strand 2: data analysis, probability, and discrete mathematics
TRANSCRIPT
-
8/14/2019 Strand 2: Data Analysis, Probability, And Discrete Mathematics
1/14
Strand 2: Data Analysis, Probability, and Discrete MathematicsEvery student should understand and use all concepts and skills from the previous grade levels. The standards are designed so that new learning builds
on preceding skills and are needed to learn new skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the
process standards that are embedded throughout the teaching and learning of mathematical strands.
Concept 1: Data Analysis (Statistics)
Understand and apply data collection, organization and representation to analyze and sort data.
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 High SchoolPO 1.Formulatequestions tocollect data incontextualsituations.
PO 1.Formulatequestions tocollect data incontextualsituations.
PO 1.Formulatequestions tocollect data incontextualsituations.
PO 1.Formulatequestions tocollect data incontextualsituations.
PO 1.Formulatequestions tocollect data incontextualsituations.
PO 1.Formulatequestions tocollect data incontextualsituations.
PO 1.Formulatequestions tocollect data incontextualsituations.
PO 1.Formulatequestions tocollect data incontextualsituations.
PO 1.Formulatequestions tocollect data incontextualsituations.
PO 1.Formulatequestions tocollect data incontextualsituations.
PO 2. Make asimple
pictograph ortally chart
withappropriatelabels fromorganizeddata.
PO 2. Make asimple
pictograph ortally chart
withappropriatelabels fromorganizeddata.
PO 2.Construct ahorizontal
bar, vertical
bar,pictograph, ortally chartwithappropriatelabels andtitle from
organizeddata.
PO 2.Construct asingle-bargraph, line
graph or twoset Venndiagram withappropriatelabels andtitle fromorganized
data.
PO 2.
Construct a
double-bar
graph, line
plot, frequency
table, or three-
set Venn
diagram with
appropriate
labels and title
from organized
data.
PO 2.Construct ahistogram,line graph,
scatter plot,or stem-and-leaf plot withappropriatelabels andtitle fromorganized
data.
PO 2.Construct acircle graphwith
appropriatelabels andtitle fromorganizeddata.
PO 2.Construct
box-and-whisker plots.
PO 2.Organizecollected datainto an
appropriategraphicalrepresentation.
PO 3.
Determinewhen it is
appropriate touse
histograms,line graphs,
double bargraphs, andstem-and-leaf
plots.
PO 3.
Determine theappropriate
type ofgraphical
display for agiven data set.
PO 3.
Display dataas lists, tables,
matrices, andplots.
Arizona Academic Content Standards: Mathematics Standard Articulated by Grade Level Approved 3/31/03
Updated 8/12/031
-
8/14/2019 Strand 2: Data Analysis, Probability, And Discrete Mathematics
2/14
Strand 2: Data Analysis, Probability, and Discrete MathematicsEvery student should understand and use all concepts and skills from the previous grade levels. The standards are designed so that new learning builds
on preceding skills and are needed to learn new skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the
process standards that are embedded throughout the teaching and learning of mathematical strands.
Concept 1: Data Analysis (Statistics)
Understand and apply data collection, organization and representation to analyze and sort data.
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 High SchoolPO 4.Constructequivalentdisplays ofthe same data.
PO 2.Interpret a
pictograph.
PO 3.Interpret
pictographs
using termssuch as most,least, equal,more than,less than, andgreatest.
PO 3.Interpret
pictographs
using termssuch as most,least, equal,more than,less than, andgreatest.
PO 3.Interpret datafound in line
plots,pictographs,and single-bargraphs(horizontaland vertical).
PO 3.Interpretgraphical
representationsand datadisplaysincludingsingle-bargraphs, circlegraphs, two-set Venndiagrams, andline graphsthat display
continuousdata.
PO 3.Interpretgraphical
representationsand datadisplaysincluding bargraphs(includingdouble-bar),circle graphs,frequencytables, three-set Venn
diagrams, andline graphs
that displaycontinuous
data.
PO 3.Interpretsimple
displays ofdata includingdouble bargraphs, tallycharts,frequencytables, circle
graphs, andline graphs.
PO 4.Interpret datadisplays
includinghistograms,stem-and leaf plots,circle graphsand doubleline graphs.
PO 4.Interpret box-and-whisker
plots, circlegraphs, andscatter plots.
PO 5.Identifygraphic
misrepresen-tations anddistortions ofsets of data.
Arizona Academic Content Standards: Mathematics Standard Articulated by Grade Level Approved 3/31/03
Updated 8/12/032
-
8/14/2019 Strand 2: Data Analysis, Probability, And Discrete Mathematics
3/14
Strand 2: Data Analysis, Probability, and Discrete MathematicsEvery student should understand and use all concepts and skills from the previous grade levels. The standards are designed so that new learning builds
on preceding skills and are needed to learn new skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the
process standards that are embedded throughout the teaching and learning of mathematical strands.
Concept 1: Data Analysis (Statistics)
Understand and apply data collection, organization and representation to analyze and sort data.
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 High SchoolPO 3.Answerquestionsabout a
pictograph.
PO 4. Answerquestionsabout
pictographsusing termssuch as most,least, equal,more than,less than, andgreatest.
PO 4.Answerquestionsabout a
pictographusing termssuch as most,least, equal,more than,less than, and
greatest.
PO 4.Answerquestions
based on datafound in line
plots,pictographs,and single-bargraphs(horizontal
and vertical).
PO 4. Answerquestions
based ongraphicalrepresentations and datadisplaysincludingsingle-bargraphs, circle
graphs, two-set Venndiagrams, and
line graphsthat display
continuousdata.
PO 4. Answer
questions based
on graphical
representations,
and data
displays
including bar
graphs
(including
double-bar),
circle graphs,
frequencytables, three-set
Venn diagrams,
and line graphs
that display
continuous
data.
PO 4. Answerquestions
based onsimpledisplays ofdata includingdouble bargraphs, tallycharts,frequency
tables, circlegraphs, andline graphs.
PO 5. Answerquestions
based on datadisplaysincludinghistograms,stem-and-leaf plots,circle graphs,and double
line graphs.
PO 5. Answerquestions
based on box-and-whisker
plots, circlegraphs, andscatter plots.
PO 5.
Identify themode(s) of
given data.
PO 5. Identify
the mode(s)and mean
(average) ofgiven data.
PO 5. Find
the mean,median (odd
number ofdata points),mode, range,and extremevalues of agivennumericaldata set.
PO 6. Find
the mean,median,
mode, andrange of agivennumericaldata set.
PO 6.
Solveproblems in
contextualsituationsusing themean,median,mode, andrange of agiven data set.
PO 6.
Identifywhich of the
measures ofcentraltendency ismostappropriate ina givensituation.
Arizona Academic Content Standards: Mathematics Standard Articulated by Grade Level Approved 3/31/03
Updated 8/12/033
-
8/14/2019 Strand 2: Data Analysis, Probability, And Discrete Mathematics
4/14
Strand 2: Data Analysis, Probability, and Discrete MathematicsEvery student should understand and use all concepts and skills from the previous grade levels. The standards are designed so that new learning builds
on preceding skills and are needed to learn new skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the
process standards that are embedded throughout the teaching and learning of mathematical strands.
Concept 1: Data Analysis (Statistics)
Understand and apply data collection, organization and representation to analyze and sort data.
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 High SchoolPO 4.Formulatequestions
based on datadisplayed ingraphs,charts, andtables.
PO 5.Formulatequestions
based ongraphs,charts, andtables.
PO 5.Formulatequestions
based ongraphs,charts, andtables.
PO 5.Formulatequestions
based ongraphs,charts, andtables tosolve
problems.
PO 6.Formulate
predictionsfrom a givenset of data.
PO 6.Formulatereasonable
predictionsfrom a givenset of data.
PO 6.Identify atrend(variableincreasing,decreasing,remainingconstant)fromdisplayed
data.
PO 7.Interprettrends fromdisplayeddata.
PO 7.Formulatereasonable
predictionsbased on agiven set ofdata.
PO 7. Makereasonable
predictionsbased uponlinear patternsin data sets orscatter plots.
PO 7.Compare twosets of datarelated to thesameinvestigation.
PO 7.Comparetrends in datarelated to thesameinvestigation.
PO 8.Comparetrends in datarelated to thesameinvestigation.
PO 8.Comparetrends in datarelated to thesameinvestigation.
PO 8. Makereasonable
predictionsfor a set ofdata,based on
patterns.
PO 5. Solveproblemsbased on
simplegraphs,
charts, andtables.
PO 6.Solve
problems
usinggraphs,charts, and
tables.
PO 6. Solveproblemsusing graphs,
charts, andtables.
PO 6. Solveproblemsusing graphs,
charts andtables.
PO 7.Solvecontextual
problemsusing graphs,
charts, andtables.
PO 8.Solvecontextual
problemsusing graphs,
charts, andtables.
PO 8. Solvecontextual
problems
using bargraphs, tally
charts, andfrequency
tables.
PO 9. Solvecontextual
problems
usinghistograms,
line graphs ofcontinuous
data, doublebar graphs,
and stem-and-leaf
plots.
PO 9. Solvecontextual
problems
using scatterplots, box-
and-whiskersplots, and
double linegraphs of
continuousdata.
PO 9. Drawinferencesfrom charts,
tables, graphs,plots, or data
sets.
Arizona Academic Content Standards: Mathematics Standard Articulated by Grade Level Approved 3/31/03
Updated 8/12/034
-
8/14/2019 Strand 2: Data Analysis, Probability, And Discrete Mathematics
5/14
Strand 2: Data Analysis, Probability, and Discrete MathematicsEvery student should understand and use all concepts and skills from the previous grade levels. The standards are designed so that new learning builds
on preceding skills and are needed to learn new skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the
process standards that are embedded throughout the teaching and learning of mathematical strands.
Concept 1: Data Analysis (Statistics)
Understand and apply data collection, organization and representation to analyze and sort data.
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 High SchoolPO 10.Apply theconcepts ofmean,median,mode, range,and quartilesto summarizedata sets.
PO 11.Evaluate thereasonable-
ness ofconclusions
drawn fromdata analysis.
Arizona Academic Content Standards: Mathematics Standard Articulated by Grade Level Approved 3/31/03
Updated 8/12/035
-
8/14/2019 Strand 2: Data Analysis, Probability, And Discrete Mathematics
6/14
Strand 2: Data Analysis, Probability, and Discrete MathematicsEvery student should understand and use all concepts and skills from the previous grade levels. The standards are designed so that new learning builds
on preceding skills and are needed to learn new skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the
process standards that are embedded throughout the teaching and learning of mathematical strands.
Concept 1: Data Analysis (Statistics)
Understand and apply data collection, organization and representation to analyze and sort data.
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 High SchoolPO 10.Evaluate theeffects ofmissing orincorrect dataon the resultsof aninvestigation(e.g., Susiesteacher
recorded a 39instead of a93 for her last
quiz, whatwill happen
to Susiesaverage?).
PO 12.Recognizeand explainthe impact ofinterpretingdata (makinginferences ordrawingconclusions)from a biased
sample.
PO 11.Identify a line
of best fit fora scatter plot.
PO 13. Drawa line of best
fit for ascatter plot.
PO 12.Distinguish
betweencausation and
correlation.
PO 14.Determine
whetherdisplayed
data has
positive,negative, or
nocorrelation.
Arizona Academic Content Standards: Mathematics Standard Articulated by Grade Level Approved 3/31/03
Updated 8/12/036
-
8/14/2019 Strand 2: Data Analysis, Probability, And Discrete Mathematics
7/14
Strand 2: Data Analysis, Probability, and Discrete MathematicsEvery student should understand and use all concepts and skills from the previous grade levels. The standards are designed so that new learning builds
on preceding skills and are needed to learn new skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the
process standards that are embedded throughout the teaching and learning of mathematical strands.
Concept 1: Data Analysis (Statistics)
Understand and apply data collection, organization and representation to analyze and sort data.
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 High SchoolPO 15.Identify anormaldistribution.
PO 16.Identifydifferences
betweensampling and
census.
PO 17.Identifydifferences
betweenbiased andunbiasedsamples.
Arizona Academic Content Standards: Mathematics Standard Articulated by Grade Level Approved 3/31/03
Updated 8/12/037
-
8/14/2019 Strand 2: Data Analysis, Probability, And Discrete Mathematics
8/14
Concept 2: Probability
Understand and apply the basic concepts of probability.
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 High School
PO 1. Name
the possibleoutcomes fora probabilityexperiment.
PO 1. Name
the possibleoutcomes fora probabilityexperiment.
PO 1. Name
the possibleoutcomes fora probabilityexperiment.
PO 1. Name
the possibleoutcomes fora probabilityexperiment.
PO 1. Name
the possibleoutcomes fora probabilityexperiment.
PO 1.
Determine theprobabilitythat a specificevent willoccur in a
single stageprobability
experiment(e.g., Find the
probability ofdrawing a red
marble from abag with 3red, 5 blue,and 9 blackmarbles.).
PO 1.
Determine theprobabilitythat a specificevent willoccur in a 2-
stageprobability
experiment.
PO 1. Find
theprobabilitythat a specificevent willoccur, with or
withoutreplacement.
Concept 2: Probability
-
8/14/2019 Strand 2: Data Analysis, Probability, And Discrete Mathematics
9/14
Strand 2: Data Analysis, Probability, and Discrete MathematicsEvery student should understand and use all concepts and skills from the previous grade levels. The standards are designed so that new learning builds
on preceding skills and are needed to learn new skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the
process standards that are embedded throughout the teaching and learning of mathematical strands.
Understand and apply the basic concepts of probability.
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 High School
PO 2. Predictthe mostlikely or leastlikelyoutcome in
probabilityexperiments.(e.g., Predictthe chance ofspinning oneof the 2
colors on a 2-coloredspinner.)
PO 2. Makepredictionsaboutthe
probability ofevents beingmore likely,less likely,equally likelyor unlikely.
PO 2.Describe theprobability ofevents as
being morelikely, lesslikely,equallylikely,unlikely,certain,
impossible,fair or unfair.
PO 2.Describe theprobability ofevents as
being:
certain
(represented by1),
impossibl
e,
(represented by0), or
neither
certain
norimpossibl
e(represented by afraction
less than1).
PO2. Expressprobabilitiesof a singleevent as adecimal.
PO 2.Compareprobabilitiesto determinethe fairness ofa contextualsituation(e.g., If Johnwins whentwo or greatershows after a
six-sidednumber cubeis rolled and
Joaquin winsotherwise, is
this a fairgame?).
PO 2. Solvecontextualsituationsusing
probability(e.g., If the
probability ofMichellemaking a freethrow is 0.25,what is the
probabilitythat she willmake three
free throws ina row?).
PO 2.Determinesimple
probabilitiesrelated togeometricfigures.
PO 3. Predictthe outcomeof a grade-levelappropriate
probabilityexperiment.
PO 3. Predictthe outcomeof a grade-levelappropriate
probabilityexperiment.
PO 3. Predictthe outcomeof a grade-levelappropriate
probabilityexperiment.
PO 3. Predictthe outcomeof a grade-levelappropriate
probabilityexperiment.
PO 3. Predictthe outcomeof a grade-levelappropriate
probabilityexperiment.
PO 3. Predictthe outcomeof a grade-levelappropriate
probabilityexperiment.
PO 3. Predictthe outcomeof a grade-levelappropriate
probabilityexperiment.
PO 3. Predictthe outcomeof a grade-levelappropriate
probabilityexperiment.
Arizona Academic Content Standards: Mathematics Standard Articulated by Grade Level Approved 3/31/03
Updated 8/12/039
-
8/14/2019 Strand 2: Data Analysis, Probability, And Discrete Mathematics
10/14
Strand 2: Data Analysis, Probability, and Discrete MathematicsEvery student should understand and use all concepts and skills from the previous grade levels. The standards are designed so that new learning builds
on preceding skills and are needed to learn new skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the
process standards that are embedded throughout the teaching and learning of mathematical strands.
Concept 2: Probability
Understand and apply the basic concepts of probability.
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 High School
PO 4. Recordthe data from
performing agrade-levelappropriate
probabilityexperiment.
PO 4. Recordthe data from
performing agrade-levelappropriate
probabilityexperiment.
PO 4. Recordthe data from
performing agrade-levelappropriate
probabilityexperiment.
PO 4. Recordthe data from
performing agrade-levelappropriate
probabilityexperiment.
PO 4. Recordthe data from
performing agrade-levelappropriate
probabilityexperiment.
PO 4. Recordthe data from
performing agrade-levelappropriate
probabilityexperiment.
PO 4. Recordthe data from
performing agrade-levelappropriate
probabilityexperiment.
PO 4. Recordthe data from
performing agrade-levelappropriate
probabilityexperiment.
PO 5.Compare theoutcome ofan experimentto predictionsmade prior to
performingtheexperiment.
PO 5.Compare theoutcome ofan experimentto predictionsmade prior to
performingtheexperiment.
PO 5.Compare theoutcome ofan experimentto predictionsmade prior to
performingtheexperiment.
PO 5.Compare theoutcome of anexperiment to
predictionsmade prior to
performingtheexperiment.
PO 5.Compare theoutcome ofan experimentto predictionsmade prior to
performingtheexperiment.
PO 5.Compare theoutcome ofan experimentto predictionsmade prior to
performingtheexperiment.
PO 5.Compare theoutcome ofan experimentto predictionsmade prior to
performingtheexperiment.
PO 5.Compare theoutcome of anexperiment to
predictionsmade prior to
performingtheexperiment.
PO 6. Make
predictionsfrom theresults ofstudent-
generatedexperiments
using objects(e.g., coins,
spinners,number
PO 6. Make
predictionsfrom theresults ofstudent-
generatedexperiments
using objects(e.g., coins,
spinners,number
PO 6. Make
predictionsfrom theresults ofstudent-
generatedexperiments
using objects(e.g., coins,
spinners,number
PO 6. Make
predictionsfrom theresults ofstudent-
generatedexperiments
using objects(e.g., coins,
spinners,number
PO 6.
Distinguishbetweenindependentand
dependentevents.
PO 6.
Distinguishbetweenindependentand
dependentevents.
Arizona Academic Content Standards: Mathematics Standard Articulated by Grade Level Approved 3/31/03
Updated 8/12/0310
-
8/14/2019 Strand 2: Data Analysis, Probability, And Discrete Mathematics
11/14
Strand 2: Data Analysis, Probability, and Discrete MathematicsEvery student should understand and use all concepts and skills from the previous grade levels. The standards are designed so that new learning builds
on preceding skills and are needed to learn new skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the
process standards that are embedded throughout the teaching and learning of mathematical strands.
cubes). cubes). cubes, cards). cubes, cards).
Concept 2: Probability
Understand and apply the basic concepts of probability.
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 High School
PO 6.Compare theresults of tworepetitions ofthe samegrade-levelappropriate
probability
experiment.
PO 6.Compare theresults of tworepetitions ofthe samegrade-levelappropriate
probability
experiment.
PO 7.Compare theresults of tworepetitions ofthe samegrade-levelappropriate
probability
experiment.
PO 7.Compare theresults of tworepetitions ofthe samegrade-levelappropriate
probability
experiment.
PO 7.Compare theresults of tworepetitions ofthe samegrade-levelappropriate
probability
experiment.
PO 7.Compare theresults of tworepetitions ofthe samegrade-levelappropriate
probability
experiment.
PO 7.Compare theresults of tworepetitions ofthe samegrade-levelappropriate
probability
experiment.
PO 7.Compare theresults of tworepetitions ofthe samegrade-levelappropriate
probability
experiment.
Arizona Academic Content Standards: Mathematics Standard Articulated by Grade Level Approved 3/31/03
Updated 8/12/0311
-
8/14/2019 Strand 2: Data Analysis, Probability, And Discrete Mathematics
12/14
Strand 2: Data Analysis, Probability, and Discrete MathematicsEvery student should understand and use all concepts and skills from the previous grade levels. The standards are designed so that new learning builds
on preceding skills and are needed to learn new skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the
process standards that are embedded throughout the teaching and learning of mathematical strands.
Concept 3: Discrete Mathematics Systematic Listing and Counting
Understand and demonstrate the systematic listing and counting of possible outcomes.
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 High School
PO 1. Make
arrangementsthat represent
the number ofcombinationsthat can beformed by
pairing itemstaken from 2
sets, usingmanipulatives(e.g., Howmany outfitscan one makewith 2different colorshirts and 2different pairsof pants?).
PO 1. Make
arrangementsthat represent
the number ofcombinationsthat can beformed by
pairing itemstaken from 2
sets, usingmanipulatives(e.g., Howmany icecream conescan one makewith 2different typesof ice creamand 2different types
of cones?).
PO 1.
Makearrangements
that representthe number ofcombinationsthat can beformed by
pairing items
taken from 2sets, usingmanipulatives(e.g., Howmany types ofsandwichescan one makewith 3different typesof fillings and2 types of
bread if onlyone type of
bread and 1
kind of fillingis used for
eachsandwich?).
PO 1. Make a
diagram torepresent the
number ofcombinationsavailablewhen 1 itemis selectedfrom each of
3 sets of 2items (e.g., 2differentshirts, 2differenthats,2different
belts ).
PO 1. Find
all possiblecombinations
when 1 itemis selectedfrom each oftwo setscontaining upto three
objects (e.g.,How manyoutfits can bemade with 3
pants and 2tee shirts?).
PO 1. Findall possiblecombinations
when 1 itemis selected
from each of2 sets of
differentitems, using a
systematicapproach
(e.g., shirts:tee shirt, tanktop,sweatshirt;
pants: shorts,jeans).
PO 1.
Determine allpossible
outcomesinvolving acombinationof 3 sets of 3items, using asystematic
approach(e.g., 3differentshirts, 3different
pairs ofpants, and 3different
belts).
PO 1.
Determine allpossible
outcomesinvolving thecombinationof up to threesets of objects(e.g., How
many outfitscan be madewith 3 pants, 2tee shirts and2 pairs ofshoes?).
PO 1.
Determine allpossible
outcomesinvolving thecombinationof two ormore sets ofobjects (e.g.,
If you roll asix-sidednumber cube4 times, howmany
possibleoutcomes are
possible?).
PO 1.
Determinethe number
of possibleoutcomes fora contextualevent using achart, a treediagram, or
the countingprinciple.
Arizona Academic Content Standards: Mathematics Standard Articulated by Grade Level Approved 3/31/03
Updated 8/12/0312
-
8/14/2019 Strand 2: Data Analysis, Probability, And Discrete Mathematics
13/14
Strand 2: Data Analysis, Probability, and Discrete MathematicsEvery student should understand and use all concepts and skills from the previous grade levels. The standards are designed so that new learning builds
on preceding skills and are needed to learn new skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the
process standards that are embedded throughout the teaching and learning of mathematical strands.
Concept 3: Discrete Mathematics Systematic Listing and Counting
Understand and demonstrate the systematic listing and counting of possible outcomes.
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 High SchoolPO 2.Determine all
possiblearrangementsgiven a setwith four orfewer objectsusing asystematiclist, table or
tree diagramwhen order isnot
important.
PO 2.Determine all
possiblearrangementsof a given set,using asystematiclist, table, treediagram, orother
representation.
PO 2.Determine all
possiblearrangementsgiven a set.(e.g., Howmany wayscan youarrange a setof 7 books on
a shelf?).
PO 2.Determinewhen to usecombinationsversus
permutationsin countingobjects.
PO 3. Usecombinations
orpermutations
to solvecontextual
problems.
Arizona Academic Content Standards: Mathematics Standard Articulated by Grade Level Approved 3/31/03
Updated 8/12/0313
-
8/14/2019 Strand 2: Data Analysis, Probability, And Discrete Mathematics
14/14
Strand 2: Data Analysis, Probability, and Discrete MathematicsEvery student should understand and use all concepts and skills from the previous grade levels. The standards are designed so that new learning builds
on preceding skills and are needed to learn new skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the
process standards that are embedded throughout the teaching and learning of mathematical strands.
Concept 4: Vertex-Edge Graphs
Understand and apply vertex-edge graphs.
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 High School
PO 1. Color
pictures withthe least
number ofcolors so thatno commonedges sharethe samecolor
(increasedcomplexitythroughoutgrade levels).
PO 1. Color
pictures withthe least
number ofcolors so thatno commonedges sharethe samecolor
(increasedcomplexitythroughoutgrade levels).
PO 1. Color
pictures withthe least
number ofcolors so thatno commonedges sharethe samecolor
(increasedcomplexitythroughoutgrade levels).
PO 1. Color
maps with theleast number
of colors sothat nocommonedges sharethe samecolor
(increasedcomplexitythroughoutgrade levels).
PO 1. Color
maps with theleast number
of colors sothat nocommonedges sharethe samecolor
(increasedcomplexitythroughoutgrade levels).
PO 1. Color
maps withthe least
number ofcolors so thatno commonedges sharethe samecolor
(increasedcomplexitythroughoutgrade levels).
PO 1. Find
the shortestroute on a
map from onesite to another(vertex-edgegraph).
PO 1. Find
the shortestcircuit on a
map thatmakes a tourof specifiedsites (vertex-edge graph).
PO 1.
Solvecontextual
problemsrepresented
by vertex-edge graphs.
Arizona Academic Content Standards: Mathematics Standard Articulated by Grade Level Approved 3/31/03
Updated 8/12/0314