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```					                                                                         LAS CRUCES PUBLIC SCHOOLS

Mathematics
Italicized standards represent content that is being reinforced or previewed

August/Sept           October          November        December           January             February              March           April      NM SBA         May
Expectations
Strand: Number and Operations
Standard: Students will understand numerical concepts and mathematical operations
Exhibit an           Demonstrate an                                                           Add and            Use visual                    Understand
understanding of     understanding      Choose                          Extend the uses       subtract           models and other              numbers, ways
the place-value      of and the         computational                   of whole numbers      fractions with     strategies to                 of representing
structure of the     ability to use:    methods based                   to the addition       common and         recognize and                 numbers,
base-ten number      (a) standard       on                              and subtraction of    uncommon           generate                      relationships
system by            algorithms for     understanding                   simple decimals       denominators       equivalents of                among
reading,             the addition and   the base-ten                    (positive numbers     using a variety    commonly used                 numbers, and
modeling, writing,   subtraction of     number system,                  to two places).       of strategies to   fractions and                 number
and interpreting     multi-digit        properties of                                         (a) recognize      mixed numbers                 systems.
whole numbers up     numbers, and       multiplication                  Use strategies to     and generate       (halves, thirds,
to 100,000; to       (b) standard       and division,                   estimate              equivalent         fourths, sixths,              Understand the
compare and          algorithms for     and number                      computations          decimal forms      eighths, tenths               meaning of
order the numbers    multiplication     relationships.                  involving fractions   of commonly                                      operations and
by; (a)              and division of                                    and decimals.         used fractions                                   how they relate
recognizing          multi-digit                                                              (b) identify the   Identify fractions            to one another.
equivalent           numbers by                                                               numbers less       as parts of unit
representations      one-digit                                                                than zero by       wholes, as parts              Compute
for the same         number (year                                                             extending the      of groups, and as             fluently and
number and           long).                                                                   number line and    locations on                  make
generating them                                                                               using negative     number lines by;              reasonable
by decomposing       Solve simple                                                             numbers            (a) using visual              estimates.
and combining        multiplication                                                           through familiar   models and other
numbers and (b)      and division                                                             applications       strategies to
identifying the      problems                                                                 (e.g.,             compare and
numbers less than                                                                             temperature,       order commonly
0 by extending the   Identify and use                                                         money)             used fractions, (b)
number line and      the relationship                                                                            using models to
using negative       between                                                                                     show how whole
numbers through      multiplication      numbers and
familiar             and division to     decimals (to the
applications         solve problems.     hundredths place)
relate to simple
Recognize            Demonstrate         fractions, (c) )
classes of           the concept of      identifying
numbers and          distributivity of   different
apply these          multiplication      interpretations of
concepts in          over addition       fractions that
problem-solving      and subtraction     include (i) division
situations. (year    (year long)         of whole numbers
long)                                    by whole
numbers, (ii)
Select and use       Demonstrate         ratio. (iii)
appropriate          multiplication      equivalence (iv)
operations           combinations        ordering of
including addition   through 12 x 12     fractions, and (v)
and subtraction to   and related         parts of a whole
solve problems.      division facts,     or parts of a set
(year long)          and use them to     (year long).
solve problems
Demonstrate          mentally and        Extend the uses
commutative,         compute related     of whole numbers
associative,         problems. (year     to the addition
identity, and zero   long)               and subtraction of
properties of                            simple decimals
Use a variety of    (positive numbers
operations on
models to show      to two places).
whole numbers        an
(year long)          understanding       Use strategies to
of multiplication   estimate
and division of     computations
Add and subtract    whole numbers       involving fractions
up to two triple                         and decimals.
digits numbers       Choose
accurately and       computational
efficiently. (year   methods based
long).               on
understanding
Demonstrate an       the base-ten
understanding of     number system,
and the ability to   properties of
use: (a) standard     multiplication
algorithms for the    and division,
subtraction of        relationships.
multi-digit
numbers. (year
long)

Use a variety of
strategies (e.g.,
rounding and
regrouping) to
estimate the
results of whole
number
computations and
judge the
reasonableness of
(year long)

Students should be able to add and subtract mentally numbers 0-20 and know multiplication facts to 12 x 12. Resources: Mad Minutes, Multiplication Charts, Frequent Practice,
Flash Masters, District Website for Homework, Software on School Servers, and other resources available at individual school sites.
Strand: Algebra
Standard: Students will understand algebraic concepts and applications.

Use and interpret     Determine the      Model problem                                                                                       Understand
variables,            value of           situations with                                                                                    patterns,
mathematical          variables in       objects and use                                                                                    relations, and
symbols, and          missing part       representation                                                                                     functions.
properties to write   problems           such as
and simplify                             pictures,                                                                                          Represent and
expressions and       Represent          graphs, tables,                                                                                    analyze
sentences by (a)      simple             and equations                                                                                      mathematical
using letters,        functional         to draw                                                                                            situations and
boxes, or other       relationships by   conclusions                                                                                        structures using
symbols to stand      (a) solving        .                                                                                                  algebraic
for any number in     simple                                                                                                                symbols.
simple                problems           Represent
expressions or        involving a        simple                                                                                             Use
equations (e.g.,      functional          functional          mathematical
demonstrate the       relationship        relationships;      models to
concept of a          between two         (a) solve simple    represent and
variable), (b)        quantities, and     problems            understand
interpret and         (b) extending       involving a         quantitative
evaluate              and recognizing     functional          relationships.
mathematical          a linear pattern    relationship
expressions using     by its rules.       between two         Analyze change
parentheses, and                          quantities,(b)      in various
(c) use and           Develop simple      extend and          contexts.
interpret formulas    formulas in         recognize a
to (a) answer         exploring           linear pattern by
questions about       quantities and      its rules ( A
quantities and        their               form of
their relationships   relationships       graphing.
(year long).          (e.g., A = L X      Introduce with
W).                 Supplemental
Explore the uses                          Material
of properties         Use and             y=x+3)
(commutative,         interpret
distributive,         formulas (e.g.,
associative) in the   Area = Length
computation of        X Width) to
Identify symbols      quantities and
and letters that      their
represent the         relationships
concept of a
variable as an        Solve problems
unknown quantity      involving
proportional
Determine the         relationships
value of variables    including unit
in simple             pricing
equations
Describe
Express               relationships of
mathematical          quantities in the
relationships         form of
using equations.      mathematical
(year long)           expressions,
equations, or
Demonstrate how inequalities.
change in one
variable can relate
to change in a
second variable
(e.g., input-output
machines, data
tables). Introduce
in August with
supplemental
materials (year
long)
Strand: Geometry
Standard: Students will understand geometric concepts and applications.
Use geometric          Describe and                         Classify two-         Predict and                        Identify,          Analyze
models, such as        compare the                          dimensional           describe the                       describe, and      characteristics
number lines, and      attributes of                        shapes according      results of                         classify two-      and properties
computer               plane and solid                      to their properties   sliding, flipping,                 dimensional        of two- and
simulations to         geometric                            and develop           and turning two-                   shapes and         three-
investigate            figures to show                      definitions of        dimensional                        three-             dimensional
number                 relationships                        classes like          shapes.(Must                       dimensional        geometric
relationships (e.g.,   and solve                            triangles by; (a)     use                                figures by their   shapes and
patterns). (year       problems by (a)                      visualizing,          Supplemental                       properties.        develop
long)                  identifying,                         describing, and       Materials)                                            mathematical
describing, and                      (b) interpreting                                         Identify,          arguments
classifying                          two-dimensional       Identify,                          compare, and       about geometric
polygons, (b)                        representations of    compare, and                       analyze            relationships.
identifying lines                    three-dimensional     analyze                            attributes of
of symmetry in                       objects (year         attributes of                      two- and three-    Specify
two-                                 long)                 two- and three-                    dimensional        locations and
dimensional                                                dimensional                        shapes and         describe spatial
shapes, (c)                                                shapes and                         develop            relationships
exploring                            Identify, compare,    develop                            vocabulary to      using
attributes of                        and analyze           vocabulary to                      describe the       coordinate
quadrilaterals,                      attributes of two-    describe the                       attributes by;     geometry and
(d) identifying                      and three-            attributes by;                     (a) building,      other
right angles,                        dimensional           (a) building,                      drawing,           representational
and (e)                              shapes and            drawing,                           creating, and      systems.
identifying,                         develop               creating, and                      describing
describing, and     vocabulary to         describing          geometric           Apply
classifying         describe the          geometric           objects, (b)        transformations
common three-       attributes by; (a)    objects, (b)        identifying lines   and use
dimensional         building, drawing,    identifying lines   that are parallel   symmetry to
geometric           creating, and         that are parallel   or                  analyze
objects.            describing            or                  perpendicular,      mathematical
geometric             perpendicular,      and (c)             situations.
Use ordered         objects, (b)          and (c)             identifying and
pairs to graph,     identifying lines     identifying and     comparing           Use
locate specific     that are parallel     comparing           congruent and       visualization,
points, create      or perpendicular,     congruent and       similar figures.    spatial
path, and           and (c) identifying   similar figures.                        reasoning, and
measure             and comparing                             Classify two-       geometric
distances within    congruent and         Explore             and three-          modeling to
a coordinate        similar figures.      relationships       dimensional         solve problems.
grid system.                              involving           shapes
(year long)         Make and test         perimeter and       according to
(Will need to       conjectures about     area by; (a)        their properties
use                 geometric             measuring the       and develop
Supplemental        properties and        area of             definitions of
Materials)          relationships and     rectangular         classes like
develop logical       shapes and          triangles and
Use geometric       arguments to          using               pyramids by; (a)
models, such        justify               appropriate         visualizing,
as number           conclusions           units, (b)          describing, and
lines, arrays,                            recognizing that    making models
and computer        Describe location     area can have       of geometric
simulations to      and movement          the same            solids in terms
investigate         using common          perimeter but       of the number
number              language and          different areas     of faces, edges,
relationships       geometric             and vice versa,     and vertices ,
(e.g., patterns).   vocabulary.           and (c) using       and (b)
(year long)                               models and          interpreting two-
Use ordered pairs     formulas to         dimensional
Use geometric       to graph, locate,     solve problems      representations
models to solve     identify points,      involving           of three-
problems in         and describe          perimeter and       dimensional
other areas of      paths in the first    area of             objects (year
mathematics         quadrant of the       rectangles and      long)
(e.g., using        coordinate plane      squares
arrays as           (Must use
models of           Supplemental          Describe
multiplication or   Materials )          location and
area).                                   movement
Use a variety of     using common
methods for          language and
measuring            geometric
distances            vocabulary
between locations
on a grid. (Use
mapping
supplements)

Create and
describe
rotational designs
using language of
transformational
symmetry.

Describe a
motion or set of
motions that will
show that two
shapes are
congruent.

Develop and use
mental images of
geometric shapes
to solve problems

Describe location
and movement
using common
language and
geometric
vocabulary
Strand: Measurement
Standard: Students will understand measurement systems and applications.

Use appropriate   Demonstrate                     Find the area of    Estimate                        Develop         Understand
units and tools   understanding                   rectangles using    perimeters,                     formulas to     measurable
to estimate,      that                            appropriate tools   areas of                        determine the   attributes of
measure, and      measurements                                        rectangles,                     surface area    objects and the
solve problems    are                             Select the          triangles, and                  and volume of   units, systems,
(e.g., length,    approximations,                 appropriate type    irregular shapes                rectangular     and process of
area, weight).    investigate                     of unit for                                         solids.         measurement.
differences in                  measuring           Find the area of
Identify          units and their                 perimeter and       rectangles,                                     Apply
properties (e.g., effect on                       size of an angle.   related triangles                               appropriate
length, area,     precision, and                                      and                                             techniques,
weight, volume) consider the                      Understand the      parallelograms.                                 tools, and
and select the    degree of                       need for                                                            formulas to
appropriate       accuracy for                    measuring with      Estimate,                                       determine
type of unit for  different                       standard units      measure, and                                    measurements.
measuring each situations.                        and become          solve problems
property.                                         familiar with the   involving length,
standard units in   area, mass,
Select and use                                    customary and       time, and
appropriate                                       metric system       temperature
measurement                                       (year long)         using
tools (ruler,                                                         appropriate
yardstick, meter                                  Identify the        standard units
stick).                                           inverse             and tools.
relationship        (Mass,
Demonstrate                                       between the size    Temperature,
understanding                                     of the units and    and Time need
to the need for                                   the number of       to be
measuring with                                    units.              supplemented)
units and
become familiar                                   Develop,            Identify
with standard                                     understand, and     common
units in the U.S.                                 use formulas to     measurements
customary                                         find the area of    of turns (e.g.,
system.                                           rectangles and      360 degrees in
related triangles   one turn, 90
Develop                                           and                 degrees in a
formulas to                                       parallelograms.     quarter-turn).
determine the
surface area of                                      Carry out simple     Use tools to
rectangular                                          conversions          measure angles
solids.                                              within a system of   (e.g., protractor,
measurement          compass)
(Must
supplement)

Strand: Data Analysis and Probability
Standard: Students will understand how to formulate questions, analyze data, and determine probabilities.
Organize,          Represent data                                                                                              Formulate          Organize,
represent, and     using tables                                                                                                questions that     represent, and
interpret          and graphs                                                                                                  can be             interpret
numerical and      (e.g., line plots,                                                                                          addressed with     numerical and
categorical data   bar graphs, and                                                                                             data and           categorical data
and clearly        line graphs).                                                                                               collect,           and clearly
communicate                                                                                                                    organize, and      communicate
findings by; (a)   Analyze data                                                                                                display relevant   findings by; (a)
choosing and       displayed in a                                                                                              data to answer     choosing and
constructing       variety of                                                                                                  them.              constructing
representations    formats to                                                                                                                     representations
that are           make                                                                                                        Select and use     that are
appropriate for    reasonable                                                                                                  appropriate        appropriate for
the data set,      inferences and                                                                                              statistical        the data set, and
and (b)            predictions,                                                                                                methods to         (b) recognizing
recognizing the    answer                                                                                                      analyze data.      the differences in
differences in     questions, and                                                                                                                 representing
representing       make                                                                                                        Develop and        categorical and
categorical and    decisions.                                                                                                  evaluate           numerical data.
numerical data.                                                                                                                inferences and
Design                                                                                                      predictions that   Compare and
Compare and        investigations                                                                                              are based on       describe related
describe related   and represent                                                                                               data.              data sets.
data sets.         data using
tables and                                                                                                                     Use the concepts
Use the            graphs                                                                                                                         of median, mode,
concepts of                                                                                                                                       maximum,
median, mode,      Use data                                                                                                                       minimum, and
maximum,           analysis to                                                                                                                    range and draw
range and draw      reasonable         a data set.
conclusions         inferences/predi
about a data        ctions and to      Demonstrate how
set.                develop            change in one
convincing         variable can
arguments from     relate to change
Describe events     data described     in a second
as “likely”,        in a variety of    variable (e.g.,
“unlikely”, or      formats            input-output
“impossible”                           machines, data
and quantify        Propose and        tables).
simple              justify
probability         conclusions
situations by (a)   and prediction
representing all    based on data.
possible
outcomes for a      Developing
simple              convincing
probability         arguments from
situation in an     data displayed
organized way       in a variety of
and (b)             formats.
expressing
outcomes of
experimental
probability
situations
verbally and
numerically
(e.g., three out
of four, ¾).

List all possible
combinations of
objects from
three sets.
(Must be
Supplemented)

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