Core Curriculum Mathematics - Grade 7

7/28/2019 Core Curriculum Mathematics - Grade 7

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College-Career Ready Common Core Standards/PA Common CorePlanning and Scheduling Timeline

3rd QuarterMath: 7th Grade

1

In the beginning of this quarterstudents willformulas. Students will understand that expreexpressions in equivalent forms, and identify ssimple one-step equations and construct andwill understand that a data distribution may nomay yield different values. Students will undervariability can be used to summarize data. Th

clusters, peaks, gaps, and symmetry within thBy the end of this quarterstudents will be aand understand properties of three-dimensionof operations to generate equivalent expressiand algebraic expressions and equations. Stua population, draw informal comparative inferThey will develop, use, and evaluate probabiliprecision are: circumference, diameter, pi, pexpressions, maximum, minimum, relevanpopulation, representative sample, inferenmeasures of variability, sample space.

l understand, write, and evaluatsions in different forms can beolutions of equations. They willnalyze tables to describe relati

t have a definite center and thatstand measures of central tendy will describe and summarize

context in which the data wasle to solve problems involving c

al shapes and their related partns and solve real-life and mathdents will be able to use randonces about two populations any models. The terms students sarallel, perpendicular, skew,information, irrelevant infores, variation/variability, distri

variable expressions usingquivalent.They will rewrite

use properties of operations to solvenships between quantities. Theythe various ways to measure centerncy and recognize that measures ofnumerical data sets, by identifying

collected. ircumference and area of a circle

. They will be able to use propertiesmatical problems using numericalsampling to draw inferences aboutinvestigate chance processes.

hould learn to use with increasedumeric expressions, algebraication, random sampling,bution, measures of center,

Performance Descriptor/ EligibleContent

PA Common CoreStandards

What will it mean for thestudent?

Performance Descriptor2.3.7.A.1Solve real-world and mathematicalproblems involving angle measure, area,surface area, circumference, and volume

Eligible ContentM07.C-G.2.2.1Find the area and circumference of acircle. Solve problems involving area andcircumference of a circle(s). Formulas willbe provided.

2.3. GeometryCCRS.7.G.4CCRS.7.G.6

Students will be able to solvepractical problems involvingcircumference and area of acircle, given the diameter orradius. Students will understandthe ratio of circumference todiameter can be expressed aspi.

Performance Descriptor2.3.7.A.2Visualize and represent geometric figuresand describe the relationships betweenthem.

Eligible ContentM7.C.1.1.3Identify parallel, perpendicular and/orskew line segments within three-dimensional figures.

2.3. GeometryCCRS.7.G.1CCRS.7.G.3

Students will be to identify,define, label, and/or describeproperties of three-dimensionalshapes and their related parts.


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Standards of Mathematical Practicesolving them; Use appropriate tools stand quantitatively; Model with matherepeated reasoning.

Non-Negotiables: Make sense of proategically; Look for and make use of satics; Attend to precision; Look for and

blems and persevere inructure; Reason abstractlyexpress regularity in

How will students apply t eir knowledge and skills? Textual References and

Proficient: Advanced:

Resources

Sample Task:Show and explain how thecircumference and area of a circleare related and explain therelationship between diameter,circumference and pi. Apply theformulas for area and circumferenceof a circle to solve problems.DiscussClarify

Sample Task:Justify the formulas for the area andcircumference of a circle, and usethem to solve problems; provide aninformal derivation of the relationshipbetween the circumference and areaof a circle. Students will be able togenerate the formulas forcircumference and area.ProveDifferentiate

See Schoolnet for Internetlinks and resources.Use this space forplanning.

Sample Task:Employ three-dimensional figures toidentify, locate, and define parallel,perpendicular and skew linesegments within three-dimensionalfigures.AnalyzeInterpret

Sample Task:Formulate and test conjecturesabout the properties of parallel andperpendicular lines based onexplorations and concrete models,recognizing when two lines areparallel, perpendicular, skew orintersecting.ProveConnect


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In the beginning of this quarterstudents willformulas. Students will understand that expreexpressions in equivalent forms, and identify ssimple one-step equations and construct andunderstand that a data distribution may not hamay yield different values. Students will undervariability can be used to summarize data. Th

clusters, peaks, gaps, and symmetry within thBy the end of this quarterstudents will be aand understand properties of three-dimensionof operations to generate equivalent expressiand algebraic expressions and equations. Stua population, draw informal comparative inferThey will develop, use, and evaluate probabiliprecision are: circumference, diameter, pi,expressions, maximum, minimum, relevanpopulation, representative sample, inferenmeasures of variability, sample space.


ve a definite center and that thestand measures of central tendey will describe and summarize

context in which the data wasle to solve problems involving ci

al shapes and their related partsns and solve real-life and mathdents will be able to use randomnces about two populations andy models. The terms students sarallel, perpendicular, skew,information, irrelevant informes, variation/variability, distri

variable expressions usingquivalent.They will rewritese properties of operations to solvenships between quantities. They willvarious ways to measure centerncy and recognize that measures ofumerical data sets, by identifying

ollected. ircumference and area of a circle

. They will be able to use propertiesmatical problems using numericalsampling to draw inferences aboutinvestigate chance processes.ould learn to use with increasedumeric expressions, algebraication, random sampling,bution, measures of center,




Performance Descriptor2.4.6.B.2Use numerical data and apply statisticalproperties to summarize and describe adistribution.

Eligible ContentM06.D-S.1.1.2Determine quantitative measures ofcenter (e.g., median, mean, and/ormode) and variability (e.g., range,interquartile range, and/or mean absolutedeviation).

2.4. Measurement, Dataand ProbabilityCCRS.6.SP.3CCRS.6.SP.4CCRS.6.SP.5

Students will be able tosummarize the measure ofcenter with the median or mean.Students will be able to find theinterquartile range (IQR) from adata set by finding upper andlower quartiles and taking thedifference or from reading a boxplot. Students will develop theseunderstandings of what themean represents byredistributing data sets to belevel or fair (equal distribution)and by observing that the totaldistance of data values abovethe mean is equal to the totaldistance of the data valuesbelow the mean (balancingpoint). Students will be able touse the concept of mean to solveproblems. Students willcalculate the mean given a dataset represented in a frequencytable.

Performance Descriptor

2.4.6.B.2Use numerical data and apply statisticalproperties to summarize and describe adistribution.

Eligible ContentM06.D-S.1.1.4Relate the choice of measures of centerand variability to the shape of the datadistribution and the context in which thedata were gathered.

2.4. Measurement, Data

and ProbabilityCCRS.6.SP.3CCRS.6.SP.4CCRS.6.SP.5

Students understand how

measures of center andmeasures of variability arerepresented by graphicaldisplays. Students will describethe context of the data, using theshape of the data and are able touse this information to determinean appropriate measure ofcenter and measure ofvariability.


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Resources

Sample Task:Calculate and/orexplain how to findthe median, mean, and/or mode andrange, interquartile range, and/ormean absolute deviation.UnderstandDevelop

Sample Task:Analyze and interpret howmeasures of center and measures ofvariability from a graphicalrepresentationCritiqueApply Concepts


Sample Task:

Explain how measures of center andmeasures of variability arerepresentedRecognizeArticulate

Sample Task:

Analyze how measures of centerand measures of variability arerepresentedDraw conclusionsSummarize


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In the beginning of this quarterstudents willformulas. Students will understand that expressiexpressions in equivalent forms, and identify solsimple one-step equations and construct and aunderstand that a data distribution may not havmay yield different values. Students will understvariability can be used to summarize data. Theyclusters, peaks, gaps, and symmetry within the

By the end of this quarterstudents will be abland understand properties of three-dimensionalof operations to generate equivalent expressionand algebraic expressions and equations. Studa population, draw informal comparative inferenwill develop, use, and evaluate probability modeare: circumference, diameter, pi, parallel, peexpressions, maximum, minimum, relevant ipopulation, representative sample, inferencmeasures of variability, sample space.

nderstand, write, and evaluateions in different forms can be eq lutions of equations. They will usalyze tables to describe relationa definite center and that the v

and measures of central tendenwill describe and summarize nu

context in which the data was co

to solve problems involving cirshapes and their related parts.s and solve real-life and mathents will be able to use random s

ces about two populations and ils. The terms students should lependicular, skew, numeric exnformation, irrelevant informas, variation/variability, distrib

ariable expressions usinguivalent.They will rewritee properties of operations to solveships between quantities. They willrious ways to measure centery and recognize that measures ofmerical data sets, by identifyingllected.

umference and area of a circlehey will be able to use propertiesatical problems using numericalampling to draw inferences aboutvestigate chance processes. Theyarn to use with increased precisionressions, algebraicion, random sampling,tion, measures of center,




Performance Descriptor2.4.6.B.2Use numerical data and apply statisticalproperties to summarize and describe adistribution.

Eligible ContentM7.E.1.1.1Analyze data and/or answer questionspertaining to data represented inhistograms, double bar graphs, multipleline graphs or stem-and-leaf plots.


Students will be able toorganize and display datausing an appropriate datadisplay, such as histograms,line graphs, double bar graphs,and stem-and-leaf plots.

Performance Descriptor2.4.7.B.1Draw inferences about populations basedon random sampling concepts

Eligible ContentM07.D-S.1.1.2Use data from a random sample to drawinferences about a population with anunknown characteristic of interest.

Example 1: Estimate the mean word lengthin a book by randomly sampling words

from the book.Example 2: Predict the winner of a schoolelection based on randomly sampledsurvey data.

2.4. Measurement, Dataand ProbabilityCCRS.7.SP.1CCRS.7.SP.2

Students will collect and usemultiple samples of data todraw inference from the data.Students will use thisinformation to draw inferencefrom the data. A randomsample must be used inconjunction with the populationto get accuracy.


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Standards of Mathematical Practice

solving them; Use appropriate tools stand quantitatively; Model with matherepeated reasoning.

Non-Negotiables: Make sense of pro

ategically; Look for and make use of satics; Attend to precision; Look for and

blems and persevere in

ructure; Reason abstractlyexpress regularity in



Resources

Sample Task:Interpret and explain data shown incomplex data displays; answerquestions that addresses the data.FormulateOrganize

Sample Task:Use numerical summaries todescribe different sets of data;interpret trends and makepredictions based on data displayedin a graph; use measures of centraltendency and spread to comparedata sets.DesignAnalyze


Sample Task:Collect random samples to use inconjunction with the population tomake accurate predictions about apopulation.Assess

Sample Task:Formulate hypothesis, drawconclusions, and make convincingarguments based on data analysis.JudgeDefend


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In the beginning of this quarterstudents willformulas. Students will understand that expreexpressions in equivalent forms, and identify ssimple one-step equations and construct andunderstand that a data distribution may not hamay yield different values. Students will undervariability can be used to summarize data. Thclusters, peaks, gaps, and symmetry within th

By the end of this quarterstudents will be aand understand properties of three-dimensionof operations to generate equivalent expressiand algebraic expressions and equations. Stua population, draw informal comparative inferThey will develop, use, and evaluate probabiliprecision are: circumference, diameter, pi,expressions, maximum, minimum, relevanpopulation, representative sample, inferenmeasures of variability, sample space.


ve a definite center and that thestand measures of central tendey will describe and summarizecontext in which the data was

le to solve problems involving cial shapes and their related partsns and solve real-life and mathdents will be able to use randomnces about two populations andy models. The terms students sarallel, perpendicular, skew,information, irrelevant informes, variation/variability, distri

variable expressions usingquivalent.They will rewritese properties of operations to solvenships between quantities. They willvarious ways to measure centerncy and recognize that measures ofumerical data sets, by identifyingollected.

ircumference and area of a circle. They will be able to use propertiesmatical problems using numericalsampling to draw inferences aboutinvestigate chance processes.ould learn to use with increasedumeric expressions, algebraication, random sampling,bution, measures of center,




Performance Descriptor2.4.7.B.2Draw informal comparative inferencesabout two populations.

Eligible ContentM07.D-S.2.1.1Compare two numerical data distributionsusing measures of center and variability.

Example 1: The mean height of playerson the basketball team is 10 cm greaterthan the mean height of players on the

soccer team. This difference is equal toapproximately twice the variability (meanabsolute deviation) on either team. On aline plot, note the difference between thetwo distributions of heights.Example 2: Decide whether the words ina chapter of a seventh-grade sciencebook are generally longer than the wordsin a chapter of a fourth grade sciencebook. Relate the choice of measures ofcenter and variability to the shape of thedata distribution and the context in which

the data were gathered

2.4. Measurement, Dataand ProbabilityCCRS.7.SP.3

CCRS.7.SP.4

Students will develop a fullunderstanding of the datarequires consideration of themeasures of variability as well asmean or median. Variability isresponsible for the overlap oftwo data sets and that anincrease in variability canincrease the overlap and medianis paired with the interquartilerange and mean is paired withthe mean absolute deviation(MAD). Students will compare

two sets of data using measuresof center (mean and median)and variability MAD.


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Standards of Mathematical Practice

solving them; Use appropriate tools stand quantitatively; Model with matherepeated reasoning.

Non-Negotiables: Make sense of pro

ategically; Look for and make use of satics; Attend to precision; Look for and

blems and persevere in

ructure; Reason abstractlyexpress regularity in



Resources

Sample Task:Give quantitative measures of center(median and/or mean) and variability(interquartile range and/or meanabsolute deviation), as well asdescribe any overall pattern and anystriking deviations from the overallpattern with reference to the contextin which the data were gathered.AnalyzeCite Evidence

Sample Task:Evaluate arguments that are basedon statistical claims. Relate thechoice of measures of center andvariability to the shape of the datadistribution and the context in whichthe data were gathered.AppraiseSupport



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Performance Descriptor2.4.7.B.3Investigate chance processes anddevelop, use, and evaluate probabilitymodels.

Eligible ContentM07.D-S.3.1.1Predict or determine whether someoutcomes are certain, more likely, lesslikely, equally likely, or impossible (i.e., aprobability near 0 indicates an unlikelyevent, a probability around 1/2 indicatesan event that is neither unlikely nor likely,and a probability near 1 indicates a likelyevent).

2.4. Measurement, Dataand ProbabilityCCRS.7.SP.5

Students recognize that theprobability of any single eventcan be expressed in terms suchas impossible, unlikely, likely, orcertain or as a number between0 and 1. Students willunderstand that the probability ofa chance event is a numberbetween 0 and 1 that expressesthe likelihood of the eventoccurring. Larger numbersindicate greater likelihood.


Eligible ContentM07.D-S.3.2.1Determine the probability of a chance

event given relative frequency. Predictthe approximate relative frequency giventhe probability.

Example: When rolling a number cube600 times, predict that a 3 or 6 would berolled roughly 200 times, but probably notexactly 200 times.


Students will approximate theprobability of a chance event bycollecting data on the chanceprocess that produces it andobserving its long-run relativefrequency, and predict theapproximate relative frequencygiven the probability.


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Resources

Sample Task:Discuss that a probability near 0indicates an unlikely event, aprobability around 1/2 indicates anevent that is neither unlikely norlikely, and a probability near 1indicates a likely event.Explain

Sample Task:Support assertions of the likelihoodof a simple real-world eventoccurring.Validate


Sample TaskPredict and compare results usingboth experimental and theoreticalprobability drawn from real-worldproblems.Investigate

Sample TaskDevelop a probability model and useit to find probabilities of events.Compare probabilities from a modelto observed frequencies; if theagreement is not good, explainpossible sources of the discrepancy.DesignAppraise


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Eligible ContentM07.D-S.3.2.2Find the probability of a simple event,including the probability of a simple eventnot occurring.

Example: What is the probability of notrolling a 1 on a number cube?


Students will be able to defineand identify what is meant by anexperiment, construct samplespaces and identify events,calculate probabilities of simpleevents, and apply the equallylikely assumption of probability.


Eligible ContentM07.E.3.1.3Use data displayed in charts, graphs, or

tallies to find experimental probability.


Students will be able to find andinterpret the experimental of anoutcome of a simple event.


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Non-Negotiables: Make sense of prorategically; Look for and make use of satics; Attend to precision; Look for and




Resources

Sample Task:Construct probability models thatshow all the possible outcomes of anevent as an organized list, table, ortree diagram, as well as show thecomplement of the event.Create

Sample Task:Analyze the results of a simpleprobability experiment to makepredictions, then compare thepredictions to the outcomes of theexperiment, and replicate theexperiment to compare results..InvestigateEvaluate


Sample TaskUnderstand and/orapply basicconcepts of probability or outcomes.ArticulateExplain

Sample TaskFormulate predictions and/ordrawconclusions based on probability.Apply Concepts


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Eligible ContentM07.D-S.3.2.3Find probabilities of independentcompound events using organized lists,tables, tree diagrams, and simulation.


Students will understand that,just as with simple events, theprobability of a compound eventis the fraction of outcomes in thesample space for which thecompound event occurs.Represent sample spaces forcompound events using methodssuch as organized lists, tablesand tree diagrams. For an eventdescribed in everyday language(e.g., "rolling double sixes"),identify the outcomes in thesample space which composethe event. Students will use treediagrams, frequency tables, andorganized lists, and simulationsto determine the probability ofcompound events.


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Resources

Sample Task:Explain the probability of acompound event is the fraction ofoutcomes in the sample space forwhich the compound event occurs.Identify the outcomes in the samplespace which compose the event.DiscussSelect

Sample Task:Design and use a simulation togenerate frequencies for compoundevents. For example, use randomdigits as a simulation tool toapproximate the answer to thequestion: If 40% of donors have typeA blood, what is the probability that itwill take at least 4 donors to find onewith type A blood?CreateApply Concepts



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Performance Descriptor2.2.7.B.3Model and solve real-world andmathematical problems by using andconnecting numerical, algebraic, and/orgraphical representations.

Eligible ContentM07.B-E.2.3.1Determine the reasonableness of ananswer(s), or interpret the solution(s) inthe context of the problem.

Example: If you want to place a towel barthat is 9 3/4 inches long in the center of adoor that is 27 1/2 inches wide, you willneed to place the bar about 9 inchesfrom each edge; this estimate can beused as a check on the exactcomputation.

2.2 Algebraic Concepts7.EE.3

Students will expressquantitative relationships byusing algebraic terminology,expressions, equations,inequalities, and graphs todetermine the reasonableness ofan answer and to interpret thesolution. Students will know thedifference between relevant andirrelevant information whensolving problems. Understandthat some ways of representinga problem are more efficient thanothers, and interpret informationcorrectly, identify the problem,and generate possible strategiesand solutions.


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Resources

Sample Task:Justify if an answer is reasonable byusing estimation and mental math.Use estimation strategies forcalculations with fractions anddecimals. Use variables to constructsimple equations and inequalitiesand solve problems in context.CreateSupport

Sample Task:Apply properties of operations,factorlinear expressions withrational coefficients, expand linearexpressions with rational coefficients,write an expression in differentforms, and understand how rewritingan expression in different forms canshow how the quantities in a problemare related.FormulateConnect



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Core Curriculum Mathematics - Grade 7

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Transcript of Core Curriculum Mathematics - Grade 7