Topic: Measurement
Performance Standard: The learner formulates real-life problems involving measurements and solves these using a variety of strategies.
Essential Understanding(s): Physical quantities are measured using different measuring devices. The precision and accuracy of measurement depend on the measuring device used.
Essential Question(s):
The learner will know:
Evidence at the level of understanding: Learner should be able to demonstrate understanding of measurement using the six (6) facets of understanding:
Explaining how to use the calibration model and find its degree of precision.
Criteria:
Interpreting through story telling situations that describe the appropriate use and choice of measuring devices.
Criteria:
Applying a variety of techniques in posing and solving daily life problems involving measurement
Revealing Empathy by role-playing the uses of the primitive measuring devices for the people who invented them and discuss how they got accurate results.
Criteria:
Manifesting Self-knowledge by assessing how one can give his/her best solution to a problem/situation on measurement.
Criteria:
1. Explore
At this stage, the teacher should be able to start with interesting exploratory activities that will hook and engage the learner on what is going to happen or where the said pre-activities would lead to.
a. Group activities
c. Reaction paper or journal writing about the group presentation.
Activity 13
Let the students answer activity sheets on identifying and describing the different measuring devices. This may be done by presenting a model/actual measuring device ( if available) or just a drawing of these measuring devices. Questions on who invented the said device may also be included. Questions about how to get accurate results must also be given consideration.
Activity 14
Give each student enough time, like 5-10 minutes to think of situations that describe the appropriate use and choice of the different measuring devices. Then, let them discuss the situations they listed with their group members. Let each group take turns in presenting their consolidated story.
Activity 15
Let each group present authentic situations showing the evolution of the different measuring devices. These
presentations may serve as one of their projects.
Activity 16
Let the students write reaction paper or journal about the group presentation.
2. Firm Up
At this stage, the teacher should be able to give sample activities or experiences that the learner will have to undergo in supporting findings in the exploratory activities and for a deeper understanding of the topic.
a. The learner shall conduct an activity
c. Performing experiments/activities that will verify formulas for finding areas of plane geometric figures and volumes of solid figures.
d. Solving teacher-made problems about measurements.
Activity 17
Let the students perform or conduct activities on actual measurements using the different measuring devices. It may be the measures of classroom table, backboard, window frames, etc. Allow the students to perform the said activity
even outside the classroom. For linear measurements, let them use different units to compare one unit with that of the other. Let them do also conversion from one unit to another using the metric converter or a conversion table.
Activity 18
Extend activity #17 to measuring objects of different shapes or even irregular shapes. Let the students discuss the similarities and the differences encountered by the groups in getting the measures of the different objects.
Activity 19
Directions:
a. Group the students into fives.
b. Pose this Activity.
Problem:
d. Allow students to make an estimate/ approximation before they compute.
e. Discuss the results.
3. Deepen
At this stage, the teacher should be able to give activities that will provide the learner the opportunity to reflect on, revisit, or rethink the lesson.
Activity 20
Let the students answer activity sheets that will identify the formula for the area or volume of a given object. The questionnaire may be in the form of multiple choice or identification. They may also be asked to explain the step by step solution on how to apply the formula.
Activity 21
Let the students write reaction paper or journal about the different activities being undertaken.
Activity 22
Ask the students to bring a box full of ping-pong balls to solve the problem below. Group the students into four members each.
Problem:
A. For a classroom of average size, do you think we could fit one million ping-pong balls?
4. Transfer
At this stage, the teacher should be able to give the learner activities that will provide him the opportunity to demonstrate his /her understanding of the topic by:
Activity 23
Group the students into four or five depending on the number of students per class. Each group will then select its leader. The group will decide on the problem to be presented making use measurements. They will visualize and
present the solution to the said problem.
Activity 24
Give each group enough time to construct scale models of either houses, toys, bridges, etc. depending on its problem indicating the use of measurements. Express dimensions of the actual structure to the scale model as ratios. This will serve as students’ project for exhibit during math expo.
Activity 25
Using the same grouping, let the students design a game. They will make use of measurements applying the set of real numbers.
Resources : See Appendix
Stage 1
Content Standard: The learner demonstrates understanding of the key concepts of measurements.Performance Standard: The learner formulates real-life problems involving measurements and solves these using a variety of strategies.
Essential Understanding(s): Physical quantities are measured using different measuring devices. The precision and accuracy of measurement depend on the measuring device used.
Essential Question(s):
- How are different measuring devices useful?
- How does one know when a measurement is precise? accurate?
The learner will know:
- the concept of measurement
- the different measuring devices and their respective uses.
- conversion of units of measure.
- rounding off numbers
- approximation.
- how to solve problems involving measurements using a variety of strategies.
- use different tools/devices and units of measures.
- cite situations where measuring tools are appropriately used.
- convert units of measure.
- round off numbers.
- cite real life situations where rounding off numbers is applied.
- approximate measurement by rounding off to its nearest desired value.
- formulate and solve real life problems applying conversion of units.
Stage 2
Explaining how to use the calibration model and find its degree of precision.
Criteria:
- Thorough
- Clear
- Accurate
- Justified
Interpreting through story telling situations that describe the appropriate use and choice of measuring devices.
Criteria:
- Illustrative
- Accurate
- Justified
- Significant
Applying a variety of techniques in posing and solving daily life problems involving measurement
- Criteria:
- Appropriate
- Practical
Revealing Empathy by role-playing the uses of the primitive measuring devices for the people who invented them and discuss how they got accurate results.
Criteria:
- Perceptive
- Open
Manifesting Self-knowledge by assessing how one can give his/her best solution to a problem/situation on measurement.
Criteria:
- Reflective
- Responsive
Evidence at the level of performance : Assessment of problems formulated based on the following suggested criteria:
- real-life problems
- problems involve measurement
- problems are solved using a variety of strategies
Tools: Rubrics for assessment of problems formulated and solved
Stage 3
Teaching/Learning Sequence: 1. Explore
At this stage, the teacher should be able to start with interesting exploratory activities that will hook and engage the learner on what is going to happen or where the said pre-activities would lead to.
a. Group activities
- Identify and describe the different measuring devices
- cite real life situations where these measuring devices are used/important.
c. Reaction paper or journal writing about the group presentation.
Activity 13
Let the students answer activity sheets on identifying and describing the different measuring devices. This may be done by presenting a model/actual measuring device ( if available) or just a drawing of these measuring devices. Questions on who invented the said device may also be included. Questions about how to get accurate results must also be given consideration.
Activity 14
Give each student enough time, like 5-10 minutes to think of situations that describe the appropriate use and choice of the different measuring devices. Then, let them discuss the situations they listed with their group members. Let each group take turns in presenting their consolidated story.
Activity 15
Let each group present authentic situations showing the evolution of the different measuring devices. These
presentations may serve as one of their projects.
Activity 16
Let the students write reaction paper or journal about the group presentation.
2. Firm Up
At this stage, the teacher should be able to give sample activities or experiences that the learner will have to undergo in supporting findings in the exploratory activities and for a deeper understanding of the topic.
a. The learner shall conduct an activity
- Using the given measuring instruments, find the measures of classroom table, backboard, window frames, etc. ( Bring the class outdoor and find familiar objects. Perform the same activity.)
- Measuring objects of different shapes.
- Approximating measurements to the nearest unit of measure.
- Estimating and finding actual measurements of objects
- Finding the perimeter and area of plane figures; surface area and volume of solid figures.
- Formulating problems based on the given information.
c. Performing experiments/activities that will verify formulas for finding areas of plane geometric figures and volumes of solid figures.
d. Solving teacher-made problems about measurements.
Activity 17
Let the students perform or conduct activities on actual measurements using the different measuring devices. It may be the measures of classroom table, backboard, window frames, etc. Allow the students to perform the said activity
even outside the classroom. For linear measurements, let them use different units to compare one unit with that of the other. Let them do also conversion from one unit to another using the metric converter or a conversion table.
Activity 18
Extend activity #17 to measuring objects of different shapes or even irregular shapes. Let the students discuss the similarities and the differences encountered by the groups in getting the measures of the different objects.
Activity 19
Directions:
a. Group the students into fives.
b. Pose this Activity.
Problem:
How long would it take you to count to one million (1, 2, 3, 4, 5, …, 1 000 000) at the rate of one number per second? (Assume that you will not stop until the task has been completed)c. Ask for the answer in more commonly understood units of time, such as days, weeks, months, or years.
d. Allow students to make an estimate/ approximation before they compute.
e. Discuss the results.
3. Deepen
At this stage, the teacher should be able to give activities that will provide the learner the opportunity to reflect on, revisit, or rethink the lesson.
- Explain thoroughly the process/procedure undertaken in every activity, including the computation part.
- Identify objects whose area/volume can be found using the formulas.
- Explore the possibilities of finding the measures of object of irregular shapes. (football, star, etc. )
- Investigate the relationship between the number of square units/cubic units in a given figure and the area/volume of the given figure.
- Write a journal on the activities undertaken.
Activity 20
Let the students answer activity sheets that will identify the formula for the area or volume of a given object. The questionnaire may be in the form of multiple choice or identification. They may also be asked to explain the step by step solution on how to apply the formula.
Activity 21
Let the students write reaction paper or journal about the different activities being undertaken.
Activity 22
Ask the students to bring a box full of ping-pong balls to solve the problem below. Group the students into four members each.
Problem:
A. For a classroom of average size, do you think we could fit one million ping-pong balls?
- List the assumptions you make in estimating your answer.
- Find the volume of the box full of ping-pong balls.
- Use a tape measure and approximate the volume of the classroom.
- Compare the volume of the classroom with the volume of the box full of ping-pong balls.
- How many ping-pong balls are there in the box?
4. Transfer
At this stage, the teacher should be able to give the learner activities that will provide him the opportunity to demonstrate his /her understanding of the topic by:
- formulating and solving a situation/problem.
- writing a report on what he/she has learned about measurement.
- Improvising measuring instruments for finding linear measures of physical objects.
- creating miniature models of your dream house.
Activity 23
Group the students into four or five depending on the number of students per class. Each group will then select its leader. The group will decide on the problem to be presented making use measurements. They will visualize and
present the solution to the said problem.
Activity 24
Give each group enough time to construct scale models of either houses, toys, bridges, etc. depending on its problem indicating the use of measurements. Express dimensions of the actual structure to the scale model as ratios. This will serve as students’ project for exhibit during math expo.
Activity 25
Using the same grouping, let the students design a game. They will make use of measurements applying the set of real numbers.
Resources : See Appendix
