 relations
 represented
 verbally,
 tabularly,

graphically,
 and
 symbolically
 define
 a
 function;

Understanding
 functions

(2)
 Linear
 functions,
 equations,
 and
 inequalities.

 The
 student

3:
 Functions
  9
 blocks
  This
 topic
 solidifies
 students'
 understanding
 of
 the

applies
 mathematical
 process
 standards
 when
 using
 properties
 of

concept
 of
 a
 function
 and
 introduces
 formal
 function

linear
 functions
 to
 write
 and
 represent
 in
 multiple
 ways,
 with
 and

notation.

 Students
 connect
 previous
 work
 with

without
 technology,
 linear
 equations,
 inequalities,
 and
 systems
 of

sequences
 to
 the
 concept
 of
 a
 function.

equations.

 The
 student
 is
 expected
 to:

(A)

 determine
 the
 domain
 and
 range
 of
 a
 linear
 function
 in

mathematical
 problems;
 determine
 reasonable
 domain
 and
 range

values
 for
 real-­‐world
 situations,
 both
 continuous
 and
 discrete;
 and

represent
 domain
 and
 range
 using
 inequalities;

(12)
 Number
 and
 algebraic
 methods. The
 student
 applies
 the

mathematical
 process
 standards
 and
 algebraic
 methods
 to
 write,

solve,
 analyze,
 and
 evaluate
 equations,
 relations,
 and
 functions.

The
 student
 is
 expected
 to:
(A)

 decide
 whether
 relations
 represented
 verbally,
 tabularly,

graphically,
 and
 symbolically
 define
 a
 function;

(B)

 evaluate
 functions,
 expressed
 in
 function
 notation,
 given
 one

or
 more
 elements
 in
 their
 domains;

Copyright
 2014
 Agile
 Mind,
 Inc.
 ®
  Page
 3
 of
 14

The
 Charles
 A.
 Dana
 Center
 at
 The
 University
 of
 Texas
 at
 Austin

  July
 11,
 2014
Agile
 Mind
 Algebra
 I
 Scope
 and
 Sequence,
 2015-­‐2016

Texas
 Essential
 Knowledge
 and
 Skills
 for
 Mathematics

(3)

 Linear
 functions,
 equations,
 and
 inequalities.
 The
 student
 applies

4:
 Exploring
 rate
 of
  7
 blocks
  Understanding
 the
 rate
 at
 which
 one
 quantity

the
 mathematical
 process
 standards
 when
 using
 graphs
 of
 linear

change
 in
 motion
  changes
 with
 respect
 to
 another
 is
 key
 to

functions,
 key
 features,
 and
 related
 transformations
 to
 represent
 in

problems
  understanding
 how
 the
 two
 quantities
 are
 related.
 In

multiple
 ways
 and
 solve,
 with
 and
 without
 technology,
 equations,

this
 topic,
 students
 explore
 the
 concept
 of
 rate
 by

inequalities,
 and
 systems
 of
 equations.
 The
 student
 is
 expected
 to:

analyzing
 motion
 over
 time.
 Students
 investigate
 the

rate
 at
 which
 distance
 changes
 numerically
 and
  (B)

 calculate
 the
 rate
 of
 change
 of
 a
 linear
 function
 represented

graphically.
  tabularly,
 graphically,
 or
 algebraically
 in
 context
 of
 mathematical
 and

real-­‐world
 problems;

(2)
 Linear
 functions,
 equations,
 and
 inequalities.

 The
 student
 applies

5:
 Exploring
 rate
 of
  7
 blocks
  This
 topic
 deepens
 student
 understanding
 of
 the

mathematical
 process
 standards
 when
 using
 properties
 of
 linear

change
 in
 other
  central
 ideas
 of
 rate
 of
 change.
 Students
 discover

functions
 to
 write
 and
 represent
 in
 multiple
 ways,
 with
 and
 without

situations
  that
 they
 can
 model
 data
 sets
 that
 have
 a
 constant

technology,
 linear
 equations,
 inequalities,
 and
 systems
 of
 equations.

rate
 of
 change
 with
 a
 linear
 function.
 Students
 also

The
 student
 is
 expected
 to:

learn
 that
 not
 all
 data
 are
 linear,
 and
 thus
 require

other
 models.
  (D)

 write
 and
 solve
 equations
 involving
 direct
 variation;

(3)

 Linear
 functions,
 equations,
 and
 inequalities.
 The
 student
 applies

the
 mathematical
 process
 standards
 when
 using
 graphs
 of
 linear

functions,
 key
 features,
 and
 related
 transformations
 to
 represent
 in

multiple
 ways
 and
 solve,
 with
 and
 without
 technology,
 equations,

inequalities,
 and
 systems
 of
 equations.
 The
 student
 is
 expected
 to:

(B)
 calculate
 the
 rate
 of
 change
 of
 a
 linear
 function
 represented

tabularly,
 graphically,
 or
 algebraically
 in
 context
 of
 mathematical
 and

real-­‐world
 problems;

Copyright
 2014
 Agile
 Mind,
 Inc.
 ®
  Page
 4
 of
 14

The
 Charles
 A.
 Dana
 Center
 at
 The
 University
 of
 Texas
 at
 Austin

  July
 11,
 2014
Agile
 Mind
 Algebra
 I
 Scope
 and
 Sequence,
 2015-­‐2016

Texas
 Essential
 Knowledge
 and
 Skills
 for
 Mathematics

Linear
 functions,
 equations,
 and
 inequalities

(2)

 Linear
 functions,
 equations,
 and
 inequalities.The
 student
 applies

6:
 Moving
 beyond
  7
 blocks
  This
 topic
 builds
 on
 student
 understanding
 of
 slope

the
 mathematical
 process
 standards
 when
 using
 properties
 of
 linear

slope-­‐intercept
  and
 y-­‐intercept
 of
 a
 linear
 function,.
 Students

functions
 to
 write
 and
 represent
 in
 multiple
 ways,
 with
 and
 without

investigate
 the
 effect
 of
 m
 and
 b
 on
 the
 graph
 of
 a

technology,
 linear
 equations,
 inequalities,
 and
 systems
 of
 equations.

linear
 function
 in
 the
 form
 y
 =
 mx
 +
 b.
 They
 also

The
 student
 is
 expected
 to:

learn
 about
 the
 x-­‐intercept
 and
 linear
 equations
 of

the
 form
 x
 =
 c.
 Students
 develop
 and
 apply
 the
  (A)
 determine
 the
 domain
 and
 range
 of
 a
 linear
 function
 in

standard
 and
 point-­‐slope
 forms
 for
 the
 equation
 of
 a
  mathematical
 problems;
 determine
 reasonable
 domain
 and
 range

line.
  values
 for
 real-­‐world
 situations,
 both
 continuous
 and
 discrete;
 and

represent
 domain
 and
 range
 using
 inequalities;
(B)
 write
 linear
 equations
 in
 two
 variables
 in
 various
 forms,
 including
 y

=
 mx
 +
 b,
 Ax
 +
 By
 =
 C,
 and
 y
 -­‐
 y1
 =
 m(x
 -­‐
 x1),
 given
 one
 point
 and
 the

slope
 and
 given
 two
 points;

(C)
 write
 linear
 equations
 in
 two
 variables
 given
 a
 table
 of
 values,
 a

graph,
 and
 a
 verbal
 description;

(E)
 write
 the
 equation
 of
 a
 line
 that
 contains
 a
 given
 point
 and
 is

parallel
 to
 a
 given
 line;

(F)

 write
 the
 equation
 of
 a
 line
 that
 contains
 a
 given
 point
 and
 is

perpendicular
 to
 a
 given
 line;

(G)

 write
 an
 equation
 of
 a
 line
 that
 is
 parallel
 or
 perpendicular
 to
 the
 X

or
 Y
 axis
 and
 determine
 whether
 the
 slope
 of
 the
 line
 is
 zero
 or

undefined;

(3)

 Linear
 functions,
 equations,
 and
 inequalities.The
 student
 applies

the
 mathematical
 process
 standards
 when
 using
 graphs
 of
 linear

functions,
 key
 features,
 and
 related
 transformations
 to
 represent
 in

multiple
 ways
 and
 solve,
 with
 and
 without
 technology,
 equations,

inequalities,
 and
 systems
 of
 equations.
 The
 student
 is
 expected
 to:

(A)

 determine
 the
 slope
 of
 a
 line
 given
 a
 table
 of
 values,
 a
 graph,
 two

points
 on
 the
 line,
 and
 an
 equation
 written
 in
 various
 forms,
 including
 y

=
 mx
 +
 b,
 Ax
 +
 By
 =
 C,
 and
 y
 -­‐
 y
 =
 m(x
 -­‐
 x );

1 1
(B)

 calculate
 the
 rate
 of
 change
 of
 a
 linear
 function
 represented

tabularly,
 graphically,
 or
 algebraically
 in
 context
 of
 mathematical
 and

real-­‐world
 problems;

(C)

 graph
 linear
 functions
 on
 the
 coordinate
 plane
 and
 identify
 key

features,
 including
 x-­‐
 intercept,
 y-­‐intercept,
 zeros,
 and
 slope,
 in

Copyright
 2014
 Agile
 Mind,
 Inc.
 ®
  Page
 5
 of
 14

The
 Charles
 A.
 Dana
 Center
 at
 The
 University
 of
 Texas
 at
 Austin

  July
 11,
 2014
Agile
 Mind
 Algebra
 I
 Scope
 and
 Sequence,
 2015-­‐2016

Texas
 Essential
 Knowledge
 and
 Skills
 for
 Mathematics

mathematical
 and
 real-­‐world
 problems;

(E)

 determine
 the
 effects
 on
 the
 graph
 of
 the
 parent
 function
 f(x)
 =
 x

when
 f(x)
 is
 replaced
 by

 af(x),
 f(x)
 +
 d,
 f(x
 -­‐
 c),
 f(bx)
 for
 specific
 values
 of

a,
 b,
 c,
 and
 d;

(2)

 Linear
 functions,
 equations,
 and
 inequalities.
 The
 student
 applies

7:
 Creating
 linear
  8
 blocks
  This
 topic
 revisits
 analyzing
 rate
 of
 change
 to

the
 mathematical
 process
 standards
 when
 using
 properties
 of
 linear

models
 for
 data
  determine
 whether
 using
 a
 linear
 model
 to
 represent

functions
 to
 write
 and
 represent
 in
 multiple
 ways,
 with
 and
 without

data
 is
 appropriate.
 It
 also
 introduces
 the
 use
 of

technology,
 linear
 equations,
 inequalities,
 and
 systems
 of
 equations.

residuals
 to
 informally
 assess
 the
 fit
 of
 a
 linear

The
 student
 is
 expected
 to:

function.
 Students
 learn
 that
 correlation
 does
 not

imply
 causation.
 They
 also
 explore
 transformations
  (B)
 write
 linear
 equations
 in
 two
 variables
 in
 various
 forms,
 including
 y

of
 functions
 by
 transforming
 the
 parent
 function
 y
 =
  =
 mx
 +
 b,
 Ax
 +
 By
 =
 C,
 and
 y
 -­‐
 y1
 =
 m(x
 -­‐
 x1),
 given
 one
 point
 and
 the

x
 to
 create
 linear
 models
 for
 data.
  slope
 and
 given
 two
 points;

(C)

 write
 linear
 equations
 in
 two
 variables
 given
 a
 table
 of
 values,
 a

graph,
 and
 a
 verbal
 description;

(3)

 Linear
 functions,
 equations,
 and
 inequalities.
 The
 student
 applies

the
 mathematical
 process
 standards
 when
 using
 graphs
 of
 linear

functions,
 key
 features,
 and
 related
 transformations
 to
 represent
 in

multiple
 ways
 and
 solve,
 with
 and
 without
 technology,
 equations,

inequalities,
 and
 systems
 of
 equations.
 The
 student
 is
 expected
 to:

(A)

 determine
 the
 slope
 of
 a
 line
 given
 a
 table
 of
 values,
 a
 graph,
 two

points
 on
 the
 line,
 and
 an
 equation
 written
 in
 various
 forms,
 including
 y

=
 mx
 +
 b,
 Ax
 +
 By
 =
 C,
 and
 y
 -­‐
 y
 =
 m(x
 -­‐
 x );

1 1
(B)

 calculate
 the
 rate
 of
 change
 of
 a
 linear
 function
 represented

tabularly,
 graphically,
 or
 algebraically
 in
 context
 of
 mathematical

and
 real-­‐world
 problems;

(C)

 graph
 linear
 functions
 on
 the
 coordinate
 plane
 and
 identify
 key

features,
 including
 x-­‐
 intercept,
 y-­‐intercept,
 zeros,
 and
 slope,
 in

mathematical
 and
 real-­‐world
 problems;

(E)

 determine
 the
 effects
 on
 the
 graph
 of
 the
 parent
 function
 f(x)
 =
 x

when
 f(x)
 is
 replaced
 by
 af(x),
 f(x)
 +
 d,
 f(x
 -­‐
 c),
 f(bx)
 for
 specific
 values
 of

a,
 b,
 c,
 and
 d;

(4)
 Linear
 functions,
 equations,
 and
 inequalities.

The
 student
 applies
 the
 mathematical
 process
 standards
 to
 formulate

statistical
 relationships
 and
 evaluate
 their
 reasonableness
 based
 on

real-­‐
 world
 data.
 The
 student
 is
 expected
 to:

Copyright
 2014
 Agile
 Mind,
 Inc.
 ®
  Page
 6
 of
 14

The
 Charles
 A.
 Dana
 Center
 at
 The
 University
 of
 Texas
 at
 Austin

  July
 11,
 2014
Agile
 Mind
 Algebra
 I
 Scope
 and
 Sequence,
 2015-­‐2016

Texas
 Essential
 Knowledge
 and
 Skills
 for
 Mathematics

(A)

 calculate,
 using
 technology,
 the
 correlation
 coefficient
 between

two
 quantitative
 variables
 and
 interpret
 this
 quantity
 as
 a
 measure
 of

the
 strength
 of
 the
 linear
 association;

(B)

 compare
 and
 contrast
 association
 and
 causation
 in
 real-­‐world

problems;
 and

(C)

 write,
 with
 and
 without
 technology,
 linear
 functions
 that
 provide
 a

reasonable
 fit
 to
 data
 to
 estimate
 solutions
 and
 make
 predictions
 for

real-­‐world
 problems.

 (2)

 Linear
 functions,
 equations,
 and
 inequalities.

8:
 Solving
 linear
  7
 blocks
  In
 this
 topic,
 students
 leverage
 the
 connections

The
 student
 applies
 the
 mathematical
 process
 standards
 when
 using

equations
 and
  among
 linear
 functions,

 linear
 equations,
 and
 linear

properties
 of
 linear
 functions
 to
 write
 and
 represent
 in
 multiple
 ways,

inequalities
  inequalities
 as
 they
 create
 and
 solve
 equations
 and

with
 and
 without
 technology,
 linear
 equations,
 inequalities,
 and

inequalities.

 They
 solidify
 and
 extend
 their

systems
 of
 equations.
 The
 student
 is
 expected
 to:

understanding
 of
 solution
 techniques
 for
 single-­‐
variable
 equations
 and
 inequalities,
 and
 they
 learn
  (C)

 write
 linear
 equations
 in
 two
 variables
 given
 a
 table
 of
 values,
 a

how
 to
 graphically
 represent
 solutions
 to
 linear
  graph,
 and
 a
 verbal
 description;

inequalities
 in
 two
 variables.

(H)

 write
 linear
 inequalities
 in
 two
 variables
 given
 a
 table
 of
 values,
 a

graph,
 and
 a
 verbal
 description;

(3)

 Linear
 functions,
 equations,
 and
 inequalities.

The
 student
 applies
 the
 mathematical
 process
 standards
 when
 using

graphs
 of
 linear
 functions,
 key
 features,
 and
 related
 transformations
 to

represent
 in
 multiple
 ways
 and
 solve,
 with
 and
 without
 technology,

equations,
 inequalities,
 and
 systems
 of
 equations.
 The
 student
 is

expected
 to:

(D)

 graph
 the
 solution
 set
 of
 linear
 inequalities
 in
 two
 variables
 on
 the

coordinate
 plane;

(5)
 Linear
 functions,
 equations,
 and
 inequalities.
 The
 student
 applies

the
 mathematical
 process
 standards
 to
 solve,
 with
 and
 without

technology,
 linear
 equations
 and
 evaluate
 the
 reasonableness
 of
 their

solutions.
 The
 student
 is
 expected
 to:

(A)

 solve
 linear
 equations
 in
 one
 variable,
 including
 those
 for
 which
 the

application
 of
 the
 distributive
 property
 is
 necessary
 and
 for
 which

variables
 are
 included
 on
 both
 sides;

(B)

 solve
 linear
 inequalities
 in
 one
 variable,
 including
 those
 for
 which

the
 application
 of
 the
 distributive
 property
 is
 necessary
 and
 for
 which

variables
 are
 included
 on
 both
 sides;

Copyright
 2014
 Agile
 Mind,
 Inc.
 ®
  Page
 7
 of
 14

The
 Charles
 A.
 Dana
 Center
 at
 The
 University
 of
 Texas
 at
 Austin

  July
 11,
 2014
Agile
 Mind
 Algebra
 I
 Scope
 and
 Sequence,
 2015-­‐2016

Texas
 Essential
 Knowledge
 and
 Skills
 for
 Mathematics

(12)
 Number
 and
 algebraic
 methods.
 The
 student
 applies
 the

mathematical
 process
 standards
 and
 algebraic
 methods
 to
 write,
 solve,

analyze,
 and
 evaluate
 equations,
 relations,
 and
 functions.
 The
 student

is
 expected
 to:

(E)

 solve
 mathematic
 and
 scientific
 formulas,
 and
 other
 literal

equations,
 for
 a
 specified
 variable.

Copyright
 2014
 Agile
 Mind,
 Inc.
 ®
  Page
 8
 of
 14

The
 Charles
 A.
 Dana
 Center
 at
 The
 University
 of
 Texas
 at
 Austin

  July
 11,
 2014
Agile
 Mind
 Algebra
 I
 Scope
 and
 Sequence,
 2015-­‐2016

Texas
 Essential
 Knowledge
 and
 Skills
 for
 Mathematics

Systems
 of
 linear
 equations
 and
 inequalities

(2)

 Linear
 functions,
 equations,
 and
 inequalities.
 The
 student
 applies

9:
 Systems
 of
 linear
  6
 blocks
  This
 topic
 builds
 on
 students'
 previous
 experiences

the
 mathematical
 process
 standards
 when
 using
 properties
 of
 linear

equations
 and
  with
 systems
 of
 linear
 equations
 and
 inequalities,
 in

functions
 to
 write
 and
 represent
 in
 multiple
 ways,
 with
 and
 without

inequalities
  which
 two
 conditions
 apply
 to
 a
 situation.
 Students

technology,
 linear
 equations,
 inequalities,
 and
 systems
 of
 equations.

review
 how
 to
 set
 up
 a
 system
 of
 linear
 equations,

The
 student
 is
 expected
 to:

solve
 it
 using
 graphs
 and
 tables,
 and
 check
 the

solution
 for
 reasonableness.
 Students
 also
 learn
 how
  (I)

 write
 systems
 of
 two
 linear
 equations
 given
 a
 table
 of
 values,
 a

to
 set
 up
 a
 system
 of
 linear
 inequalities
 and
 solve
 it
  graph,
 and
 a
 verbal
 description.

by
 graphing.

(3)

 Linear
 functions,
 equations,
 and
 inequalities.
 The
 student
 applies

the
 mathematical
 process
 standards
 when
 using
 graphs
 of
 linear

functions,
 key
 features,
 and
 related
 transformations
 to
 represent
 in

multiple
 ways
 and
 solve,
 with
 and
 without
 technology,
 equations,

inequalities,
 and
 systems
 of
 equations.
 The
 student
 is
 expected
 to:

(F)

 graph
 systems
 of
 two
 linear
 equations
 in
 two
 variables
 on
 the

coordinate
 plane
 and

 determine
 the
 solutions
 if
 they
 exist;

(G)

 estimate
 graphically
 the
 solutions
 to
 systems
 of
 two
 linear

equations
 with
 two
 variables
 in
 real-­‐world
 problems;
 and

(H)

 graph
 the
 solution
 set
 of
 systems
 of
 two
 linear
 inequalities
 in
 two

variables
 on
 the
 coordinate
 plane.

(5)
 Linear
 functions,
 equations,
 and
 inequalities. The
 student
 applies

the
 mathematical
 process
 standards
 to
 solve,
 with
 and
 without

technology,
 linear
 equations
 and
 evaluate
 the
 reasonableness
 of
 their

solutions.
 The
 student
 is
 expected
 to:
(C)

 solve
 systems
 of
 two
 linear
 equations
 with
 two
 variables
 for

mathematical
 and
 real-­‐world
 problems.

(2)

 Linear
 functions,
 equations,
 and
 inequalities.
 The
 student
 applies

10:
 Other
 methods
 for
  7
 blocks
  Continuing
 with
 the
 exploration
 of
 systems
 of
 two

the
 mathematical
 process
 standards
 when
 using
 properties
 of
 linear

solving
 systems
  linear
 equations,
 this
 topic
 addresses
 two
 algebraic

functions
 to
 write
 and
 represent
 in
 multiple
 ways,
 with
 and
 without

methods
 for
 solving
 systems:
 the
 substitution

technology,
 linear
 equations,
 inequalities,
 and
 systems
 of
 equations.

method
 and
 the
 linear
 combination
 method.

The
 student
 is
 expected
 to:

(I)

 write
 systems
 of
 two
 linear
 equations
 given
 a
 table
 of
 values,
 a

graph,
 and
 a
 verbal
 description.

(3)

 Linear
 functions,
 equations,
 and
 inequalities.
 The
 student
 applies

the
 mathematical
 process
 standards
 when
 using
 graphs
 of
 linear

functions,
 key
 features,
 and
 related
 transformations
 to
 represent
 in

multiple
 ways
 and
 solve,
 with
 and
 without
 technology,
 equations,

Copyright
 2014
 Agile
 Mind,
 Inc.
 ®
  Page
 9
 of
 14

The
 Charles
 A.
 Dana
 Center
 at
 The
 University
 of
 Texas
 at
 Austin

  July
 11,
 2014
Agile
 Mind
 Algebra
 I
 Scope
 and
 Sequence,
 2015-­‐2016

Texas
 Essential
 Knowledge
 and
 Skills
 for
 Mathematics

inequalities,
 and
 systems
 of
 equations.
 The
 student
 is
 expected
 to:

(F)

 graph
 systems
 of
 two
 linear
 equations
 in
 two
 variables
 on
 the

coordinate
 plane
 and

 determine
 the
 solutions
 if
 they
 exist;

(G)

 estimate
 graphically
 the
 solutions
 to
 systems
 of
 two
 linear

equations
 with
 two
 variables
 in
 real-­‐world
 problems;
 and

 (5)
 Linear
 functions,
 equations,
 and
 inequalities. The
 student
 applies

the
 mathematical
 process
 standards
 to
 solve,
 with
 and
 without

technology,
 linear
 equations
 and
 evaluate
 the
 reasonableness
 of
 their

solutions.
 The
 student
 is
 expected
 to:
(C)

 solve
 systems
 of
 two
 linear
 equations
 with
 two
 variables
 for

mathematical
 and
 real-­‐world
 problems.

Relationships
 that
 are
 not
 linear

11:
 Laws
 of
 exponents
  6
 blocks
  This
 topic
 is
 a
 refresher
 on
 laws
 of
 exponents.
 It
  (11)
 Number
 and
 algebraic
 methods. The
 student
 applies
 the

mathematical
 process
 standards
 and
 algebraic
 methods
 to
 rewrite

reviews
 principles
 for
 multiplying
 and
 dividing

exponential
 expressions
 with
 common
 bases.
 It
 also
  algebraic
 expressions
 into
 equivalent
 forms.
 The
 student
 is
 expected
 to:
(B)

 simplify
 numeric
 and
 algebraic
 expressions
 using
 the
 laws
 of

uses
 explorations
 of
 number
 patterns
 to
 develop
 the

meanings
 of
 positive
 and
 negative
 exponents,
 as
 well
  exponents,
 including
 integral
 and
 rational
 exponents.
as
 zero
 as
 an
 exponent.
 The
 topic
 also
 introduces

students
 to
 fractional
 exponents.

(6)
 Quadratic
 functions
 and
 equations.
 The
 student
 applies
 the

12:
 Nonlinear
  9
 blocks
  As
 a
 prelude
 to
 students'
 study
 of
 exponential
 and

mathematical
 process
 standards
 when
 using
 properties
 of
 quadratic

relationships
  quadratic
 functions,
 this
 topic
 introduces
 nonlinear

functions
 to
 write
 and
 represent
 in
 multiple
 ways,
 with
 and
 without

relationships
 between
 two
 quantities—specifically,

technology,
 quadratic
 equations.
 The
 student
 is
 expected
 to:

quadratic
 and
 exponential
 relationships.

(A)
 determine
 the
 domain
 and
 range
 of
 quadratic
 functions
 and

represent
 the
 domain
 and
 range
 using
 inequalities;

(9)
 Exponential
 functions
 and
 equations.
 The
 student
 applies
 the

mathematical
 process
 standards
 when
 using
 properties
 of
 exponential

functions
 and
 their
 related
 transformations
 to
 write,
 graph,
 and

represent
 in
 multiple
 ways
 exponential
 equations
 and
 evaluate,
 with

and
 without
 technology,
 the
 reasonableness
 of
 their
 solutions.
 The

student
 formulates
 statistical
 relationships
 and
 evaluates
 their

reasonableness
 based
 on
 real-­‐world
 data.
 The
 student
 is
 expected
 to:

(A)

 determine
 the
 domain
 and
 range
 of
 exponential
 functions
 of
 the

form
 f(x)
 =
 abx
 and
 represent
 the
 domain
 and
 range
 using
 inequalities;

Copyright
 2014
 Agile
 Mind,
 Inc.
 ®
  Page
 10
 of
 14

The
 Charles
 A.
 Dana
 Center
 at
 The
 University
 of
 Texas
 at
 Austin

  July
 11,
 2014