SPELS Book

7/27/2019 SPELS Book

1/8

Attribute or Skill Novice Apprentice Proficient Master

Experimenter

I rarely start problemswithout assistance bytrying different things.

I rarely collect data andresults.

I rarely find evidence ofclaims viaexperimentation.

I have problems providingconcrete examples whenfaced with abstract

problems.

I occasionally startproblems withoutassistance by tryingdifferent things.

I collect data and resultsbut dont know what to dowith them.

I occasionally findevidence of claims viaexperimentation.

I sometimes provide

concrete examples whenfaced with abstractproblems.

I regularly start problemswithout assistance bytrying different things.

I collect data and resultsand use them todetermine what to do next.

I find evidence of claimsvia experimentation.

I provide concreteexamples when faced withabstract problems.

I am proficient AND:

I look at my results andask myself, Does this

make sense? If it doesnot, I check my results forerrors.

I share myexperimentation methodswith others.

Guesser

I make an estimate of ananswer and am very farfrom the mark.

I never create areasonable range for my

final solution.

I rarely use guess andcheck when confrontedwith a problem I dontknow how to do.

I make an estimate of ananswer and am withinseveral orders ofmagnitude.

I sometimes create a

reasonable range for myfinal solution.

I sometimes use guessand check whenconfronted with a problemI dont know how to do.

I make an estimate of ananswer and am within anorder of magnitude.

I create a reasonablerange for my final solution.

I use guess and checkwhen confronted with aproblem I dont know howto do.


I can make estimations ofbroad problems using noadditional facts (aka Fermiestimation).

(For example, can youestimate how manybaseballs it would take tofill up the classroom?)


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Conjecturer

I rarely make statementsbased on data.

I accept others statements

whether they are true or not.

I rarely come up with rulesto describe situations.

I make statements based ondata but do not test them.

I test the statements of

some other students fortruth, but accept thestatements of the smartkids.

I create rules that describesituations, but they aresomewhat inaccurate.

I make statements based ondata and test them to see ifthey are accurate.

I test othersstatements to

see if they are true or not.

I create a rule for a situationthat describes it accuratelyand generally.


I can generalize mostsituations I come across.

Visualizer

I draw pictures of situationsthat are inaccurate.

My visuals are not easilyunderstood by others.

I can rarely interpretpictures of others.

I can draw pictures of aproblem that are somewhat

accurate to what is goingon.

My visuals are understoodby others whenaccompanied by anexplanation.

I can sometimes interpretthe pictures of others to

understand what ishappening.

I can, given a problem, drawa picture that accurately

represents what is going onin the problem.

I can create a visual of aprocess that isunderstandable by others.

I can interpret the picturesof other to understand whatis happening in a problem.


I can accurately makechanges to diagrams whenthe parameters of a problemchange.


3/8


Tinkerer

I rarely wonder.

I rarely investigatesituations.

I do not know which tools tochoose to work on aproblem.

I occasionally wonder whathappens when I changesomething.

I sometimes investigatesituations by asking What ifI do this? and then doing it.

I occasionally chooseappropriate tools to bestdiscover new data about aproblem.

I wonder what happenswhen I change something.

I investigate situations by

asking What if I do this?and then doing it.

I choose appropriate tools tobest discover new dataabout a problem.


I encourage other studentsto wonder and be playful to

help them understand asituation.

Describer

I cannot explain mymathematical ideas clearly.

I rarely choose my wordscarefully so it is oftenunclear what I am referringto..

I rarely choose the bestlevel of precision in aproblem given thatproblems constraints.

I can explain mymathematical ideas

somewhat clearly, so thatthey are understandable byothers.

I explain my ideas bothverbally, but not in writing.

I usually choose my wordscarefully, but sometimes it isunsure what I mean.

I sometimes choose thebest level of precision in aproblem given thatproblems constraints.

I can explain mymathematical ideas clearly,

so that they areunderstandable by others.

I explain my ideas bothverbally and in writing.

I choose my words carefully,so that they are preciselywhat I mean and noambiguity exists about my

statements.

I choose the best level ofprecision in a problem giventhat problems constraints.


I can explain processes tohelp other studentsunderstand what is goingon.


4/8


Pattern Sniffer

I rarely detect patterns.

I can describe the rules forgenerating a pattern using

one out of words, pictures,or mathematical notation.

I rarely use patterns topredict future results.

I occasionally detectpatterns by noticingrepeated changes.

I can describe the rules forgenerating a pattern inwords, pictures, ormathematical notation, butnot all three.

I occasionally use patternsto predict future results.

I can ignore irrelevant

information that distractsfrom the patterns, but do notalways..

I detect patterns by noticingrepeated changes.

I can describe the rules for

generating a pattern inwords, pictures, andmathematical notation.

I use patterns to predictfuture results.

I ignore irrelevantinformation that distractsfrom the patterns.


I can extend complex visualpatterns far into the future.

Inventor

I rarely create shortcuts towork more efficiently.

I rarely generalize patternsand create models torepresent situations.

I rarely create new methodsfor solving problems andshare those methods withothers,

I occasionally createshortcuts to work moreefficiently.

I occasionally generalizepatterns and create modelsto represent situations.

I occasionally create newmethods for solvingproblems and share thosemethods with others,

I create shortcuts to workmore efficiently.

I generalize patterns andcreate models to representsituations.

I create new methods forsolving problems and sharethose methods with others,


I share my inventions withother students to make iteasier for everyone to learn.


5/8


QuantitativeReasoning

I can compare ratios andrates of different situations.

I can use units to verify thatthe correct steps in aprocess have been made.

I can compare quantitiesthat use different units byconverting units.

I can choose units and scalethat are appropriate for agiven problem.

IdentifyingVariables

I can determine whichquantities in a problem arevariables and which areconstant.

I can determine whichvariables are independentand which are dependent.

I can explain how changingthe variables in a problemaffects the result.

I can create a problem thatuses given variables andexplain my process.

RearrangingFormulas

I can explain therelationships between the

variables in formulas.

I can isolate a variable in aliteral equation.

I can make calculationseasier by identifying a

desired quantity andrearranging the formula tomake that quantity easier tocalculate.

I am able to analyze anyerror that my classmates or

I make in rearrangingformulas and explain how tofix that error.

IdentifyingModels

I can identify differentfunctions.

I can identify whether aproblem should be modeledby linear, exponential, orquadratic functions.

I can tell which function is abetter model quantitatively.

I can identify differentfunctions and explain theirappropriateness orinappropriateness for a

given real-world situation.

InterpretingFunctions

I can explain the definitionof a function and how it isdifferent from a relation.

I can explain what happensto the input of a function toreach the output.

I can identify when arelationship between twoquantities is a function andwhen it is not.

I can identify the domainand range of a function andexplain why they areappropriate.


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Function Notation

I can write functions usingfunction notation.

I can evaluate functionswritten in function notationfor various input values.

I can describe how afunction changes based onthe change in the notation.(e.g. f(x + k)

I can create a situation thatis modeled by a givenfunction.

IdentifyingFunctionFeatures

I can identify when afunction is increasing ordecreasing.

I can identify the interceptsof a function and explainwhat they mean in context.

I can identify the minimumsand maximums of a functionand explain what they meanin context.

I can describe the behaviorof a function over time,including rate of change andend behavior.

ComparingFunctions

I can identify which functiongrows fasters.

I can identify which functionhas a greater y-intercept.

I can describe thesimilarities and differencebetween the graphs of twofunctions.

I can compare two real-world function examplesand explain theirsignificance.

Building LinearFunctions

I can identify the rate ofgrowth and starting value ina problem.

I can describe how afunction grows linearly andextend it to distant inputs.

I can write a linear functionthat accurately models areal-world situation.

I can prove that linearfunctions grow at a constantrate.

Solving LinearEquations

I can solve a linear equationin one variable when:

- combining like terms isrequired


- the distributive property isrequired


- the variable appears onboth sides of the equation


- some coefficients/constants are fractions

I can explain the stepsrequired to solve.


7/8


Solving Linear

Inequalities

I can solve a linearinequality in one variablewhen:

- the distributive property isrequired

I can solve a linearinequality in one variablewhen:

- the variable appears onboth sides of the inequality- some coefficients are

negative

I can explain whyinequalities change whenmultiplying by a negative.

I can explain the stepsrequired to solve aninequality. I can create aninequality in relation to a

real-world scenario.

SketchingFunctions

I can draw the shape of themother functions.

I can draw the shape ofgraphs based on knowledgeof their rates, intercepts,and function family.

I can explain how differentrates, intercepts, andextreme points affect theshape of a graph.

I can draw sketches of rarefunctions like the step function.

GraphingEquations

I can accurately graph alinear equation given inslope-intercept form.

I can accurately graph andwrite a linear equation givena point and the slope.

I can accurately graph andwrite a linear equation giventwo points.

I can accurately graph alinear equation when the x-axis and y-axis havedifferent scales.

GraphingInequalities

I can accurately graph alinear inequality when it isboth a strict inequality and anon-strict inequality.

I can use test points todetermine which region toshade when graphing alinear inequality.

I can explain the differencein the graph of strictinequality and a non-strictinequality and why that

difference occurs.

I can explain the differencein a the graph of strictinequality and a non-strictinequality and why that

difference occurs in relationto a real world situation.

Systems ofEquations

I can solve a system ofequations graphically.

I can solve a system oflinear equationsalgebraically, usingelimination or substitution.

I can identify when a systemof equations has no solutionor infinite solutions.

I can model a problem as asystem of equation andexplain how the solutionmakes sense to myclassmates.


8/8


LinearProgramming

I can graph multiple linearinequalities and identify thefeasible region contained bythem.

I can find the optimalsolution to a linearprogramming problem.

I can explain how changingcertain constraints affect thefeasible region.

I can explain how changingcertain constraints affect thefeasible region. I can modelthis problem to my

classmates.

InterpretingGraphs

I can identify the domainand range of a graph andexplain what they mean.

I can explain what the keypoints (vertex, roots,intercepts) mean in a givengraph.

I can use the graph of afunction to identify importantvalues in the model anddetermine future behavior.

I can use the graph of afunction in relation to a real-world scenario. I can makepredictions and determinefuture behavior from thisgraph.

ExponentialFunctions

I can use the exponent rules(multiplication, division,powers of powers) tocombine differentexponential expressions.

I can explain why anexponential function willalways grow faster thanpolynomial functions, in thelong run.

I can explain why anexponential function has ahorizontal asymptote.

I can model all aspects ofexponential functions to myclassmates and explainusing real world examples.

ExponentialGrowth and

Decay

I can determine if a functionis growth or decay.

I can determine how much aquantity will grow or decaygiven a growth rate and a

time period.

I can use trial and error todetermine a growth rategiven a target value and a

time period.

I can use trial and error todetermine a time periodrequired given a growth rate

and a target value.

Rate of Change ofa Function

I can calculate the slope oflinear functions given agraph or two points.

I can determine the averagerate of change of a functionover a certain time period.

I can create first differenceand second differencecharts for functions andexplain what they mean.

I can explain the differencein rates of growth ofdifferent functions.

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SPELS Book