Lesson Title: Mean, Median, and Mode: Using Digital Spreadsheet
Subject Area: Mathematics (Pre Algebra or Algebra 1)Grade Level: 8-9 grades
I. Lesson Summary
This lesson will serve as an introduction to the concepts of means, medians, and modes with solving various problems. In addition, students will acquire the kills of utilizing on-line digital spreadsheet application and incorporating the concepts of means, medians, and modes with the technological application through obtaining new knowledge, internet activities, and real-life applications.II. GDOE Standards
Standard 6: Use mathematical models to represent and understand quantitative relationships.
[8.6.1] Model and solve problems using tables, graphs and equations.Standard 9: Specify locations and describe spatial relationships using coordinate geometry and other representational systems.
[8.9.2] Plot graphs from tables and construct tables from graphs.
Standard 14: Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.
[8.14.1] Collect data to answer questions about characteristics of two or more populations.Standard 15: Select and use appropriate statistical methods to analyze data.
[8.15.1] Find the mean, median and mode of a set of data presented in a frequency table.[1ALG.15.1] Use measures of central tendency (i.e., mean, median, mode)
III. SAT 10 Standards
Number Sense and Operations:
Identify and use field properties of addition and multiplication
Data, Statistics, and Probability:
Analyze data and draw inferences from tables and graphs
Determine and use measures of central tendency
IV. National Educational Technology Standards for Teacher (NETS-T)
All classroom teachers should be prepared to meet the following standards and performance indicators.
1. Technology Operations and Concepts
Teachers demonstrate a sound understanding of technology operations and concepts. Teachers:a. demonstrate introductory knowledge, skills, and understanding of concepts related to technology (as described in the educational standards for students.)
b. demonstrate continual growth in technology knowledge and skills to stay abreast of current and emerging technologies.
2. Planning and Designing Learning Environments and Experiences
Teachers plan and design effective learning environments and experiences supported by technology.
Teachers:
a. design developmentally appropriate learning opportunities that apply technology-enhanced instructional strategies to support the diverse needs of learners.
b. apply current research on teaching and learning with technology when planning learning environments and experiences.
c. identify and locate technology resources and evaluate them for accuracy and suitability
d. plan for the management of technology resources within the context of learning activities.
e. plan strategies to manage student learning in a technology-enhanced environment.
3. Teaching, Learning, and the Curriculum
Teachers implement curriculum plans that include methods and strategies for applying technology to maximize student learning.
Teachers:
a. facilitate technology-enhanced experiences that address content standards and student technology standards
b. use technology to support learner-centered strategies that address the diverse needs of students.
c. apply technology to develop students’ higher order skills and creativity
d. manage student learning activities in a technology-enhanced environment
4. Assessment and Evaluation
Teachers apply technology to facilitate a variety of effective assessment and evaluation strategies.Teachers:
a. Apply technology in assessing student learning of subject matter using a variety of assessment techniques
b. Use technology resources to collect and analyze data, interpret results, and communicate findings to improve instructional practice and maximize student learning
c. Apply multiple methods of evaluation to determine students’ appropriate use of technology resources for learning, communication, and productivity.
5. Productivity and Professional Practice
Teachers use technology to enhance their productivity and professional practice.Teachers:
a. use technology resources to engage in ongoing professional development and lifelong learning.
b. continually evaluate and reflect on professional practice to make informed decisions regarding the use of technology in support of student learning.
c. apply technology to increase productivity.
d. use technology to communicate and collaborate. with peers, parents, and the larger community in order to nurture student learning.
6. Social, Ethical, Legal and Human Issues
Teachers understand the social, ethical, legal, and human issues surrounding the use of technology in PK-12 schools and apply that understanding in practice.Teachers:
a. model and teach legal and ethical practice related to technology use.
b. apply technology resources to enable and empower learners with diverse backgrounds, characteristics, and abilities.
c. identify and use technology resources that affirm diversity.
d. promote safe and healthy use of technology resources.
e. facilitate equitable access to technology resources for all students.
V. Analyze LearnersThe students for this lesson are eight to ninth grades involved in a general mathematics educational class. This class includes approximately 30 students. Male and female students occupy sixty percent and forty percent of the class respectively. One student in this class has a Specific Learning disability. Most students are Guamanian (born and raised in Guam), some students are other islanders (moved to Guam from other islands such as Palau, Yap, and Chuuk), and few students are Asian. Most students from other islands and Asia are categorized in English as a Second Language (ESL). However, the classroom environment is pretty good regularly, except rare few disturbances. Students tend to be involved in the class activities pretty much if they are forced to participate in or know their rewards in the end if they do good work. According to previous observation of students in the class, most students are visual and tactile learners and some are auditory learners. Since students can discuss about the activities in their group, auditory learners also benefit in group assignment. The levels of students’ mathematic skills in this class show a bell curve shape. Some students are in high and low levels and the majority of students cluster together in the middle area in bell curve shape (average level).
VI. State Objectives
Using spread sheets, students will be able to demonstrate how to
1. compute mean, median, and mode manually,2. collect the data,
3. input given or obtained data into digital spreadsheet,
4. measure mean, mode, and median,
5. create a bar graph,
6. interpret the meanings of the results,
by using and operating functions of a spread sheet application with ninety-five percent accuracy.
VII. Select Media, Materials, and Methods
Teacher will need:
-Computer with internet access-Overhead projector
-Color printer
-Worksheet for collecting data: The record of hours spent for the listed items
Each student will need:
-Computers with internet access -Gmail registration (http://www.gmail.com)
-Pencil and paper
-Notebook or three-ring binder with filler papers
-Optional: Calculator
VIII. Utilize Media, Materials, and Materials
1. Introduce students to the ideas of mean, median, and mode and have them practice calculating simple given data manually with calculator in the notebook or the three-ring binder with filler papers.
2. Using a computer hooked up to the overhead projector, explain and demonstrate how to register for g-mail account, to activate, to operate, and to utilize the digital spreadsheet provided by g-mail.
3. Using a computer with internet access, have students seated in front of computer, ask them to go to http://www.gmail.com, and register for g-mail account as following instructions demonstrated on the overhead projector.
4. Divide the class into groups of four to five. Students will collect the data for two or three days, recording hours spent for the listed items such as homework, reading book, phone use (including texting), internet use, and chores.
5. When all students complete ‘worksheet for collecting data,’ they will input the data collected from group members into the appropriate cells in the digital spreadsheet application.
6. Have students (1) calculate sum of each columns and rows, and means, median, and mode of the data collected using the function of digital spreadsheet application provided, and (2) create a bar graph operating the functions of a digital spreadsheet application.
7. Have students print out the tables they create in digital spreadsheet and the results of the data.
8. Using papers and pencils, have students write one page reflection paper considering the relationship between the results of data such as sum, mean, median, and mode and their grades.
IX. Require Learner Participation
Students will be involved in inside- and outside-classroom activities throughout the digital spreadsheet lesson. They will have chances to participate in collecting data, inputting data, utilizing digital spreadsheet application to obtain mean, median, and mode of data, and applying the results to their own real lives. This must ensure that every student is gaining necessary knowledge of digital spreadsheet and related-mathematic concepts from this lesson. In addition, all students will participate in the activities shown below.
1. Collecting Data Activities – Outside the class
-Students will be divided into groups of four to five
-Each group member will record the hours or minutes spent for the listed items in ‘the worksheet for collecting data’ for two days. An example of worksheet is given below.
<Worksheet for Collecting Data: The record of hours spent for the listed items>
| Date | Homework | Reading | Phone Use | Internet Use | Chores |
7/10/11 | 3 hrs | 2 hrs | 5 hrs | 2 hrs | 0.5 hrs |
7/12/11 | 1 hrs | 4 hrs | 0.5 hrs | 6 hrs | 1 hrs |
Total |
2. Processing Data Activities – Inside the class
[5 min] Review and discussion about lesson
[25 min] Practice calculating mean, median, and mode manually for given simple data examples.
[25 min] Instruction and class conversation
1) Demonstrate how to create the charts in the digital spreadsheet
2) Introduce the form of charts students will create in the digital spreadsheet as shown below| Student Name | Homework | Reading | Phone Use | Internet Use | Chores | Total |
Mike | 6 hrs | 1 hr | 3 hrs | 6 hrs | 0.5 hrs | |
Julia | 4 hrs | 3 hrs | 0.5 hrs | 1 hr | 3 hrs | |
Total |
3) Inform students how to obtain mean, median, and mode from the digital spreadsheet application.
[25 min] Group work and individual work
1) Students will work in groups to collect the data from group members.
2) Each student will create his/her own charts and input the collected data in the digital spreadsheet. 3) Utilizing the function of the digital spreadsheet application, students will obtain the sum, mean, median, and mode of the data.
[20 min] Writing a reflection paper
1) Students will write one page reflection paper considering about effects of time spent for each items (homework, reading, phone use, etc) on their grades.
[5 min] Wrap up
Have students turn in the worksheet for collecting data, the results printed out, and a reflection paper
*If students cannot finish their reflection paper, it will be homework.
X. Evaluate and Revise
1. Tables, graphs, and results of measurement-
1. Tables, graphs, and results of measurement-
Next class, Students will take the test. Two types of test will be given to students. The first type of test is to calculate manually mean, median, and mode from given simple data. The second type of test is to use digital spreadsheet application with same items as students have used in the previous class. However, different values of data will be given to students to assess their understandings of related mathematic concepts and the use of digital spreadsheet application. Manual test will be evaluated in percentile methods and digital spreadsheet test will be assessed with performance rubric presented below.
(1) Example of manual calculation test
The list below shows students’ monthly hours spent commuting to school. Find the mean, median, and mode from the given information
Hours spent commuting: 16, 20, 15, 34, 7, 28, 9, 11, 35, 26, 6, 18, 14
Answer) Mean Median Mode
(2) Performance Rubric
Name: Date:
Class/Period: Grade: | Level | Description |
Excellent (4) | Mean, median, and mode are correctly calculated and all data are inputted in relevant place of cells in spreadsheet. Bar graphs appear accurately. All parts of the problem are answered correctly and completely, showing all necessary process. The work is neat. |
Very Good (3) | The student makes few errors in inputting data in spreadsheet. All parts of problem are answered using appropriate functions of digital spreadsheet application and the work is neat. |
Acceptable (2) | The student makes some errors in inputting data in spreadsheet. The student answers all parts of the problem but uses occasionally inappropriate functions of digital spreadsheet application. The work may be sloppy |
Poor (1) | Spreadsheet is incomplete or sloppy. Answers are incorrect and the work is sloppy. |
2. One page reflection paper rubric
(1) Guided Questions for reflection paper
1. Describe personal effects of time spent for each items (homework, reading, phone use, etc) on your grades; good or bad?
2. Explain the meaning of mean, median, and mode
3. Describe what you learn through this lesson.
(2) Reflection Rubric
Name: Date:
Class/Period: Grade: | Skills | 5 | 4 | 3 | 2 | 1 |
Depth of reflection | Demonstrate a conscious and thorough understanding of the writing prompt and the subject matter. | Demonstrate a thoughtful understanding of the writing prompt and the subject matter. | Demonstrate a basic understanding of the writing prompt and the subject matter. | Demonstrate a limited understanding of the writing prompt and subject matter. | Demonstrate little or no understanding of the writing prompt and subject matter. |
Use of textual evidence and historical context | Use specific and convincing examples of related concepts to support claims in their writing, making insightful and applicable connections between items and grade. | Use relevant examples of related concept to support claims in their writing, making applicable connections between items and grade. | Use examples of concepts to support most claims in their writing with some connections between items and grade. | Use incomplete or vaguely developed examples to only partially support claims with no connections between items and grade. | No examples are used and claims in their writing are unsupported and irrelevant to the topic at hand. |
Language use | Use stylistically sophisticated language that is precise and engaging, with notable sense of voice, awareness of audience and purpose, and varied sentence structure. | Use language that is fluent and original, with evident a sense of voice, awareness of audience and purpose, and the ability to vary sentence structure. | Use basic but appropriate language, with a basic sense of voice, some awareness of audience and purpose and some attempt to vary sentence structure. | Use language that is vague or imprecise for the audience or purpose, with little sense of voice, and a limited awareness of how to vary sentence structure. | Use language that is unsuitable for the audience and purpose, with little or no awareness of sentence structure. |
This Reflection Rubric is amended and adapted to fit into the given situation from the source of http://www.sites4teachers.com/links/redirect.php?url=http://readwritethink.org/lesson_images/lesson963/Rubric.pdf
3. Participation and worksheet for collecting data
Students will be evaluated based on teacher observation of how much time and effort they put into preparing worksheet for collecting data and cooperating with other students.
XI. Adaptation
1. Students with learning disability - Accommodations and Modifications will be offered to students with learning disability. Examples are to extend due date for homework, to allow an oral report instead of a written one, to reduce the amount of writing-reflection paper, to describe each action taking in great detail and using concrete words, to provide visual aid, to show a model of the end product of direction (e.g. a completed worksheet, charts, graph, and reflection paper), and to allow the student to complete an independent project as an alternative work.
2. ESL/Bilingual students – Majority of ESL/Bilingual students are composed of islanders from different area. According to my observation, cultural trends of students from same island highly are to be strongly bonded and help each other. Therefore, when dividing the class into groups of four to five, ESL/Bilingual students from same areas will be grouped together. So they can help each other using their own languages.
XII. Useful Internet Resource
1. International Society for Technology in Education:
http://www.iste.org/Libraries/PDFs/NETS_for_Teachers_2000.sflb.ashx
2. Google:
http://www.gmail.com
3. Purplemath:
http://www.purplemath.com/modules/meanmode.htm
