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ED 125 921
DOCUMENT RESUME
95 SE^021
TITLE Mathematics^ K-12,^ Number^ and^ Numeration.^ Utica^ City School District Articulated Curriculum: Project
SEARCH, 1975.
INSTITUTION Utica^ City^ School^ District,^ N.Y.
SPONS AGENCY Eureau^ of^ Elementary^ and^ Secondary^ Education (DHEVOE), Washington, D.C.
PUB DATE 75
NOTE 19p.;^ For^ related^ documents,^ see^ SE^021 195-200;
light and broken type throughout
EDRS PRICE MF-$0.83^ Plus^ Postage.^ HC^ Not^ Available^ from^ EDRS.
DESCRIPTORS Behavioral Objectives; Curriculum; *Curriculum Guides; *Elementary School Mathematics; Elementary Secondary lAucation; Mathematics Education; *Number Concepts; Number Systems; *Objectives; *Secondary
School Mathematics
IDENTIFIERS Elementary^ Secondary^ Education^ Act^ Title^ III;^ ESEA
Title III
ABSTRACT
This document is one of six which set forth the mathematics components of the Project SEARCH Articulated Curriculum developed by the Utica (New York) City School District. Each volume deals with a broad area of mathematics and lists objectives related tc that area for all grades from K through 12. Each objective listed is described first in general terms and then in terms of spesific skills which students should exhibit. This volume concerns numbers and systems of numeration. The topics range from counting and recognition of numerals at the early levels to use of nondecimal systems, permutations and combinations, and interpretation of
percents at upper levels. (SD)
**************************************************************i******** Documents acquired by ERIC include many informal unpublished
- materials not available from other sources. ERIC makes every effort *
- to obtain the best copy available. Nevertheless, items of marginal *
- reproducibility are often encountered and this affects the quality *
- of the microfiche and hardcopy reproductions ERIC makes available *
- via the ERIC Document Reproduction Service (EDRS). EDRS is not
- responsible for the quality of the original document. Reproductions *
* supplied by EDRS are the best that can be.made from the original. *
******************************************tA***************************
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U,S.DEPARTMENTOFHEALTH. NATIONALINSTITUTEOF EDUCATION&WELFARE EDUCATION
EOUCATIONPOSITIONORPOLICY SENTOFFICIALNATIONALMNSTITUTEOF STATED00NOTNECESSARILYREPRE ATINGITPOINTSorVIEWOROPINIONS THEPERSONORORGANIZATIONORIGIN. OUCEOEXACTLYASRECEIVEDFROM THISDOCUMENTHASBEENREPRO.
C\I
PedQS'e
/97S"
TENK
LEADERS: 7,-
David
(^) Schmidt,
(^) Cornelia
(^) Vitagliano,
(^) Anne
(^) Wright
TEACHERS:
James
(^) Adesak,
(^) James
(^) Allen,
(^) Russell
(^) Ayers,
(^) Richard
(^) Brady,
(^) Elizabeth
(^) Bonsai,
(^) Angela
(^) Brooks,
Nicholas
Cardinale,
(^) Linda
(^) Clark,
(^) Richard
(^) D'Allesandro,
(^) Georgeanne
(^) papa,
(^) Richard
(^) DePhillips,
(^) Dolores
DOrozynski,
(^) Thomas
(^) Fletcher,
(^) Carta
(^) Fox,
(^) David
(^) Foxy,
(^) Ed (^) Freedman,
(^) Frank
(^) Giotto,
(^) Andrew
(^) Buzzetti,
Igor (^) Hrebinka,
(^) Janice
(^) Huss,
(^) Mary
(^) Johnson,
(^) Donald
(^) Jory,
(^) Raymond
(^) NolwaitB,
(^) Lorraine
(^) Maneen,
(^) Frank
Manley,
(^) Patrick
(^) Moccaldi,
(^) Adele
(^) Nowak,
(^) Linda
(^) Poccis,
(^) Michael
(^) Puleo,
(^) Marilyn
(^) Racha,
(^) Nary
(^) Rintrona;
Carla
(^) Risucci,
(^) Gary
(^) Rosato,
(^) Barbara
(^) Trybalski,
(^) Ruth
(^) Ward,
(^) George
(^) Whit,
(^) Regina
(^) Web.
Page
(^2)
PROJECT
SEARCH
ARTICULATED
CURRICULUM
EDWARD
J.
PERRY
Superintendent
(^) of (^) Schools
Project
SEARCH
(^) Administrative
Team
BERNADETTE
EICHLER:
Administrator for
(^) Elementary
(^) Education
SLUATRO
D.
(^) LALEtLA:
Administrator
(^) for (^) Secondary
(^) Education
DR.
ANGELA
M.
ELEFANTE:
Cbcrdinator,
(^) Project
SEARCH
GERARD
GRAOIERO:
Member,
(^) Beard
(^) of (^) Education
UTICA
BOARD
OF
EDUCATION
MR.
JOSEPH
H.
HOBIKA
(^) President
MR.
JAMES
W.
ALLEN
(^) Vice
(^) President
MRS.
JEANNE
ARCURI
MR.
THOAS
CARVILLE
MR.
GE1ARD
GRANIERO
MRS.
FRANCIS
MARINO
I.
VITO
MONTEGALATO
August
(^1975)
MRS.
NOSE
DAHELLA
(^) and (^) NORMAN
I.
SIEGEL,
(^) both
(^) former
Board
(^) Members
(^) deserve
special
(^) mention
(^) for (^) all (^) their
(^) efforts
(^) on behalf
(^) of (^) Pr (^) jest
(^) SEARCH.
UTICA
CITY
SCHOOL
DISTRICT
(^) Elizabeth
(^) Street
Utica,
(^) New
(^) York
(^13501)
--------Writing
the (^) ordinal
(^) position
(^) of (^) an (^) object
(^) in (^) a (^) given
sequence
the (^) missing
(^) number
(^) in (^) a (^) given
(^) series
Counting
the (^) counting
(^) order
(^) of (^) numbers
(^) by (^) 1's,
(^) 51s,
(^) 10's
to (^) 100.
Grade
(^) K
circle
(^) the (^) desire
(^) object
(^) (first,
(^) fifth,
(^) etc.).
fill (^) in (^) the (^) number
(^) that
(^) comes
(^) before
(^) and (^) after
(^) a
given
(^) number
(^) or (^) Writethe
(^) number
(^) coming
(^) in (^) between
two (^) numbers.
Grade
(^1)
count
(^) orally
(^) by (^) 1's,
(^) 5,s (^) and (^) 101s
(^) te100.
the (^) counting
(^) order
(^) of (^) numbers
(^) by (^) 2's (^) to (^) 20.
count
(^) orally
(^) by (^) 2's (^) to (^) 20.
the (^) cardinal
(^) numbers
(^) to (^) 100.
the (^) greater
(^) (greatest),
(^) smaller
(^) (smallest)
numbers
(^) for (^) numbers
(^) to" (^) 7.00.
0
state,
(^) select
(^) and/or
(^) write
(^) the (^) cardinal
(^) number
(^) of (^) a
structured
(^) group
(^) to (^) 100.
select
(^) which
(^) of (^) two (^) (or (^) three)
(^) numbers
(^) is (^) greater
(greatest)
(^) or (^) smaller
(^) (smallest)
(^) for (^) numbers
(^) to (^) 100.
the (^) ordinal
(^) positions
(^) to (^) tenth.
place
(^) an (^) x (^) on (^) the (^) object
(^) with
(^) the (^) specified
(^) ordinal
position
(^) to (^) tenth.
the (^) counting
(^) of (^) numbers
(^) on (^) 0. (^) number
(^) line.
given
(^) a (^) number
(^) and (^) a (^) number
(^) line,
(^) the'
(^) student
(^) will
mark (^) its (^) place
(^) on (^) the (^) number
(^) line.
Reading=
the (^) number
(^) words
(^) from
(^) zero
(^) to (^) ten.
read (^) words
(^) orally
(^) and (^) match
(^) words
(^) with
(^) numerals
(^) and/or
structured
(^) groups.
the (^) reading
(^) of (^) numerals
(^) from
(^0) (^) to (^) 100.
given
(^) an (^) ordered
(^) arrangement
(^) of (^) numerals,
(^) to (^) 100,
the (^) student
(^) will
(^) read
(^) them
(^) on (^) request
(^) from
(^) any (^) starting
point.
the (^) missing
(^) number
(^) in (^) a (^) given
(^) series
(^) of (^) numbers. -
(^) identify
(^) what
(^) number
(^) comes
(^) after,
(^) before
(^) or (^) between
any (^) given
(^) numbers
(^) for (^) numbers.
Page
2
Writing
the (^) writing
(^) order
of (^) numerals
(^) from
(^) o (^) to (^) 100.
the (^) greater or
(^) lesser
numbers
(^) in (^) numbers
to (^) 100.
the (^) writing
(^) of (^) numerals
(^) with
(^) tens
and (^) ones.
the (^) digits
(^) in (^) the (^) 10Is
(^) and
l's (^) places. Counting
the (^) counting
(^) order
(^) by10's
(^) from
(^) any (^) starting
point
(^) (limit
(^) of (^) 500).
the (^) counting
(^) order
(^) by (^) 2Is (^) from
(^) any (^) starting
point
(^) to (^) 500.
the (^) difference
(^) between
(^) odd (^) or (^) even
(^) numbers
to
the (^) counting
(^) order
(^) by (^) 5's (^) from
(^0) (^) to 500 (^) start-
ing (^) at (^) multiples
(^) of (^) 5.
the (^) counting
(^) order
(^) by (^) 2's,
51s, (^) 10'is
(^) on (^) a (^) num-
ber (^) line
(^) (limit
(^) of (^) 20).
Readin&
the (^) terms
(^) of (^) comparison
(^) more-fewer,
(^) most-fewest
(to (^) 20).
Page
(^3)
Grade
(^1)
write
(^) numerals
froi (^1) (^) - (^100) (^) in (^) sequential
(^) order
or (^) for (^) an (^) ordered
(^) set (^) of (^) pictures
(^) for (^) small
(^) blocks
of (^) numbers.
place
or
between
(^) two (^) numbers
(^) to (^) indicate
(^) the
greater
(^) or (^) lesser
(^) number,
(^) with
(^) or (^) without'
(^) structured
groups,
(^) to (^) 100.
write
(^) the (^) numeral
(^) which
(^) names
(^) a (^) structured
(^) group
(^) of
up (^) to (^100) (^) objects
(^) as
tens (^) and
ones.
write
(^) the (^) digit
(^) which
(^) is (^) in (^) the (^) 10's
(^) or (^) l's (^) place
(^) as
requested
(^) for (^) a (^) given
(^) number
(^) and (^) state
(^) the (^) place
(^) value
of (^) a (^) particular
(^) digit.
Grade
(^2)
be (^) given
(^) a (^) zet (^) that
(^) contains
(^) multiples
(^) of (^) 10, (^) the (^) stu-
dent (^) will
(^) count
(^) the (^) elements
(^) by (^) 10's
(^) to (^) a (^) limit
(^) of (^) 500.
be (^) given
(^) an (^) incomplete
(^) wequence
(^) of (^) multiples
(^) of (^) 2, (^) the
student
(^) will
(^) supply
(^) the (^) missing
(^) multiples
(^) to (^) 500.
be (^) given
(^) a (^) complete
(^) sequence
(^) of (^) multiples
(^) by (^) 2's,
(^) the
student
(^) will
(^) identify
(^) odd (^) or (^) even
(^) numbers.
be (^) given
(^) an (^) incomplete
(^) sequence
(^) of (^) multiples
(^) of (^) 5's,
the (^) student
(^) will
(^) supply
(^) the (^) missing
(^) multiples
(^) to (^) a
limit
(^) of (^) 500.
be (^) given
(^) a (^) number
(^) and (^) a (^) number
(^) line,
(^) the (^) student
(^) mill
identify
(^) same
(^) by (^) ordinal
(^) position.
Grade
(^2)
be (^) given
(^4) (^) sets
(^) of (^) objects
(^) containing
(^) unequal
(^) objects
the (^) child
(^) will
(^) mark
(^) with
(^) an (^) x (^) the (^) set (^) with
(^) the (^) most
sets (^) to (^20) (^) (opposite
(^) terms
(^) more-fewer,
(^) most-fewest.)
CountnjEL
the cardinal
(^) numbers
(^) froM
(^1) (^) to (^) 1,000.
(lip (^) ordinal
numerals.
Reading
the (^) reading
(^) of the (^) sequetce
(^) of (^) numbers
(^) from
any (^) starting
(^) point
(^) to 1,000.
Writing
the (^) writing
(^) of the (^) sequence
(^) of (^) numbers
(^) from'
any (^) starting
(^) point
(^) from'l
(^) to (^) 1,000.
number
(^) words
(^) to (^) an including
(^) ). place
(^) numerals.
the (^) Roman
(^) numerals
froN
(^1) to (^) 100.
expanded
(^) notation
(^) up (^) to and (^) including
(^) ). place
numerals.
skip-counting
(^) upto
(^) 1,
(^) (backward
(^) and (^) forward)
the (^) inequality
symbols;
up (^) to (^) 1,000.
Counting
the (^) counting
(^) order
(^) to.1,000,
(^) starting
(^) at (^) nny
Grade
(^3)
be (^) given
(^) sets
(^) around
(^) the (^) room,
outdoors,
(^) the (^) student
will (^) identify
(^) the (^) number
(^) in (^) each
(^) set. N
be (^) given
(^) sets
(^) of (^) concreteobjects,
(^) the
student
will
identify
(^) the (^) position
(^) of (^) an (^) element
(^) in (^) the (^) set.
Grade
(^3)
be (^) given
(^) a (^) chart
(^) cl,f (^1) (^) to 1,000,
(^) the (^) student
(^) will
(^) be
able (^) to (^) read
(^) a (^) series
(^) of (^) numbers
(^) in (^) sequence
(^) from
(^) one
starting
(^) point
(^) to (^) another.
be (^) given
(^) an (^) incomplete
(^) number
line (^) with
(^) starting
(^) and
ending
(^) numbers
(^) identified,
(^) the (^) student
(^) will
(^) fill
(^) in (^) the
missing
(^) numerals.
read, (^) write
(^) and (^) use (^) nurier
words
(^) from
(^1) (^) to (^) 1,000.
road (^) and (^) write
(^) Roman
(^) numerds
(^) from
(^1) to (^) 100.
be (^) able
(^) to (^) read
(^) and (^) write
expanded
(^) numbers.
Page
5 be (^) given
(^) the (^) nultipie,
(^) the (^) student
(^) will
(^) be (^) able
(^) to
recite
(^) and (^) write
(^) series
(^) up (^) to (^) 1,
(^) e.g.,
(^) 2's,
(^) 3's,
Ws, (^) 51s;
(^) etc.
be (^) given
(^) the (^) numrals,
(^) the (^) student
(^) will
(^) rend,
(^) write
(^) and
provide
(^) correct
(^) inequality
(^) symbols
(^) up (^) to (^) 1,
(^) (on (^) ).
place
(^) numbers).
Grade (^)!
be (^) given
(^) a (^) specific
(^) number,
(^) c (^) g,,
10,986,
(^) the (^) child
will (^) orally
(^) count
(^) to (^) another
(^) spebifically
(^) given
(^) number,
e.g., (^) 11,175.
Counting
the (^) counting
(^) order
by (^) tens
(^) starting
(^) at (^) any
point.
the (^) counting
(^) order
by (^) 2's, (^) 3's, (^) )14's
(^) and (^) 5's
to (^) 1,000,
(^) starting
(^) at (^) any (^) point.
Reading
the (^) numerals
(^) to 1,000,
(^) starting
(^) at (^) any
point.
the (^) Roman
(^) numerals
from (^) one (^) to (^) one (^) thousand
the (^) symbols
(^) for
less (^) than
(^) (-()
(^) and (^) greater
than (^) ( (^) >) (^) and (^) their
(^) place
(^) in (^) numbers
(^) to
the (^) identification
(^) ofplace
(^) value
(^) digits
(^) to
the (^) odd (^) and (^) even
(^) 4umbers
(^) up to (^) 1,000,000. Writing
the (^) expanded
notation,
(^) words/numbers
(^) and (^).
signs
(^) of (^) numbers
(^) to (^) 1,000,000.
the (^) number
(^) words
(^) ofnumbers
(^) to (^) 1,000,000.
the (^) numerals
(^) to (^) 1,000,
starting
(^) at (^) any
po5nt.
Page
Grade
(^4)
be (^) given
(^) thu (^) number
(^) the (^) child
(^) will
(^) count
(^) by
ten's
(^) to (^) 7,500.
be (^) given
(^) a (^) specificstarting
(^) point,
(^) the (^) child
(^) will
count
(^) by (^) 2's,
(^) 3's,
(^) Wsp (^) 5's,
(^) to (^) another
(^) given
(^) number.
be (^) given
(^) a (^) specific
(^) listof
(^) numbers,
(^) the (^) child
(^) will
be (^) able
(^) to (^) read
(^) the (^) list.
be (^) given
(^) a (^) specific
(^) list
(^) of (^) Romannumerals,
(^) the (^) child
will (^) be (^) able
(^) to (^) road
(^) the (^) corresponding
(^) Arabic
(^) numeral
to (^) 1000.
be (^) given
(^) two (^) specific
(^) numbers,
(^) thestudent
(^) will
(^) be
able (^) to (^) place
(^) the (^) greater
(^) than
(^) or (^) less
(^) than
(^) symbols
between.
be (^) given
(^) a (^) specific
(^) number,
(^) thestudent
(^) will
(^) be (^) able
to (^) orally
(^) identify
(^) the (^) place
(^) value
(^) of (^) each
(^) digit.
be (^) given
(^) a (^) random
(^) list
(^) of (^) numerals
between
(^) and
(^) the (^) student
(^) will
(^) circle
(^) the (^) even
(^) numerals.
be (^) given
(^) an (^) abacus
(^) representing
(^) any (^) given
(^) numeral
from (^1) (^) to (^) 1,000,000,
(^) the (^) student
(^) will
(^) be (^) wile
(^) to (^) write
the (^) numeral
(^) correctly,
(^) and (^) vice-versa.
be (^) given
(^) a (^) list
(^) of (^) words
(^) representing
(^) numerals
(^) from
to (^) 1,000,000,
(^) the (^) student
(^) will
(^) be (^) able
(^) to (^) write
(^) them
by (^) number
(^) words
(^) and (^) vire-versa.
be (^) given
(^) a (^) specific
(^) number
(^) orally,
(^) the (^) student
(^) will
write
(^) the (^) number.
(^) to (^) 1,000,000).,
Reading
(^) and (^) Writing
the (^) reading
(^) and (^) writing
(^) of (^) numerals
(^) up (^) to
how (^) to (^) round
(^) numbers
(^) to (^) 1,000,000,
the (^) different
(^) periods
(^) and (^) what
(^) `they
(^) represent.
expanded
(^) notation.
the (^) concept
(^) of (^) negative
(^) whole
(^) numbers.
Counting
the (^) base
(^10) (^) number
(^) system
(^) is (^) a (^) positional
system.
Reading
that (^) our (^) number
(^) system
(^) is (^) a (^) positional
(^) one.
the (^) Roman
(^) system
(^) is (^) non-pokitional
(^) with
(^) ad-
ditive
(^) and (^) subtractive
(^) patterns.
the (^) prime
(^) and (^) composite
(^) numbers.
the (^) symbols>
(^) and (^) <
Writing
that (^) a (^) number
(^) may (^) be (^) approximated
(^) or (^) rounded
to (^) a (^) more
(^) practical
(^) or (^) convenient
(^) number.
Fare
8
Grade
(^5)
be (^) given
(^) several
(^) numbers
(^) orally,
(^) the (^) student
(^) will
write
(^) them.
round
(^) given
(^) numbers.
be (^) given
(^) written
(^) numbers,
(^) the (^) student
(^) will
(^) identify
the (^) period
(^) designated.
be (^) given
(^) a (^) standard
(^) numeral,
(^) the (^) student
(^) will
(^) write
it (^) in (^) expanded
(^) notation.
be (^) given
(^) a (^) thermometer,
(^) the (^) eStudent
(^) will
(^) read
(^) and
write
(^) temperatures
(^) below
(^) zero.
Grade
(^6)
be (^) given
(^) numbers
(^) to (^) 1,000,000,000,
(^) the (^) student
(^) will
identify
(^) place
(^) value.
be (^) given
(^) numbers
(^) to (^) 1,000,000,000,
(^) the (^) student,
(^) w
read (^) them.
be (^) given
(^) Roman
(^) uumerals,
(^) he (^) win (^) road
(^) them
(^) using
symbols
(^) I, (^) V, (^) X, (^) L, (^) C.D, (^) 11.
be (^) given
(^) numbers,
(^) students
(^) will
(^) test
(^) to (^) determine
if (^) it (^) is (^) prime
(^) or (^) complete.
be (^) given
(^) number
(^) sentences
(^) involving
(^) symbols,
(^) students
will (^) label
(^) as (^) true
(^) or (^) false.
be (^) gjpen
(^) numbers,
(^) student
(^) will
(^) write
(^) them
(^) in (^) their
rounded
(^) form
(^) to (^) 10's',.1001s
(^) and (^) 1,0001s
(^) usiit
up (^) to
a 6-digit
(^) nu6Cral.
Writing
that (^) en (^) exponent
tells
(^) how (^) ma (^) times
(^) a (^) base
number
(^) is (^) used
(^) as (^) a (^) factor.
that (^) our (^) number
(^) system
(^) is (^) a (^) pUtional
(^) one.
that (^) a (^) bar (^) indicates
nultiPlicaon
(^) by (^) a
thousand
(^) when
(^) working
(^) with
(^) Rom.numerals.
that (^) other
(^) base (^) systems
(^) exist
(^) .iich
(^) are
positional
(^) like
(^) base
(^) 10.
expanded
(^) notation
(^) to (^) 100;bi1li,.
the (^) GCF (^) of (^) a (^) pair
(^) of (^) numerals.
that (^) a (^) system
(^) of (^) numeration
ac,...A
R.3.1u4i
the numbers. (^) Romar
(^) and Azyptian
Numtvation
(^) System.
the (^) Hirai-Arab:Le
(^) or (^) Doe Imal (^) s:,-stem
(^) of
the (^) ccacept
(^) of (^) Place
(^) Value
the (^) concept
(^) 0. (^) Cardinal
and (^) Urdinal
(^) limbers
PIZe
9
1,{
Grade
(^6)
be (^) given
(^) numbers,
he (^) will
(^) write
(^) them
(^) in (^) their
exponential
(^) form.
be (^) given
(^) numbers
(^) to1,000,000,000,
(^) student
(^) will
(^) write
them (^) in (^) numeral
(^) and (^) word
(^) form,
using
(^) the (^) bar,
(^) thestudent
(^) will
(^) write
(^) Roman
(^) numerals.
be (^) given
(^) numbers,
students
(^) will
(^) write
(^) them
(^) in (^) base
and (^) base
(^) 2, (^) and (^) change
(^) them
(^) from
(^) base
(^5) and (^) base
(^2)
to (^) base
(^) 10, (^) vice-versa.
be (^) given
(^12) (^) digit
(^) number,
student
(^) will
(^) use (^) expanded
notation.
be (^) given
(^) a (^) pail'
(^) of (^) numerals,
student
(^) will
(^) determine
factor
(^) sets
(^) to (^) find
(^) common
(^) factors
(^) and (^) the"
(^) GCF.
'Grade
(^7) (^) - (^8)
:bow:
(^) by (^) the (^) use (^) of (^) n (^) tnllyAna
(^) ,Jvuom,
alrs%J.Lelic
n:Jr:,ers
(^) and (^) symbols.
wri (^) e (^) Roman
(^) and Egyptian
(^) Numerals.
reatRoman
(^) and (^) Egyptian
(^) Numerals.
crecto
(^) his (^) own Number
(^) system.
writ) (^) arS. (^) number
in (^) this
(^) system
(^) by (^) using:
.., zero,
(^) as (^) a (^) place
(^) holder
:. the (^) idea
(^) of (^) place
(^) value.
wr:Ae.the
(^) pattern
(^) of (^) the (^) Place
(^) Values
(^) as (^) powers
(^) of
Tor_ (^) and (^) the (^) decimal
(^) places
(^) as (^) wal.
show (^) that
(^) Cardinal
(^) numbers
(^) are used (^) to (^) tell
(^) how (^) many.
How (^) to (^) find
(^) the (^) square
(^) rootof
(^) a (^) number
(^) through
a mathematical
(^) solution.
How (^) to (^) round-off
(^) a (^) number
(^) to correct
(^) place
value.
That (^) digital,
(^) computers
(^) use (^) the
base (^1) (^) system.
That (^) a (^) computer
(^) is (^) composed
(^) of (^) an input,
(^) output,
arithmetic,
(^) logical,
(^) control
(^) and (^) memory
(^) unit.
That (^) the (^) component
(^) parts
(^) ofa (^) computer
(^) are
interrelated.
That (^) some
(^) computer:,
(^) such
(^) as (^) Monroe,
(^) use
the
Octal
(^) system
(^) rather
(^) than
(^) the (^) binary
(^) system
(^) for
storing
(^) information.
The (^) meaning
(^) of ratio
(^) and (^) proportion
.
The (^) Decimal
(^) Numbers
The (^) Common
(^) Multiples
Grade
(^9)
-Find
(^) the (^) square
(^) root
(^) of (^) a (^) number.
round-off
(^) a (^) number
(^) to (^) a (^) given
(^) place
Grade value.
(^9) (^) = (^12)
Convert
(^) a (^) base
(^) two (^) number
(^) to (^) a (^) base
(^) 10number
(^) and
vice (^) versa.
List (^) in (^) writing
(^) the (^) component
(^) its
of (^) a (^) computer.
Draw (^) the (^) interrelationship
of (^) the (^) component.
(^) parts
and (^) describe
(^) in (^) writing
(^) the (^) function
(^) of (^) each
(^) com-
ponent
(^) part.
Convert
(^) a (^) base
(^)? (^) number
(^) to
abase
number
and
vice. (^) versa.
Grade
(^10)
compute
(^) the (^) mean
(^) proportion
(^) given
(^) the (^) extremes
of (^) the (^) proportion.
Grade
(^10) (^) - (^12)
a. (^) read
(^) given
(^) decimal
(^) numbers.
b. (^) write
(^) given
(^) decimal
(^) numbers.
c. (^) convert
(^) decimals
(^) to (^) fractions.
d. (^) convert
(^) fractions
(^) to (^) decimals
a. (^) calculate
(^) the (^) least
(^) common
(^) multiple
b. (^) calculate
(^) the (^) greatest
(^) common
(^) divisor
c: (^) factor
(^) a (^) given
(^) numbe.e.
Pagel.).
-,The
(^) Prime
(^) Numbers
The (^) structure
(^) of (^) the (^) real
(^) number
system
through
(^) complex
(^) numbers.
-The (^) postulates
(^) of (^) a (^) number
(^) field.
The (^) operations
(^) on (^) numbers
(^) in specified
(^) sets.
The (^) operations
(^) on (^) fractions.
The (^) operations
(^) on (^) real
numbers
(^) involving
exponents
(^) and (^) radicals.
The (^) operations
(^) on (^) complex
numbers.
Factorial
notation.
The (^) formula
(^) for (^) permutations
of (^) n (^) things
taken
(^) r (^) at (^) a (^) time.
The (^) formula
(^) for (^) combinations
(^) of (^) n things
taken
(^) r (^) at (^) a (^) time.
Grade
(^10) (^) - (^12)
a. (^) factor
(^) a (^) given
(^) numberinto
(^) primes
b. (^) draw
(^) a (^) factor
(^) tree
Grade
(^11)
a. (^) compare
(^) the (^) relationships
(^) among
the (^) various
sets (^) of (^) numbers
(^) which
(^) make
(^) up (^) the (^) set (^) of (^) reals.
b. plot (^) a (^) complex
(^) number
(^) on (^) complex
(^) plane.
a. (^) list
(^) the (^) postulates
(^) of the (^) number
(^) field.
b. (^) recognize
(^) which
(^) postulates
(^) are (^) or (^) are (^) not (^) uatisified
by (^) the (^) various
(^) number
(^) sets.
factor
(^) expressions
(^) using
(^) commonfactors,
(^) difference
of (^) two (^) squares,
(^) quadratic
(^) trinomial
(^) (including
(^) per=
fect (^) square
(^) trinomials
(^) (4x
hx (^) - (^) 3).
a. (^) perform
(^) the (^) four
(^) fundamental
operations
(^) on (^) fractions.
b. (^) simplify
(^) complex
(^) fractions.
perform
(^) ;mid (^51) (^) i ip (^) iisy (^) exponentials
(^) and (^) radicals.
apply
(^) the (^) postulates
(^) of (^) the (^) number
field
(^) to (^) complex
numbers.
.Grade
(^11) (^) - (^12)
evaluate
(^) a (^) factorial
(^) 2h.
evaluate
(^) a (^) formula
(^) for (^) permutations
(^) of (^) n (^) things
taken
(^) r (^) at (^) a (^) time.
(^5) P (^) = (^) 5. (^) - (^20)
evaluate
(^) a (^) formula
(^) for (^) the (^) combination
(^) of (^) n (^) things
taken
(^) r (^) at (^) a (^) time
M5.T. (^4) A 10
2
Page
12
The (^) structure
(^) of (^) the (^) set (^) of (^) real
(^) numbers
The (^) structure
(^) of (^) the (^) field
(^) of (^) complex
numbers.
The (^) techniques
(^) needed
(^) to (^) change
(^) from
(^) logarthmic
to (^) exponential
(^) notation,
(^) and (^) reverse.
The (^) techniques
(^) needed
(^) to (^) change
(^) from
(^) one
logarithmic
(^) base
(^) to (^) another.
The (^) use (^) of (^) natural
(^) logarithmics.
The (^) conversion
(^) from
(^) revtangular
(^) to (^) polar
coordinates,
(^) and (^) reverse.
Grade
(^12)
Prove
(^) that
(^2) (^) is (^) irrational.
prove
(^) the (^) communitive
(^) and (^) associative
(^) properties
for (^) the (^) field
(^) of (^) complex
(^) numbers
(^) using
(^) definition
of (^) addition
(^) and (^) multiplication
(^) by (^) ordered
(^) pairs.
change
(^) equations
(^) from
(^) logarithmic
(^) notation
(^) to
exponential
(^) equation,
(^) and (^) reverse.
change
(^) equations
(^) froM
(^) ono
logarithmic
(^) base
(^) to (^) another.
compute
(^) problems
(^) using
(^) base
(^) e.
convert
(^) rectangular
(^) to (^) polar
(^) coordinates,
and (^) reverse.
Page
