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Module 46
Data AnalysisGrades 3 – 5
Sandra Trotman
Introduction & 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.
Reflections
Take 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 day
Data Analysis provides opportunities for computational activities in a meaningful context
Data Analysis provides opportunities for developing collaborative and critical thinking skills
Steps of Data AnalysisInstructional programs should enable students to:
Common Misunderstandings
Students may:◦Experience confusion about the
meanings of concepts◦Lack of familiarity with terminology◦Lack of familiarity with different
symbols or problem situations
Question:Are there other misunderstandings that children may have about data analysis?
Vocabulary PowerUsing Graphic Organizer to
review vocab. for this lesson
Vocab. Strategy: Morphemic Analysis
To paint To write
Pictograph Template: http://www.beaconlearningcenter.com/documents/2351_5255.pdf
Let’s find out!Objective: To plan and conduct a
surveySteps:1. Think of a question you would like to
answer:a. Questions about yourselvesb. Questions about opinions or feelingsc. Questions about the worldd. …(Your input/suggestions)
2. Plan the survey by answering these questions.
a. Where or from whom will I collect the data?b. How will I collect the data?c. Your turn….
3. Collect data
Activity 4: Integrating mathand Literature
Book: “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 family’s preferences.
Data CollectionActivity 5 Collection Methods
Activity 6 Using Pictographs◦Math 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
Review
Discuss what format may be used to complete a review of this session/lesson.
It’s your turn to add to this slide!!
Suggestions
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 Power
Vocab.: Using Venn Diagrams
Sort the review words into the Vann diagram.
Graphs Tables
Activity: Completion
Complete 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 thinking
Growing PatternsUsing Cubes or Connecting Cubes
Creating Graphs
Key features ◦Write a clear and descriptive title.◦Use a uniform scale◦Mark categories clearly◦Make bars the same width◦Write a legend or a key
Question: ◦Why is it important for the bars in a Bar graph to be the same width?
Double Bar Graphs
On a Double Bar graph, each set of bars uses a different scale. Is this graph useful? Explain!
Category 1
Category 2
Category 3
Category 4
0 1 2 3 4 5 6
Series 3Series 2
Choosing an Appropriate Graph
Which 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. Tuesday’s attendance at the movie
What data is counted?Into what categories is the data
classified?
88 24 73 82 36
Movie 1 Movie 2 Movie 3 Movie 4 Movie 5
Continuous 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 participant’s hand span(Pinkie to the thumb).
0 5 10 15 cmThe lengths can be shown on a number line usingsmaller units such as mm.
Activity 2: Which one?
Categ
ory
1
Categ
ory
2
Categ
ory
3
Categ
ory
40
1
2
3
4
5
6
Series 2Series 3
Category 1 Category 2 Category 3 Category 40
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Series 1Series 2
Discrete 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 Graphs
Mostly used for discrete or separate and distinct data
Each bar represents part of the data or the category
The length of the bar shows the number of counted values for that category
Easy to interpret; often use for quick, visual comparisons of categories of data
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: DETERMINATION
Purpose: 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
Emphasize
◦Choose a scale and interval that fit the data◦You do not always have to begin your scale with 0.
Activity:
◦Model making a line plot for the following data: 40, 31, 20, 32, 61
Questions:◦ What numbers determine the line’s 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, 40…60 is an outlier
◦ Give one reason why we should use a line plot to organize data. (see range and clustering of data)
Review
I It’s your turn to add to this slide!!
Suggestions !!
Thank you for participating in this session.
Analyzing and Interpreting Data
Module 48
Analyzing 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 Objectives
Participants 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 Analysis
Reviewing and Extending Collecting and Organizing Data
From concrete to symbolic representation
Begin by working with concrete objects in the environment◦Example: Favorite fruitCollect, count and sort fruits into categories, then display them in an organized fashion
Concrete to Symbolic representation
Move to the Pictorial representationDraw the selected fruit on an index card and form a chain to build a pictograph
Express the same information more symbolically by using a bar graph
Additionally, give students a blank paper and encouraged to organize and report their data on the page in a way that makes sense to them.
Data Sense
What is data sense and how is it developed?”
“What should be the goal for teaching Data Analysis?”
Reading 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
Data MaximumRange MinimumMost ScaleIncrease Decrease
Reading Graphs Critically
Participants 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:◦Explain◦Describe◦Analyze
Problem Solving Tips
An 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 information
Problem: The temperature reading at two places are given below. Which of the two places is more likely to have snow?
Place Day of the Week
Monday Wednesday
Thursday Saturday
A 63 75 39 66
B 57 80 45 39
Creating 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)
Assessment: Creating a scoring rubric
Criteria Gradation of Quality
No Response
Limited Response
AcceptableResponse
Superior Response
Pose a problem
Select a method
Collect data
Organize data
Review
Suggestions!!
Thank you for participating in this Session
The Food PyramidOrange = Grains Green = VegetablesRed = Fruits Blue = MilkPurple = Meat and Beans Yellow = Oils
Activity Sheets
Vocabulary 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.htm
Go Math Florida, Big Idea , Ch. 2 (Grade 5)
Go Math Florida, Big Idea , Ch. 5 (Grade 3)Houghton Mifflin Harcourt
Reys, et. Al. (2009). Helping Children Learn Mathematics.
