Strand 2: Data Analysis, Probability, And Discrete Mathematics

8/14/2019 Strand 2: Data Analysis, Probability, And Discrete Mathematics

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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 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


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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.


Updated 8/12/032


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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.


based onsimpledisplays ofdata includingdouble bargraphs, tallycharts,frequency

tables, circlegraphs, andline graphs.


based on datadisplaysincludinghistograms,stem-and-leaf plots,circle graphs,and double

line graphs.


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.


Updated 8/12/033


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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.


based ongraphs,charts, andtables.


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. 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.


problems

usinghistograms,

line graphs ofcontinuous

data, doublebar graphs,

and stem-and-leaf

plots.


problems

using scatterplots, box-

and-whiskersplots, and

double linegraphs of

continuousdata.

PO 9. Drawinferencesfrom charts,

tables, graphs,plots, or data

sets.


Updated 8/12/034


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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.


Updated 8/12/035


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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.


Updated 8/12/036


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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.


Updated 8/12/037


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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


PO 1. Name


PO 1. Name


PO 1. Name


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.



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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.
















Updated 8/12/039


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PO 4. Recordthe data from

performing agrade-levelappropriate























PO 5.Compare theoutcome ofan experimentto predictionsmade prior to

performingtheexperiment.





PO 5.Compare theoutcome of anexperiment to

predictionsmade prior to








PO 5.Compare theoutcome of anexperiment to

predictionsmade prior to


PO 6. Make

predictionsfrom theresults ofstudent-

generatedexperiments

using objects(e.g., coins,

spinners,number

PO 6. Make




spinners,number

PO 6. Make




spinners,number

PO 6. Make




spinners,number

PO 6.

Distinguishbetweenindependentand

dependentevents.

PO 6.

Distinguishbetweenindependentand

dependentevents.


Updated 8/12/0310


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cubes). cubes). cubes, cards). cubes, cards).




PO 6.Compare theresults of tworepetitions ofthe samegrade-levelappropriate

probability

experiment.


probability

experiment.


probability

experiment.


probability

experiment.


probability

experiment.


probability

experiment.


probability

experiment.


probability

experiment.


Updated 8/12/0311


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Concept 3: Discrete Mathematics Systematic Listing and Counting

Understand and demonstrate the systematic listing and counting of possible outcomes.


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.


outcomesinvolving thecombinationof up to threesets of objects(e.g., How

many outfitscan be madewith 3 pants, 2tee shirts and2 pairs ofshoes?).

PO 1.


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.


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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.


Updated 8/12/0313


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Concept 4: Vertex-Edge Graphs

Understand and apply vertex-edge graphs.


PO 1. Color

pictures withthe least

number ofcolors so thatno commonedges sharethe samecolor

(increasedcomplexitythroughoutgrade levels).

PO 1. Color




PO 1. Color




PO 1. Color

maps with theleast number

of colors sothat nocommonedges sharethe samecolor


PO 1. Color

maps with theleast number

of colors sothat nocommonedges sharethe samecolor


PO 1. Color

maps withthe least



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.


Updated 8/12/0314

Strand 2: Data Analysis, Probability, And Discrete Mathematics

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Transcript of Strand 2: Data Analysis, Probability, And Discrete Mathematics