Module 46

Module 46Data AnalysisGrades 3 5

Sandra TrotmanIntroduction & ReviewConnecting with the standards: NGSSS Benchmarks for Grades 3 5MA.3.A.4.1 Create, analyze, and represent patterns and relationships using words, variables, tables and graphs.MA.3.S.7.1 Construct and analyze frequency tables, bar graphs, pictographs, and line plots from data, including data collected through observations, surveys, and experiments.Show what you Know!Participants will complete a 5 item Diagnostic test on Data Analysis in elementary school.ReflectionsTake a minute to reflect on this assessment. QuestionsWere some problems easier than others?What factors made them easier?What do you want to learn more about in order to help children understand data analysis?

Reasons for including Data Analysis in Grades 3 - 5

Children encounter ideas of data Analysis outside of school every dayData Analysis provides opportunities for computational activities in a meaningful contextData Analysis provides opportunities for developing collaborative and critical thinking skillsReys, Lindquist, Lambdin & Smith. (2009). Helping children learn math. Wiley.5Steps of Data AnalysisInstructional programs should enable students to:

Formulate and pose a question Collect dataOrganize and display dataAnalyze data and communicate results

6Common MisunderstandingsStudents may:Experience confusion about the meanings of conceptsLack of familiarity with terminologyLack of familiarity with different symbols or problem situations

Question:Are there other misunderstandings that children may have about data analysis?Miscount tally marks in the tally table and write the wrong number in the related frequency table.Computation error when making or using a tableMay not understand what each symbol in a pictograph represents

7Vocabulary PowerUsing Graphic Organizer to review vocab. for this lesson

Vocab. Strategy: Morphemic AnalysisTo paintTo writePictograph Template: http://www.beaconlearningcenter.com/documents/2351_5255.pdf

Go Math Florida, Ch. 2 Definition: A pictograph is a graph that uses symbols to represent data. Students will need to look carefully at the key to determine how many items are represented by each symbol. These are also known as picture graphs. http://www.superteacherworksheets.com/pictograph.html

Strategies for ESOL:Have students look at the graph as you give vocab. practice through questioning: What pictures do you see on the pictographWhat do the pictures stand for?What can you find out by looking at the pictograph?Describe the graph you will make to show the number of boys and girls in your class.

Go Math Florida Grade 3. See Ch 2. Lesson 3 Understand Pictographs pp.69 & 77

9Lets find out!Objective: To plan and conduct a surveySteps:Think of a question you would like to answer:Questions about yourselvesQuestions about opinions or feelingsQuestions about the world(Your input/suggestions)Plan the survey by answering these questions.Where or from whom will I collect the data?How will I collect the data?Your turn.Collect dataOurselves: class typical height/weight/shoe sizeOpinions/Feelings: What should be done about pollution; wghhat is your favorite tv show/song/book/colorWorld: Which month has the most birthdays; popular car/color car ; paper towels consumed in a day

Survey Questions:How much data to collect?When will I collect the data?How will I records the data as it is collected?What else should be done before I collect the data?

10Activity 4: Integrating mathand LiteratureBook: The best vacation ever by S. J Murphy. NY: 1997 A girl with an active, overscheduled family puts math to work to coordinate a family expedition. She uses charts to plot her familys preferences.

This MathStart series demonstrates that collecting data and tabulating results can help the decision-making process.11Data CollectionActivity 5 Collection Methods

Activity 6 Using PictographsMath Forum. http//mathforum.org/mathtools (applets for use in generating data to graph)Super teacher worksheets. a graph.http://www.superteacherworksheets.com/pictograph/elm-street-picto.pdf

ReviewDiscuss what format may be used to complete a review of this session/lesson.

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Module 47

Graphing Data

Benchmarks

MA. 3. A.4.1 Create, analyze, and represent patterns and relationships using words, variables, tables and graphs.MA.3.S.7.1 Construct and analyze frequency tables, bar graphs, pictographs, and line plots from data, including data collected through observations, surveys, and experiments.MA. 5. A.4.2 Construct and describe a graph showing continuous data, such as a graph of a quantity that changes over time.MA. 5. A.7.1 Construct and analyze line graphs and double bar graphs.MA. 5. A.7.2 Differentiate between continuous and discrete data and determine ways to represent those using graphs and diagrams.Vocabulary PowerVocab.: Using Venn DiagramsSort the review words into the Vann diagram.

Graphs Tables

Activity: CompletionComplete the sentences using the list of words.

Participants will create a sentence completion activity that students use to develop vocabulary power.For example,The first value in an ordered pair is the _____________ . (x-coordinate)A Search for PatternsEarly work on graphs can begin with a search for patterns.Use cubes to continue a patternNumber sequence (Odd numbers; Even numbers)SymbolsGrowing patternsEncourage critical thinkingGrowing PatternsUsing Cubes or Connecting Cubes

Creating GraphsKey features Write a clear and descriptive title.Use a uniform scaleMark categories clearlyMake bars the same widthWrite a legend or a keyQuestion: Why is it important for the bars in a Bar graph to be the same width?

Response: To prevent misinterpreting the data

21Double Bar GraphsOn a Double Bar graph, each set of bars uses a different scale. Is this graph useful? Explain!

Response: No, the different scales do not allow for easy comparison of data

22Choosing an Appropriate GraphWhich type of graph is appropriate for displaying discrete data, and which for displaying continuous data?Discrete DataDiscrete data has a countable number of values and can often be classified into categories. Tuesdays attendance at the movie

What data is counted?Into what categories is the data classified?8824738236Movie 1Movie 2Movie 3Movie 4Movie 5The data consists of counted number of people and is classified into categories by show.

* Example, a surveyyes/no response24Continuous DataContinuous data can be measured with and broken down into smaller increments and still have meaning.Make a table to show the length of each participants hand span(Pinkie to the thumb).

0 5 10 15 cmThe lengths can be shown on a number line usingsmaller units such as mm.

Continuous data: hourly temperature (temperature real and measurable between those hours)Line plot deals with numerical data.It is used to organize data on a number line.Organizing data into a line plot allows you to see the range and clustering of data.When developing a line plot, use the data to help choose appropriate intervals and end points.The least and greatest numbers from the data will determine the end points of the scale.You do not always have to begin your scale at 025Activity 2: Which one?A line graph is a good way to display data that changes over time.You can look for trends/patterns/general movement in one direction: increase, decrease, unchanged; (fewer and fewer books were sold each day implies a downward trend)The line in a line represents all values between graphed points. For any point between measurements, a meaningful value can be found by using the line in the line graph.A line graph is an appropriate graph for displaying continuous data over time.26Double bar graph used to compare two similar kind of data.Choose an appropriate scale and increment.The scale should start at 0 and end at a number greater than the highest value.The increments or differences between the values on the scale, should be equal.Whats missing from this graph?27Discrete vs. Continuous DataSusie is growing a lima bean plant for a science experiment. She measures the height of the plant each day at the same time and records her data in a table.STOP & THINK!

Could the data be measured by using smaller units?Is the data counted?Is the data collected continuous or discrete?

Jason is bird watching. He marks a tally for each bird he sees. At the end of the day, he counts the total number of tally marks for each species of bird and records the numbers in his journal.

STOP & THINK!Could the data be measured by using smaller units?Is the data counted?Is the data collected continuous or discrete?

Bar GraphsMostly used for discrete or separate and distinct dataEach bar represents part of the data or the categoryThe length of the bar shows the number of counted values for that categoryEasy to interpret; often use for quick, visual comparisons of categories of data

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Using Technology Participants will:Discuss how these tools might be used with their students.2. Use the tools, and then re-evaluate the benefits to be derived from incorporating the use of such tools in their instructional process.3. Suggest alternative tools and websites that may be used to teach data collection and representation.Creating a Bar GraphParticipants will be given with raw data from a Bar graph and ask to recreate the graph without seeing the original graph.

Participants will compare their graph with the original graph discussing any differences between the two graphs.

Activity Card: DETERMINATIONPurpose: Meeting individual needs to collect and organize data.Give students a series of cards spelling the word DETERMINATION for them to make as many 2, 3, 4, 5, and 6 digit words.Students will complete the table by writing each word under the correct number of letters.Students will shade the number of words made in each column.Students will write at least 2 sentences to describe what they have just created.

Quick & Easy Graphing MaterialsUsing Connecting CubesCounters in an ice tray/egg carton (Yes/No)Paper clips or interlocking linksSelf sticking notes/Post its

Modeling: Using appropriate intervals

EmphasizeChoose a scale and interval that fit the dataYou do not always have to begin your scale with 0.Activity:Model making a line plot for the following data: 40, 31, 20, 32, 61Questions:What numbers determine the lines end points? (20 and 61 or the least and the greatest numbers from the data)Into what interval would it be best to divide the line? units of 10 (Explain!) The difference between the numbers are 20, 30, 4060 is an outlierGive one reason why we should use a line plot to organize data. (see range and clustering of data)

Make a pictograph of student favorite pet.Ask: What symbols would you use?How many students should 1 symbol represent?36Review

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Analyzing and Interpreting DataModule 48Analyzing and Interpreting Data

Benchmark

MA. 3. A.4.1 Create, analyze, and represent patterns and relationships using words, variables, tables and graphs.MA. 3. A.4.2 Construct and describe a graph showing continuous data, such as a graph of a quantity that changes over time.MA.3.S.7.1 Construct and analyze frequency tables, bar graphs, pictographs, and line plots from data, including data collected through observations, surveys, and experiments.Module 48 ObjectivesParticipants will:Discuss what is data sense and how is it developedIdentify goals for teaching Data Analysis in the elementary mathematics curriculumInterpret pictographs and bar graphsAnalyze and compare different graphs that show the same informationUse different strategies and technology to solve problemsCreate an assessment rubric to assess student level of strengths and weaknesses in Data AnalysisReviewing and Extending Collecting and Organizing Data From concrete to symbolic representation

Begin by working with concrete objects in the environmentExample: Favorite fruitCollect, count and sort fruits into categories, then display them in an organized fashion

Concrete to Symbolic representationMove to the Pictorial representationDraw the selected fruit on an index card and form a chain to build a pictographExpress the same information more symbolically by using a bar graphAdditionally, give students a blank paper and encouraged to organize and report their data on the page in a way that makes sense to them.Reys, et. al. (2009), p. 38742Data SenseWhat is data sense and how is it developed?

What should be the goal for teaching Data Analysis?Reys et al. (2009)43Levels of Graph ComprehensionProgression from lower-level to higher-level questionsTeach students to move beyond lower-level thinking and to ask and answer higher-level questions.44Reading the data. Students can answer specific questions to which the answer is prominently displayed.Example, Which bar is the highest?Reading between the data. Students can fins relationships in the data, such as comparison. Example, How many students prefer chocolate to vanilla ice cream?Reading beyond the data. Student can predict or make inferences.Example, What shoe size sells the most? The least? What advice can you give to the show shop owner about purchasing shoes.Data Analysis Word Wall Participants will develop a Word Wall for students to refer to when describing the shape and important features of a set of data, and comparing related data sets

DataMaximumRangeMinimumMostScaleIncreaseDecrease

Participants will develop a word wall for students to refer to when describing the shape and important features of a set of data.Using a Word Wall has proven to be an effective way to teach children how to decode new words. This is a newer way to teach Phonemic Awareness or Phonics.Source: http://makeworksheets.com/samples/langarts/wordwall1.html46Reading Graphs CriticallyParticipants will propose and justify conclusions that are based on the data. (E.g., Why the data look the way they do?)Interpreting GraphsQuestions:What do you notice about the graph, the shape of the data in the graph, predict outcomes or what the data might be.Encourage students to:ExplainDescribeAnalyzeProblem Solving TipsAn appropriate problem solving environment provides opportunities for questioning:What information in the graph is not needed to answer a question?How can making a model help you find the range of a problem? (Pictograph/key)How can making a list help you find the .?What part of the graph tells you what the point means?Insufficient or too much informationGiven a problem, participants will discuss how they can help students determine if all the information is given; and what is missing.Participants create a list of questions that a student may use to help determine if any information is missing.Activity 3 ProblemA difficult problem may have insufficient or missing information. It cannot be solved unless you have more informationProblem: The temperature reading at two places are given below. Which of the two places is more likely to have snow?

Place

Day of the WeekMondayWednesdayThursdaySaturdayA63753966B57804539The information in a pictograph shows the number of cakes sold in one week, from Monday to Friday. Students are asked to find the difference in the number of cakes sold on Tuesday and Saturday. 51Creating a scoring rubric Design a holistic scoring rubric to assess student understanding of the main features of a graph (e.g., bar graph or pictograph), and difference between graphs. Each group of 3 assigned a specific graphing problem. They will discuss ways in which they can assess student ability to pose a problem, collect, organize and represent data... Criteria and levels of gradation (No response, limited response, acceptable response, and superior response)Participants will present their rubrics and discuss the reasonableness of the gradations and the rubric itself in measuring the different criteria.52Assessment: Creating a scoring rubricCriteriaGradation of Quality

No ResponseLimited ResponseAcceptableResponseSuperior ResponsePose a problemSelect a methodCollect dataOrganize dataReview Suggestions!!

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The Food PyramidOrange = GrainsGreen = VegetablesRed = FruitsBlue = MilkPurple = Meat and BeansYellow = Oils

Eat your veggies. NCTM Illuminations/resources for teaching math/Lesson 1To begin a discussion of healthy foods, show the class the Kids Health web site. Go to the Food Guide Pyramid game, then call on volunteers to click on the name of any food group and answer the questions that are shown at that destination. Repeat until all the food groups have been explored.To introduce the tally chart, invite the students to place, one at a time, a tally in the correct row to describe how they feel about eating carrots.

55Activity SheetsVocabulary Development: Which category am I in?Card Activity Instructions/Collecting and organizing data &Eat your Veggies: Tally Time

ReferencesNVLMNCTM.org/IlluminationsExcel Charts: http://video.about.com/spreadsheets/Charts-in-Excel.htmGo Math Florida, Big Idea , Ch. 2 (Grade 5)Go Math Florida, Big Idea , Ch. 5 (Grade 3)Houghton Mifflin HarcourtReys, et. Al. (2009). Helping Children Learn Mathematics.