34 sorting the mix cover 2017nov8 - inside mathematics the... · and solving non-routine problems...

ProblemoftheMonth SortingtheMix Page1©SiliconValleyMathematicsInitiative2014.ThisworkislicensedunderaCreativeCommonsAttribution-NonCommercial-NoDerivatives3.0UnportedLicense(http://creativecommons.org/licenses/by-nc-nd/3.0/deed.en_US).

Problem of the Month: Sorting the Mix

TheProblemsoftheMonth(POM)areusedinavarietyofwaystopromoteproblemsolvingandtofosterthefirststandardofmathematicalpracticefromtheCommonCoreStateStandards:“Makesenseofproblemsandpersevereinsolvingthem.”ThePOMmaybeusedbyateachertopromoteproblemsolvingandtoaddressthedifferentiatedneedsofherstudents.AdepartmentorgradelevelmayengagetheirstudentsinaPOMtoshowcaseproblemsolvingasakeyaspectofdoingmathematics.POMscanalsobeusedschoolwidetopromoteaproblem-solvingthemeataschool.Thegoalisforallstudentstohavetheexperienceofattackingandsolvingnon-routineproblemsanddevelopingtheirmathematicalreasoningskills.Althoughobtainingandjustifyingsolutionstotheproblemsistheobjective,theprocessoflearningtoproblemsolveisevenmoreimportant.TheProblemoftheMonthisstructuredtoprovidereasonabletasksforallstudentsinaschool.ThestructureofaPOMisashallowfloorandahighceiling,sothatallstudentscanproductivelyengage,struggle,andpersevere.ThePrimaryVersionisdesignedtobeaccessibletoallstudentsandespeciallythekeychallengeforgradesK–1.LevelAwillbechallengingformostsecondandthirdgraders.LevelBmaybethelimitofwherefourthandfifthgradestudentshavesuccessandunderstanding.LevelCmaystretchsixthandseventh-gradestudents.LevelDmaychallengemosteighthandninth-gradestudents,andLevelEshouldbechallengingformosthighschoolstudents.Thesegrade-levelexpectationsarejustestimatesandshouldnotbeusedasanabsoluteminimumexpectationormaximumlimitationforstudents.Problemsolvingisalearnedskill,andstudentsmayneedmanyexperiencestodeveloptheirreasoningskills,approaches,strategies,andtheperseverancetobesuccessful.TheProblemoftheMonthbuildsonsequentiallevelsofunderstanding.AllstudentsshouldexperienceLevelAandthenmovethroughthetasksinordertogoasdeeplyastheycanintotheproblem.TherewillbethosestudentswhowillnothaveaccessintoevenLevelA.Educatorsshouldfeelfreetomodifythetasktoallowaccessatsomelevel.OverviewIntheProblemoftheMonth,SortingtheMix,studentsusemathematicalconceptsofstatisticsincludingaverage,consistency,andoptimization.ThemathematicaltopicsthatunderliethisPOMaremeasuresofcenter,measuresofdispersion,thedistributionofdata,andtheinterpretationofdatasets.Thelaterlevelsinvolvemixtureproblemsthatrequirestudentstounderstandrateasameasure.Mixtureproblemsinvolveunderstandingasetofunknownsandasetofconstraints.Studentsuseequationstodeterminethevaluesofunknowns.InLevelAofthePOM,studentsexamineandmakesenseofadatasetaroundthemeasuresofcenterandtherange.InLevelB,thestudentsaregiventwosetsof

ProblemoftheMonth SortingtheMix Page2©SiliconValleyMathematicsInitiative2014.ThisworkislicensedunderaCreativeCommonsAttribution-NonCommercial-NoDerivatives3.0UnportedLicense(http://creativecommons.org/licenses/by-nc-nd/3.0/deed.en_US).

temperaturesfromcitiesinthecoldestpartsofthelower48UnitedStates.ThedataincludessignnumbersoftemperaturesreadinginCelsius.Studentsaretomakeargumentswhyonecityiscolderthantheothercity.Theythenhavetousethesamedatatomakethereverseargument.InLevelC,studentsinvestigateaprobleminvolvingthestatisticalmeasureofthemean.Theyusetheirconceptualunderstandingofthatmeasuretosolveproblems.InLevelD,theproblemisposedthatanallgirls’schoolinvitesabusloadofboysfromanallboys’schooltoadance,thenthebustakesasame-sizeloadofstudents,boysandgirls,backtotheboys’schooldance.Thequestioniswhichschoolhasagreaterratioofonegendertotheother.InLevelE,thestudentsaregivenfourproblemsthatinvolvemixtures.Thestudentsaretosolvetheproblemsandexplainthesolutionssothatthecharactersintheproblemconceptuallyunderstandthemathematics.MathematicalConceptsStatisticalmeasuresareusedtofindthecenter,middleortypicalvalueofasetofdata.Oftenthisvalueisreferredtoastheaverageofthedata.Instatistics,thereareseveralmeasuresthatmaybeusedtorepresenttheaverageofasetofdata.Themostcommonofthesearecalledmeasuresofcenterandincludethemean,themedian,themode,andthemidrange.

Problem of the Month Sorting the Mix Page 1 © Silicon Valley Mathematics Initiative 2009. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 Unported License (http://creativecommons.org/licenses/by-nc-nd/3.0/deed.en_US).

LevelAMs.Gavinaskedherclasstomakeachartofthepeoplewholivedwiththem,includingthestudentsthemselves.Thenineteenstudentseachrecordedtheirnumberinthefollowingchart.

8 4 2 10 4 5 66 3 6 8 7 3 52 6 8 6 4

Whatisthemostcommonnumberofpeoplewholivetogether(mode)?Explain.Whatisthemiddlenumberifallnumberswerearrangedinorder(median)?Showhowyoufigureditout.Supposetwonewstudentsjoinedtheclass.Theyeachaddthenumberofpeoplewholiveintheirhomestothechart.Themiddlenumbernowswitchedtoadifferentnumber.Whatnumberscouldhavebeenadded?Explain.Notonlydidthemiddlenumberchange,butnowthemostcommonnumberalsochanged.Whichnumberscouldhavebeenadded?

Problem of the Month

Sorting the Mix


Youfindoutthatthemiddlenumberchangedtoasmallernumber;whatisthenewmiddlenumber?Whatisthenew,mostcommonnumber?Whatnumberswereadded?Howdoyouknowforsure?


LevelBTwodifferentcitiesinthelower48statesofAmericaclaimtheyarethecoldestcities.ThecitiesareRogersPass,Montana,andPeter’sSink,Utah.Belowaretablesthatindicatetheminimumandmaximumtemperatureforeachmonthlastyear.AlltemperaturesaremeasuredinCelsius. Rogers Pass,

Montana Minimum

Temperature Maximum

Temperature Jan -12 0 Feb -9 3 Mar -6 7 Apr -1 12 May 3 17 Jun 7 22 Jul 10 26 Aug 9 26 Sep 4 20 Oct 0 14 Nov -6 5 Dec -10 1 Analyzethetemperaturesinthetables.Comparethetwocities.Whichcitywouldyousaywasthecoldestinthelowerforty-eightstates?Usemathematicaldatatosupportyourclaimandexplainyourreasoning.Supposetherewasacontesttobenamedthecoldestcityinthelowerforty-eight.IfyouwerethemayorofRogersPass,whatargumentwouldyoumaketoconvincethejudgesyourcitywasthecoldest?IfyouwerethemayorofPeter’sSink,whatargumentwouldyoumaketoconvincethejudgesyourcitywasthecoldest?

Peter's Sink, Utah

Minimum Temperature

Maximum Temperature

Jan -13 1 Feb -7 4 Mar -6 6 Apr -2 10 May 4 18 Jun 6 21 Jul 12 28 Aug 7 26 Sep 4 19 Oct -1 16 Nov -7 4 Dec -9 3


LevelCAsurveyof14middleschoolstudentsshowedthemeannumberofminutesstudentstalkedonthecellphonesinaweekwas133.Whatisthetotalnumberofminutesthosestudentstalkedinaweek? Whatwasthetypicalamountoftimeastudenttalkedinaday?Explain.Anothersurveyaskedthesame14studentsplus5otherstudentshowlongtheytalkedforthesameweek.Thissurveysaidthemeannumberofminutesallthestudentstalkedwas171minutes.Whatwasthemeannumberofminutestheadditional5otherstudentstalked?Showyoursolution.Whatwasthetypicalamountoftimeoneofthe5studentstalkedinaday?Explain.


LevelDTherearetwoschoolsandbothschoolshavethesamenumberofstudents.HillaryHighisanall-girlschool.BarackAcademyisanall-boyschool.Eachschoolisholdingadance.AbusiscompletelyfilledwithboysfromtheAcademyandthebustakestheboysovertoHillaryHightoattendthedance.Afteranhour,studentsfromthedanceincludingbothgirlsandboysdecidetogoovertothedancethatisbeingheldatBarackAcademy.Thesamebusisfilledwithacombinationofboysandgirls.TheytravelbackovertoBarackAcademytoattendthatdance.

Atthattime,doesHillaryHighhavemoreboysoncampusthanBarackAcademyhavegirlsoncampus,orisittheotherwayaround?Explain.


LevelEYouworkforafooddistributor.Youarethemathematicianattheheadquarters.Youcomeinthemorningandyougetthesefouremails.Pleaseanswereachemailandexplainyourreasoning,sothatinthefuturetheycanfigurethesethingsoutontheirownandyouwon’tcontinuallybebotheredbytheserequests.EmailfromPonchoBuenoHelp!!Twohundredlitersofapunchthatcontain35%fruitjuicewasmixedwith300litersofanunknownpunch.Wefoundthemixtureisnow20%fruitjuice.Canyoupleasetelluswhatpercentoffruitjuicewasinthe300litersofunknownpunch?Weneedtoknowsothismistakewon’tbemadeagain.EmailfromMelK.SnaxHopeyoucananswerthisquestion,becauseweneeditASAPinordertogetourpackaginglabeledcorrectly.Weaddedanadditionaltengramsofsugartoa40gramservingofourFlakeyOatsbreakfastcereal.Thatcerealcomesnaturallywith30%sugar.Whatisthepercentconcentrationofsugarinthecerealnow?Weneedthatpercentageforthelabelonthebox.EmailfromEdA.BullHey,wehaveapricingprobleminproduce.Weneedtocreateavegetablemedleyoflimabeansandcornthatcosts65centsperpound.Wehavealreadyadded16poundsofcornthatcosts50centsperpound.Wehavelimabeansthatcost90centsapound.Howmanypoundsoflimabeansshouldweaddtomakethepriceright?Pleaseletusknowquicklyasthesevegetablesperishquickly.EmailfromO.J.EnglassTheyaddedanewworkertoourforce.Withoutknowingit,hemixedan800-litercontaineroftheorangesoda.Buthemadeitsothatitonlyhas15%concentrationoforangejuice.Asyouknow,ourorangesodamusthaveexactly20%concentrationoforangejuice.Howmuchofthe100%concentrationofpureorangejuicedoweneedtoaddtohismixturetomakeitthe20%concentrationrequiredbyourcompany?Pleaseletusknowsoon,beforehegetsusallfired!!!


PrimaryVersionLevelAMaterials:Post-itnotes,classline-plot,individuallineplot,squarecounters,paperandpencil.Discussionontherug:Teachertellstheclass, “We are going to make a special math chart to learn about our class. We call it a line plot, because it looks like a number line.” Teachershowslineplot–seeexample.Teachersays, “I want you to think about how many brothers or sisters each of you have. Some of us don’t have brothers or sisters. How many would that person have as a total?” Studentsrespondandteacherre-voicesandwrites‘zero’onapost-itnote,thenputsthenoteonthelineplotabovezero. “This is how the student would show us on the line-plot.” Theteacherasksanddemonstratesotherexamplesofcalculatingthetotalnumberofsiblings,thenmakesapost-it[withwordsonpost-itsnotnumbers]andfinallyplacesthepost-itsontheline-plot.Theteacherdemonstrateshowtoputonepost-itaboveanotherpost-itifstudentshavethesametotal.Theteacherusesthelanguage‘totalofbrothersandsisters’todistinguishbetweenthefrequencynumberofpost-itsonaparticulartotal.Finally,theteacherclearsthelineplotandasksstudentstorecordtheactualdatawitheachstudentplacingtheirpost-itontheline-plot. Insmallgroups: Eachstudenthasaccesstosquarecountersandaline-plot.Thestudentsaretoldtomakeanexactcopyoftheirclass’line-plot.Teacherchecksandprovideshelp.Theteacherasksthestudentsthefollowingquestions:

Problem of the Month

Sorting the Mix


“Look at our line-plot, when there is no post-it on a total brothers and sisters, what does that mean?” “Which totals are like that on our line-plot?” “Which totals of brothers and sisters happen only once in our class? How do you know?” “Which total of brothers and sisters is most common in our class? How do we know?” “How many of our friends have that same total?” “Can we count to make sure of that number?” Attheendoftheinvestigationhavestudentseitherdiscussordictatearesponsetotheseprompts: “Which total of brothers and sisters happened only once?” “Which total of brothers and sisters happened two times?” “How many of our friends have a total of three brothers or sisters?” “How can we tell by the line-plot?” “Which total of brothers and sisters is most common in our class?” “How do we know?” “How many of our friends have that same total?”


0 1 2 3 4 5 6 7 8

CCSSMAlignment:ProblemoftheMonth SortingtheMix Page1©SiliconValleyMathematicsInitiative2014.ThisworkislicensedunderaCreativeCommonsAttribution-NonCommercial-NoDerivatives3.0UnportedLicense(http://creativecommons.org/licenses/by-nc-nd/3.0/deed.en_US).

ProblemoftheMonth

Sorting the MixTaskDescription–LevelA

This task challenges students to use a data set and solve problems involving the measures of center. The students are presented data from a class about the number of people who live with them. Students examine and make sense using the mean, median and mode.

CommonCoreStateStandardsMath-ContentStandardsMeasurement and Data 1.MD Represent and interpret data. 4. Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

CommonCoreStateStandardsMath–StandardsofMathematicalPracticeMP.1 Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. MP.2 Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. MP.7 Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 x 8 equals the well-remembered 7 x 5 + 7 x 3, in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 x 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.


ProblemoftheMonth

Sorting the MixTaskDescription–LevelB

This task challenges a student to use sign numbers and measures of center to solve problems involving temperatures. The students are presented with a family tree. The students are given two sets of temperatures from cities in the coldest parts of the lower 48 United States. The data includes sign numbers of temperatures reading in Celsius. Students are to make arguments why one city is colder than the other city. They then have to use the same data to make the reverse argument.

CommonCoreStateStandardsMath-ContentStandardsOperations and Algebraic Thinking 3.OA Solve problems involving the four operations, and identify and explain patterns in arithmetic. 8. Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Statistics and Probability 6.SP Develop understanding of statistical variability. 3. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. The Number System 6.NS Apply and extend previous understandings of numbers to the system of rational numbers. 5. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. 7. Understand ordering and absolute value of rational numbers.

CommonCoreStateStandardsMath–StandardsofMathematicalPracticeMP.2 Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. MP.7 Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 x 8 equals the well-remembered 7 x 5 + 7 x 3, in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 x 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.


ProblemoftheMonth

Sorting the MixTaskDescription–LevelC

This task challenges a student to investigate a problem involving the mean of a data set. The students investigate a problem involving the statistical measure of the mean. They use their conceptual understanding of that measure to solve problems. The students have to re-evaluate the mean when more students join the group.

CommonCoreStateStandardsMath-ContentStandardsStatistics and Probability 6.SP Develop understanding of statistical variability. 3. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. Summarize and describe distributions. 5. Summarize numerical data sets in relation to their context, such as by: c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.



ProblemoftheMonth:

Sorting the MixTaskDescription–LevelD

This task challenges a student to investigate a problem involving mixture. The problem is posed that an all girls’ school invites a busload of boys from an all boys’ school to a dance, then the bus takes a same-size load of students, boys and girls, back to the boys’ school dance. The question is which school has a greater ratio of one gender to the other.

CommonCoreStateStandardsMath-ContentStandardsStatistics and Probability 7.SP Use random sampling to draw inferences about a population. 1. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

CommonCoreStateStandardsMath–StandardsofMathematicalPracticeMP.1 Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. MP.4 Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.


ProblemoftheMonth

Sorting the MixTaskDescription–LevelE

This task challenges a student to investigate real-life problems involving mixtures and rates. The students are given four problems that involve mixtures. The students are to solve the problems and explain the solutions so that the characters in the problem conceptually understand the mathematics.

CommonCoreStateStandardsMath-ContentStandardsHigh School – Algebra Creating Equations★ A -CED Create equations that describe numbers or relationships 1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.

CommonCoreStateStandardsMath–StandardsofMathematicalPracticeMP.2 Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. MP.4 Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.


ProblemoftheMonth

Sorting the MixTaskDescription–PrimaryLevel

This task challenges students to represent, determine and compare quantities. The students, as a class, construct a line plot of the number of brothers and sisters they all have. The students copy the line plot and then answer questions about the quantities on the graph.

CommonCoreStateStandardsMath-ContentStandardsMeasurement and Data K.MD Classify objects and count the number of objects in each category. 3. Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. Measurement and Data 1.MD Represent and interpret data. 4. Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. Measurement and Data 2.MD Represent and interpret data. 10. Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put together, take-apart, and compare problems4 using information presented in a bar graph.


34 sorting the mix cover 2017nov8 - inside mathematics the... · and solving non-routine problems...

Documents