MATHEMATICS I
General Standard: The learner demonstrates understanding of key concepts and principles of number and number sense as applied to measurement, estimation, graphing, solving equations and inequalities, communicating mathematically and solving problems in real life.
Quarter I
Real Number System, Measurement and Scientific Notation
Topic: Real Number System
Time Frame: 20 days
Stage 1
Content Standard: The learner demonstrates understanding of key concepts of real number system. | Performance Standard: The learner formulates real life problems involving real numbers and solves these using a variety of strategies. | ||
Essential Understanding(s): Daily tasks involving measurement, conversion, estimation and scientific notation making use of real numbers. | Essential Question(s): How useful are real numbers? | ||
The learner will know: • the real number system • rational and irrational numbers • the importance of order axioms • fundamental operations with real numbers • the application of real numbers to daily life. | The learner will be able to: • apply real numbers in a variety of ways to other disciplines. • identify/give examples of rational and irrational numbers • illustrate rational and irrational numbers in practical situations • use the appropriate symbolic notation to illustrate the order axioms. • cite examples/situations where order axiom is applied. • perform the sequence of operations with real numbers. • solve problems in other disciplines such as science, art, agriculture, etc. | ||
Stage 2 | |||
Product or Performance Task: Problems formulated 1. are real –life related 2. involve real numbers, and 3. are solved using a variety of strategies. | Evidence at the level of understanding Learner should be able to demonstrate understanding of the real number system using the six (6) facets of understanding: Explaining how numbers are expressed in different ways. Criteria: Thorough Coherent Clear Interpreting the differences and similarities between rational and irrational numbers. Criteria: Thorough Illustrative Creative Applying a variety of techniques in solving daily life problems. Criteria: Appropriate Practical Accurate Relevant Developing Perspective on the types of real numbers. Criteria: Perceptive Open-minded Sensitive Responsive Showing Empathy by describing the difficulties one can experience in daily life whenever tedious calculations are done. Criteria: Open Sensitive Responsive Manifesting Self-knowledge by assessing how one can give his/her best solution to a problem/situation. Criteria: Reflective Responsive Relevant | Evidence at the level of performance Assessment of problems formulated based on the following suggested criteria: · real-life related problems · problems involve real numbers. · 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: a. give the learner hands-on activities on how to identify /name a real number: · Locating numbers on the number line · Giving the coordinate of a point on the number line · Naming a real number between two given numbers. b. self-evaluate the learner by giving him activity sheets containing questions ( including HOTS) on real numbers . c. let the learner share what he has learned about real number system through journal writing. d. allow the learner to apply the concept to real life by solving worded problems involving real numbers. Activity 1. Let some selected students line up to form/picture a number line. Make one student, probably the middle one, represents 0. Use this to determine the coordinate of a point represented by a student on that number line. Let the students explain their answer. You may introduce this activity as a game. Help the students by giving activity cards with guided instructions. Activity 2. Let a student choose a partner. Then, give each pair an activity sheet containing the number line being drawn either on a graphing paper or activity card. Guided instructions must be given. Let the students play by taking turns in naming a number between two given numbers. The teacher may initially give the two numbers and must be ready to check if the number to be given is between the other two. The game may start with whole numbers, then integers, and later on with rational or irrational numbers. In the end, they must identify the kind of number being inserted. Activity 3. Give each student enough time, like 5-10 minutes, to think of a situation and formulate a real life problem involving the basic operations on real numbers. Then, if they are ready, they will take turn in presenting the problem. Any student can give the answer to the problem. The teacher will ask the one who gave the problem if the presented solution is correct. Activity 4. Guessing Game: Directions:
Note: The answer is taken by subtracting the sum of digits that are not circled from a multiple of nine that is greater than but closer to the sum of the digits. Example: Let the four-digit number be: 1 472
Note that: The multiple of nine that is greater than but closer to 10 is 18.
Activity 5. Let the students answer an activity sheet where the questions are simple problems they experienced in daily life. They must explain the solution to the problem. 2. Firm Up At this stage, the teacher should be able to: a. ask the students to conduct an investigation considering the following steps: · Give a list of different numbers · Change the form of the given set of numbers by doing the basic operations and simplifying the results. · Analyze/Observe the results · Classify the numbers as to their types. · Classify the numbers into rational or irrational b. perform fundamental operations on real numbers and classify results c. cite examples/situations where order axiom is applied. d. solve daily life problems involving different operations on real numbers. Activity 6. Apply cooperative learning. First, group the students into 4. Let each group be working on an activity sheet where one is different from the other. Ask each group to investigate a given set of numbers. Guide questions must be given. Expect them to have analyzed and classified each of the numbers after changing its form. Let them explain the results. Activity 7. Ask the students to answer several activities on the operations applied to the set of real numbers including the order axiom. Let them write the complete solution to each number. Activity 8. Let the students answer activities on solving daily life problems involving different operations on real numbers. 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. a. Explain thoroughly the difference between rational and irrational numbers by giving several examples. b. Investigate on the relationship (similarity or difference) between rational and irrational numbers. c. Investigate patterns on rational or irrational numbers ( both manually and with the use of calculators) d. Generalize and write a report of what has been discovered about real numbers e. Formulate/Solve problems they experienced in daily life. Activity 9. Instruct the students to be ready for an oral/written test which is in the form of a team competition. The test will include investigating patterns on rational or irrational numbers( they are allowed to use a calculator), similarity or difference between rational and irrational numbers, problem solving involving the different operations on real numbers. Activity 10. Give each student enough time, like 10-15 minutes, to answer activities that will provide them the opportunity to reflect on or rethink of the lesson on real numbers. It may be in the form of journal writing, or application of the concept to problems they experienced in daily life. 4. Transfer At this stage, the teacher should be able to demonstrate his/her understanding of the topic by :
Activity 11. 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 of the set of real numbers. They will visualize and present the solution to the said problem. Activity 12. Give each group enough time to construct scale models of either houses, toys, bridges, etc. depending on its problem indicating the use of real numbers. This will serve as students’ project for exhibit during math expo. | |||
Resources/Materials: See Appendix | |||
