ANOTHER LOOK AT DATA (HISTOGRAMS AND BAR GRAPHS)
ESTIMATED TIME TO COMPLETE: 75 minutes
MODULE OBJECTIVES:
Students will construct and distinguish among the appropriate uses of bar graphs and histograms through activities with Interactive software
CONCEPT(S) LEARNED IN THIS MODULE:
Appropriate uses of bar graphs and histograms
STANDARDS ADDRESSED BY UNIT MODULES:
- Praxis(0016):
- Curriculum components - Appropriate materials and technology
- Problem solving
- Investigate and understand content
- Formulate problems for everyday situations
- Verify and interpret results
- Build student confidence
- Solve problems that are developmentally appropriate
- Probability and Statistics
- Counting
- Organizing
- Representing
- Interpreting data
- Hand-held calculators and computers - Computer based interactive tool used in problem solving and concept development
- Classroom management and motivation
- Problem solving
- Experimentation
- Small group instruction
- Whole group construction
- Efficient instruction
- Analysis of students’ work - Use of rubrics
- Use of manipulatives and developmentally appropriate materials - Variety and reliability
- Content-specific pedagogy - Theories necessary for implementing sound representations of numeric and algebraic concepts
- Science as inquiry - Development of ability to ask questions, investigate, observe, construct explanations and communicate results
- Praxis(0069):
- Organize data into an appropriate presentation - Use of computer based interactive tool for organizing data
- Read and analyze data presented in various forms
- Solve problems involving average
- Draw conclusions from data
- MSPAP K-8:
- Environmental Science - Students will use scientific skills and process to explain the interactions of environmental factors (living and non-living) and analyze their impact from a local to a global perspective.
- Life Science - Students will use scientific skills and processes to explain the dynamic nature of living things, their interactions, and the results from the interactions that occur over time.
- Algebra, Patterns, and Functions - Students will algebraically represent, model, analyze, and solve mathematical and real-world problems involving patterns and functional relationships.
- Statistics and Probability - Students will collect, organize, display, analyze and interpret data to make decisions and predictions and will use experimental methods and theoretical reasoning to determine probabilities to make predictions.
- Number Relationships and Computation - Students will describe, represent and apply numbers and their relationships and will estimate and compute using mental strategies and paper/pencil.
- Processes of Mathematics - Students will use reasoning to solve problems in mathematics, be able to communicate the processes used and the solution(s) while making connections within mathematics, to other disciplines, and to the real world.
TECHNOLOGY - ENHANCED INSTRUCTIONAL STRATEGIES UTILIZED IN THIS MODULE:
Computer based estimation, analysis and visualization
Component |
Brief Description of Module Activities |
Student Grouping |
Materials/Technology |
Engagement |
Have students use unifix cubes to construct a 3-D bar graph display of surface area of oceans of the world.
|
Small Group |
Unifix Cubes, data sheets |
Exploration |
Use Histogram tool in Interactivate at www.shodor.org site to distinguish the differences between bar graphs and histograms |
Individual or Small Group |
Computer with web access, computer projection device |
Explanation |
Teacher directed activity on changing scales on histogram to affect visual interpretation |
Whole class |
Computer with web access, computer projection device |
Extension |
Students will independently explore the other data sets in Histogram tool to gain insight into visual manipulation of data. |
Individual |
Computer with web access |
Evaluation |
Students would find sets of environmentally related data and construct a bar graph & two histograms (different intervals) |
Individual |
Computer with web access |
EXPECTED MODULE OUTCOMES:
Students will be able to:
- Construct a bar graph and a histogram
- Demonstrate and explain the effect of changing scale and range on bar graphs and histograms
- Demonstrate when it is appropriate to use a bar graph and a histogram to display data
PERFORMANCE BASED ASSESSMENT OF MODULE OUTCOMES:
Students will construct three displays - one bar graph and two histograms (different intervals) - and complete a compare and contrast chart of the information shown. A three-circle Venn Diagram is recommended for chart.
SCORING RUBRIC:
|
Analysis |
Displays |
2 |
- Correct displays are constructed
- Intervals are appropriate
- At least four statements entered in compare/contrast chart
|
- Each has title and labels
- Each is neatly constructed
|
1 |
- Correct displays are constructed
- Scale is not appropriate or less than four statements in chart
|
- Each has title and labels
- Each is neatly constructed
|
0 |
- Incorrect display or two or less observation statements conclusion
|
- Missing title or labels
- Scale is not uniform
|
TEACHER NOTES:
- Engagement Activity:
The following data applies to surface area of the four main oceans (in square miles): Pacific- 63,800,000, Atlantic- 31,830,000, Indian- 28,360,000, Arctic- 5,440,000. Teacher should allow students to determine the appropriate scale to represent the data and ask comparative questions.
- Exploration and Explanation:
Using the histogram Interactivate tool and the discussion questions found in Interactivate , the teacher should conduct class wide discussion to demonstrate the effect of changes of scale and range. Use of classroom projector to display histogram and familiarize students with the tool is recommend.
- Evaluation:
Data sets may be obtained at:
- Scoring Rubric for Culminating Activity:
|
Abstract(s) |
Presentation |
2 |
- Meets all criteria (measures of central tendency, histogram, box and whisker plot) and explains the contribution of each
|
- Typed
- Displays from article are included
- Source of article is given
|
1 |
- Contains two of the three criteria
|
- Meets all criteria above.
|
0 |
- Contains only one of the criteria
|
- Above criteria are incomplete
|
Unit Description
Module 1 2 3 4