Statistics and probability - UBC Blogs



centercenterstatistics and probability mathematicsGrade 4/5 – Bothwell ElementaryTanya WinshipUniversity of British Columbia9410077300statistics and probability mathematicsGrade 4/5 – Bothwell ElementaryTanya WinshipUniversity of British ColumbiaTable of ContentsUnit Rationale2Guiding Goals2Assessment3Curriculum Connections4Unit Timeline7Unit Overview8Extensions and Adaptations14Statistics and ProbabilityGrade Level: 4/5 Timeline: 3 weeksUnit RationaleThis unit focuses on Prescribed Learning Outcomes in Mathematics for both grades 4 and 5. The unit itself may vary slightly in order to meet these outcomes for each grade. This unit will largely be an introductory unit to the topic and will allow students to begin to understand what probability is and how statistics are used. The basic premise for the unit is to allow students to make connections to other areas of mathematics (rates, percentages, fractions, and data). This unit will be based on a number of hands-on, interactive activities that may be different than traditional math lessons; students will engage in experimentation and exploration and will determine if reality matches up to mathematical assumptions. Guiding GoalsThe Prescribed Learning Outcomes for this unit vary between grades 4 and 5 (as described below).The guiding goals for this unit have been taken from the BC Ministry of Education curriculum document. Grade FourD1 demonstrate an understanding of many-to-one correspondenceD2 construct and interpret pictographs and bar graphs involving many-to-one correspondence to drawconclusions Grade FiveD1 differentiate between first-hand and second-hand data D2 construct and interpret double bar graphs to draw conclusions D3 describe the likelihood of a single outcome occurring using words such as impossible, possible, certain D4 compare the likelihood of two possible outcomes occurring using words such as less likely, equally likely, more likelyAssessmentAssessment for this unit will surround participation and understanding on in-class activities. There will also be required completion and understanding through worksheets, textbook work, a group project, quizzes, and a final test. I will use the following questions to guide my assessment:Can the student distinguish between events that are likely or unlikely, possible or impossible, probable or improbable, certain or uncertain?Can the student use the terminology of probability appropriately when describing his or her thinking about activities in the unit?Can the student interpret measures if chance in real-world contexts, such as understanding the implication of a weather report that indicates an 80 percent chance of rain or knowing that 50-50 means the chance of winning is the same for both teams?Can the student assign numerical probabilities to outcomes – for example, that the probability of getting heads when a penny is tossed 1 out of 2 (1/2) or 50 percent, or that the chance of drawing a yellow tile from a bag out of four tiles, one yellow, one blue, one green, and one red, is 1 out of 4 (1/4) or 25 percent?Can the student interpret and use statistical data to make conjectures about probability activities?Can a child formulate theories about the probabilities of situations, such as “This is more likely because…” or “They’re equally likely because…”?Curriculum ConnectionsGr. 4 – Mathematics Prescribed Learning OutcomesSuggested Achievement IndicatorsIt is expected students will be able to…D1? demonstrate?an?understanding?of?many‐to‐one?correspondence compare?graphs?in?which?different?intervals?or?correspondences?are?used?and?explain?why?the?interval?or?correspondence?was?used? compare?graphs?in?which?the?same?data?has?been?displayed?using?one‐to‐one?and?many‐to‐one?correspondences,?and?explain?how?they?are?the?same?and?different? explain?why?many‐to‐one?correspondence?is?sometimes?used?rather?than?one‐to‐one?correspondence? find?examples?of?graphs?in?which?many‐to‐one?correspondence?is?used?in?print?and?electronic?media,?such?as?newspapers,?magazines?and?the?Internet,?and?describe?the?correspondence?used?D2? construct?and?interpret?pictographs?and?bar?graphs?involving?many‐to‐one?correspondence?to?draw?conclusions? identify?an?interval?and?correspondence?for?displaying?a?given?set?of?data?in?a?graph?and?justify?the?choice? create?and?label?(with?categories,?title,?and?legend)?a?pictograph?to?display?a?given?set?of?data?using?many‐to‐one?correspondence,?and?justify?the?choice?of?correspondence?used? create?and?label?(with?axes?and?title)?a?bar?graph?to?display?a?given?set?of?data?using?many‐to‐one?correspondence,?and?justify?the?choice?of?interval?used? answer?a?given?question?using?a?given?graph?in?which?data?is?displayed?using?many‐to‐one?correspondenceGr. 5 – MathematicsPrescribed Learning OutcomesSuggested Achievement IndicatorsIt is expected students will be able to…D1differentiate between first-hand and second-hand dataexplain the difference between first-hand and second-hand dataformulate a question that can best be answered using first-hand data and explain whyformulate a question that can best be answered using second-hand data and explain whyfind examples of second-hand data in print and electronic media, such as newspapers, magazines, and the internetD2construct and interpret double bar graphs to draw conclusionsdetermine the attributes (title, axes, intervals, and legend) of double bar graphs by comparing a given set of double bar graphsrepresent a given set of data by creating a double bar graph, label the title and axes, and create a legend without the use of technologydraw conclusions from a given double bar graph to answer questionsprovide examples of double bar graphs used in a variety of print and electronic media, such as newspapers, magazines, and the internetsolve a given problem by constructing and interpreting a double bar graphD3describe the likelihood of a single outcome occurring using words such asimpossiblepossiblecertainprovide examples of events that are impossible, possible, or certain from personal contextsclassify the likelihood of a single outcome occurring in a probability experiment as impossible, possible, or certaindesign and conduct a probability experiment in which the likelihood of a single outcome occurring is impossible, possible, or certainconduct a given probability experiment a number of times, record the outcomes, and explain the resultsD4compare the likelihood of two possible outcomes occurring using words such asless likelyequally likelymore likelyidentify outcomes from a given probability experiment which are less likely, equally likely, or more likely to occur than other outcomesdesign and conduct a probability experiment in which one outcome is less likely to occur than the other outcomedesign and conduct a probability experiment in which one outcome is equally as likely to occur as the other outcomedesign and conduct a probability experiment in which one outcome is more likely to occur than the other outcomeMONDAYTUESDAYWEDNESDAYTHURSDAYFRIDAYMarch 31st Lesson 1: Interpreting GraphsApril 1st Lesson 2: Statistics, What are they and how are they used?April 2nd Lesson 3: Statistics, Connecting them to the Real WorldApril 3rd Lesson 4: Connecting Statistics to ProbabilityApril 4th Lesson 4 (cont’d)April 7th Lesson 5: StationsApril 8th Lesson 5 (cont’d)April 9th Lesson 6: Language of Probability, Single OutcomesApril 10th Lesson 7: Comparing OutcomesApril 11th Lesson 8: ReviewApril 14th Lesson 8 (cont’d)April 15th Lesson 9: Create a Chance GameApril 16th Lesson 10: Wrap-UpApril 17th Unit TestApril 18th NO SCHOOLUnit TimelineUnit OverviewTopicLearning Outcomes(SWBAT)ActivitiesMaterialsAssessment1Interpreting Graphs: A Review- apply prior knowledge of bar/line graphs- illustrate different ways to share informationShow students a number of graphs (line graph, bar graph, pie chart). Ask students what they can tell from each graph. Demonstrate different ways to collect information.Worksheet on graphing (collecting and analyzing data, completing graphs).SMARTBoardExamples of various graphsWorksheetWriting toolsColouring toolsobservation of participationworksheet2Statistics: What are they and how are they used?- apply prior knowledge of bar/line graphs- illustrate different ways to share information- explain how and why they collected their dataExplain what “statistics” are, connect to prior knowledge of graphing.Each student should then come up with a question and 3-4 possible responses to ask their classmates (i.e. What is your favourite colour?) Students will then go around and survey their classmates. After they have surveyed the entire class, they must create a graph that represents the data they have collected.Time permitting, students will share their findings with the class. Writing toolsGraph paperColouring toolsparticipation and completion of surveyaccurate completion of corresponding graph3Statistics: Connecting them to the Real World- understand how and why statistics are used (census, development)- draw connections to the real worldUse real-life examples to get students to think about statistics, such as census, weather information, development of new buildings. Worksheet on real-life examples/journal entry. contribution of ideas to class discussioncompleted worksheetjournal entry4Connecting Statistics to Probability - access prior knowledge re: fractions- understand the difference between statistics and probabilityProvide examples of questions (such as those asked by the students when collecting data). Without the data, what were the chances that I would pick “pink” (for example)? Explain that chance connects to the number of options available, like a fraction. The “chance” of choosing something is related to the number of each choice compared to the total number of options.Do some examples as a class using the SMARTBoard.Worksheet or textbook work.Question examples (student work)SMARTBoardWorksheet (or textbook)Writing toolsaccurate completion of work5Connecting Statistics to Probability (cont’d)- understand the difference between statistics and probability- demonstrate knowledge by completing a number of activities Review work from previous day. Address any issues or questions. Collect work to be checked. Explain today’s activity: we are going to do some activities surrounding chance. Will the results match the chance? (i.e. If I roll a die 6 times, will I get each of the possible results?) Have students write down their predictions. Explain that students will be divided into 5 groups and will move from station to station. At each station, they will complete a chance activity and record their results. Divide students into 5 groups. Each station will include a card explaining the activity, explain the “rules,” and provide the probability for each outcome. Students must record the outcome (as provided) and their results. {For this activity, each probability should be 1/total.}Station 1: Draw a card from a deck. What are the odds the card is red? Black? Station 2: Pull a ball out of a bag. What are the odds the ball is a specific colour?Station 3: Spinners – What are the odds I will land on a specific number/colour? Station 4: Dice – What are the odds I will roll each number?Station 5: Heads or Tails – If I flip a coin, what are the odds that I will get heads? Tails?After the students have spent 10 minutes at each station, bring the students back to their seats. Ask the students what surprised them the most? The least? What were their results? Did any of their results match the predicted outcome? Students should then complete an exit slip, sharing one of their aha moments from the day (answering one of the above questions). Students should hand in their workbook (including predictions and exit slips). Instruction sheets for each station5 decks of cards5 bags with 4 different coloured balls5 spinners with pointers or paper clips5 dice5 coinsWorkbookWriting toolsparticipation in activitiescompletion of workbook (must be handed in and must be neatly recorded)predictionsexit slips6Language of Probability: Single Outcomes- accurately describe outcomes as possible, impossible, improbable, or probableGive each student a die. Ask the students to roll a 7. What about a 0? Students may need to try, but most will inherently respond, “it’s impossible!”Introduce the terms possible, impossible, and probable, explaining what each one means. Brainstorm with students situations in which the outcome would be impossible, probable, possible, or improbable. Worksheet or textbook work, labelling outcomes as probable, improbable, possible, or impossible. Dice, one for each studentSMARTBoardWorksheet (or textbook)Writing toolscontribution to brainstorm activityaccurate completion of work7Language of Probability: Compared to Other Outcomes- use equally likely, less likely, or more likely to describe possible outcomes- understand when they would use likely, unlikely, or equally likely compared to when to use impossible, possible, probableShow students a number of spinners. Ask students what the possible outcomes are for each of them. See if students can recognized that if the pieces are not equal (the same size) or if there are more of one number or colour, the chances of landing on that piece are higher. Explain to students that in the last class’ activity, each of the possible outcomes was “equally likely” to occur.Give each group a spinner and see if they can accurately label it as equally likely or not. If it is not equally likely, what is it?Ask students to share their thoughts. Explain that outcomes may be more likely or less likely than others based on circumstances. Brainstorm some things that may be more likely or less likely to occur. Worksheet or textbook work, labelling outcomes as unlikely, equally likely, or more likely. 5-8 spinners, each with different possible outcomesSMARTBoard (with spinners on notebook)Worksheet (or textbook)Writing toolscontribution to class discussionparticipation in spinner activityaccurate completion of work8Review of Probability- use time wisely to review concepts and materialStudents should use this time to ask questions, confirm understanding, and review information. Students will complete a review package, to be handed in in advance of the unit test. Review packageWriting toolsColouring toolscompletion of review package (to be graded)9Create a Chance Game- complete review package- work with others to create a game that demonstrates understanding of chanceOnce students have completed their review package, they may work in groups (up to 3 people) to create a game of chance.The game must have a set of rules and should include a section in the rules that explains why or how it is a game of chance. Review packageOutlines for board gamesMaterials for gamesWriting/Colouring toolsapplication of knowledge towards creation of game10Wrap-Up- complete all work for unit- engage in further chance games/activitiesStudents must complete their review package. Students may continue to work on their games of chance.Students who are finished will be free to play each others’ games. Students who have completed their review package will also use this time to work with the teacher to conference about areas they may need more help with. Chance gamesReview packageWriting tools11Unit Test- demonstrate knowledge of all conceptsStudents will write the unit test, exploring topics of both statistics (data) and probability or chance. Unit TestWriting toolsgraded unit test Extensions and AdaptationsThere is some time built into this unit should lessons be longer than anticipated. Quizzes may also be used to assess students’ understanding as we go through the unit. The completion of the group project (create a game of chance) is negotiable and may not be used for assessment purposes. In order to address students who may require adaptations or modifications, they will be addressed on an individual basis. Students with IEPs will be considered in regards to completion of the overall unit. As the grade 4s are not required to learn probability, this will be taken into consideration when assigning a final grade for the unit. It also may affect their unit test, which will place a heavier emphasis on statistics and use of data. ................
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