ACTIVITY 1: 3rd Year High School
The students will be able to make at least 4 real life application of Statistics using the measures of
Performance Task Content Illustrating Student Progress Date
• Finding the MEDIAN height in odd • Correctly identifying the median height in a
grouped students, through visual group of students.
• Arranging the group members according to
• Finding the MODAL height in a group their height and correctly identify the modal
of students by arranging the students height.
of the same height.
• Adding all the height of the students and
• Locating the MEAN height in a group subtracting it to the number of students in a
of students by adding all their height group.
and getting their average.
• Finding the tallest and the smallest
• Finding the RANGE of the height in a member in a group the subtracting them.
group of students.
Based on the performance tasks, the students will be able to understand and apply in real life events
the importance of identifying the central tendency from a raw data. In understanding the problem, the
students will identify special factors that influence the approach before starting in dealing with the problem.
Likewise, the performance task enhances the ability of the students to think critically and develop
their own learning by doing the tasks themselves. With this, the teacher will be confident enough to assume
that the students indeed have learned the lesson and that the teacher’s learning strategy is effective.
Level: 3rd year high school
Class size: 30
Duration: 1 hour
Topic: Measure of Central Tendency
Reference: introduction to Statistics 3rd edition
Author: Ronald E. Walpole
At the end of the 1-hour session, 100% of 3rd year section Rizal students will be able to make 4 real
life application of Statistics using the measures of central tendency.
• Have an odd number of students stand in the front of the classroom, arrange themselves in terms of
ascending heights. The height of the person standing in the middle is the median height.
• Repeat the activity with an even number of students. The median will be halfway between the heights
of the two students standing in the middle.
• Have students give the definition of median in their own words.
• For the groups of students standing at the front of the room, if there are some who are the same
height, then the height that occurs most frequently is the mode. (It is possible that no two students
are the same height. It is also possible to have more than one mode.)
• Have students give the definition of mode in their own words.
• Have students compute this by adding up the heights and dividing by the number of students in the
sample. For the sake of expediency, convert heights to inches before doing the arithmetic.
• It is important for the teacher to have the students look at their answer in relation to the entire list of
• Have everyone except the tallest and shortest students in that group sit down. Measure the distance
from the top of one of their heads to the top of the other person's head. That is the range. Guide
students to tell you that subtraction can be used to find this.
Criteria Distinguished - 4 Proficient - 3 Apprentice - 2 Novice - 1
Identifies special Understands Doesn't
Understands the factors that Understands the enough to solve understand
Problem influences the problem part of the problem enough to get
approach before or to get part of the started or make
starting the problem solution progress
Explains why Uses some Uses
Uses Information certain information Uses all appropriate appropriate inappropriate
Appropriately is essential to the information information information
solution correctly correctly
Explains why Applies completely Applies some Applies
Applies procedures are appropriate appropriate inappropriate
Appropriate appropriate for the procedures procedures procedures
Uses a Uses a
Uses Uses a Uses a representation that representation
Representations representation that representation that gives some that gives little or
is mathematical clearly depicts the important no significant
precise. problem information about information about
the problem the problem
Correct solution of Copying error, No answer or
Answers the problem and made Correct solution computational error, wrong answer
Problem a general rule about partial answer for based upon an
the solution or problem with inappropriate plan
extended the multiple answers,
solution to a more no answer
complicated statement, answer
solution labeled incorrectly
One form of authentic assessment being widely adapted in schools today is portfolio assessment.
Diane Hart defines a portfolio as quot;a container that holds evidence of an individual's skills, ideas, interests,
and accomplishments.quot; The ultimate aim in the use of portfolios is to develop independent, self-directed
learners. Long-term portfolios provide a more accurate picture of students' specific achievements and
progress and the areas of needed attention.
Portfolios make it easier to develop grading schemes that emphasize assessing individual student
growth rather than competition with other students. As self-evaluation is an integral part of portfolio
assessment, a highly competitive climate will prove counterproductive. Students will be reluctant to focus
upon their deficiencies if they believe it will put them at a disadvantage in the competition for the top grades.
Often portfolios are used to supplement, not replace, traditional assessment procedures.
1. Remember, portfolios should be developed by the students, not the teacher. Students should have
freedom in selecting items to include in their portfolios. It is advantageous to make the whole portfolio
process a collaborative teacher-student effort, with the teacher becoming more of a consultant to the
student. The teacher functions more as a coach than a director.
2. Any item that provides evidence of a student's achievement and growth can be included in a
portfolio. Commonly used items include:
a. Examples of written work
b. Journals and logs
c. Standardized inventories
d. Videotapes of student performances
e. Audiotapes of presentations
f. Mind maps and notes
g. Group reports
h. Tests and quizzes
i. Charts, graphs
j. Lists of books read
k. Questionnaire results
l. Peer reviews
3. Each item in the portfolio should be dated to facilitate the evaluation of progress through the year.
4. Typically, teachers hold periodic individual conferences with their students to review their portfolios.
During this interview it is important to listen to the students' assessments of the items in their
portfolio. The focus of the discussion should be upon the products included in the portfolio. The
teacher and student work together to set a limited number of objectives for future work. Strive to
achieve a dialogue, not a lecture.
5. Much of the value of portfolios derives from the students' reflection on which items are worth
including in their portfolios.
6. The portfolios may be kept in folders, file boxes, assigned drawers, or other appropriate containers.
Whatever the storage container, it must be readily accessible to the students.
7. Portfolios are especially helpful at parent conferences. Help the parent examine the portfolio, pointing
out evidence of progress and areas of needed improvement.
8. Be patient. Portfolios are a new concept to most students and parents. There is a learning curve
involved in adapting to the process. Experiment to determine what works and feel free to modify as
9. In some schools students' portfolios are made available to their teachers the following year to aid in
diagnosis. A few schools are experimenting with the development of a permanent portfolio that
follows the students throughout their total school experience. (This would be separate from their
cumulative record folder.) Upon graduation the students would keep their portfolios.
10. Develop your own teaching portfolio as a means of facilitating your professional development. It also
can prove invaluable in tenure assessments and future job searches. Your professional portfolio
might include videotapes of successful classes, curriculum materials you have developed, course
syllabi, sample lesson plans, professional development goals and objectives, workshop classes
attended, publications written, student evaluations, awards, certificates, professional affiliations,
principal's and supervisor's evaluations, and your teaching philosophy.
11. A large three-ring binder is a practical way to organize your portfolio. Use tabs to indicate the various
categories. You might occasionally share your portfolio with students to model the processes you are
urging them to follow.
The ultimate aim of education is to produce lifelong, independent learners. An essential component of
autonomous learning is the ability to assess one's own progress and deficiencies. Student self-assessment
should be incorporated into every evaluation process. Its specific form may vary with the developmental
level of the student, but the very youngest students can begin to examine and evaluate their own behavior
1. Instead of grading all assignments, allow students to correct some themselves. You may choose to
randomly collect these and check for accuracy.
2. Share the specific evaluation criteria (or rubric) students should employ in assessing various tasks or
assignments. Provide them with criteria check sheets (or have the class generate them) that specify
exactly what constitutes a good product.
3. Provide models of successful products, answers, or performances. These might be tacked to the
bulletin board, in a display case, or on videotape. It is best to share the model before students begin
the project. For creative activities, avoid encouraging students to simply copy someone else's
product. It is helpful to lead students through an evaluation of the outstanding model, using the
evaluation criteria to demonstrate why the model is an exemplar. To minimize peer pressure or
harassment, it is generally best to use a previous student's work for the model rather than a current
Attempt to schedule individual sessions to discuss a student's progress. Have the student evaluate his or
her own performance. Encourage the student to apply specific criteria in making the self-assessment.
Self-assessment requires students to evaluate their own participation, process, and products. Evaluative
questions are the basic tools of self-assessment. Students give written or oral responses to questions like:
• What was the most difficult part of this project for you?
• What do you think you should do next?
• If you could do this task again, what would you do differently?
• What did you learn from this project?
Many teachers find that authentic assessment is most successful when students know what teachers
expect. For this reason, teachers should always clearly define standards and expectations. Educators often
use rubrics, or established sets of criteria, to assess student work. Because authentic assessment
emphasizes process and performance, it encourages students to practice critical-thinking skills and to get
excited about the things they are learning.
Most state assessments include open response or extended response questions. Generally, the
purpose is to test the student's ability to apply or extend content knowledge. In order to optimize students'
performance and to instill confidence, teachers should:
• Explicitly teach the rubric so that students internalize performance levels.
• Analyze student models of good work with the class.
• Model the thinking process involved in answering open response.
• explicitly teach test-taking strategies
• Provide opportunities for students to practice answering teacher-generated questions and released state
• Offer specific, corrective feedback.
Open-response questions, like short investigations, present students with a stimulus and ask them to
respond. Responses include:
• a brief written or oral answer
• a mathematical solution
• a drawing
• a diagram, chart, or graph
Many teachers use short investigations to assess how well students have mastered basic
concepts and skills. Most short investigations begin with a stimulus, like a math problem, political
cartoon, map, or excerpt from a primary source. The teacher may ask students to interpret, describe,
calculate, explain, or predict. These investigations may use enhanced multiple-choice questions. Or
they may use concept mapping, a technique that assesses how well students understand
relationships among concepts.