Q2 Lesson Exemplar for Mathematics Grade 7, DepED, 2024-2025 PDF

7 Quarter 1 Lesson 1 2 Lesson Exemplar Lesson for Mathematics 1 IMPLEMENTATION OF THE MATATAG K TO 10 CURR...

7 Quarter 1 Lesson 1 2 Lesson Exemplar Lesson for Mathematics 1 IMPLEMENTATION OF THE MATATAG K TO 10 CURRICULUM Lesson Exemplar for Mathematics Grade 7 Quarter 2: Lesson 1 (Week 1) SY 2024-2025 This material is intended exclusively for the use of teachers in the implementation of the MATATAG K to 10 Curriculum during the School Year 2024- 2025. It aims to assist in delivering the curriculum content, standards, and lesson competencies. Any unauthorized reproduction, distribution, modification, or utilization of this material beyond the designated scope is strictly prohibited and may result in appropriate legal actions and disciplinary measures. Borrowed content included in this material are owned by their respective copyright holders. Every effort has been made to locate and obtain permission to use these materials from their respective copyright owners. The publisher and development team do not represent nor claim ownership over them. Development Team Writer: Renato V. Herrera Jr. (West Visayas State University) Validator: Clemente M. Aguinaldo Jr. (Philippine Normal University – North Luzon) Management Team Philippine Normal University Research Institute for Teacher Quality SiMERR National Research Centre Every care has been taken to ensure the accuracy of the information provided in this material. For inquiries or feedback, please write or call the Office of the Director of the Bureau of Learning Resources via telephone numbers (02) 8634-1072 and 8631-6922 or by email at [email protected]. MATHEMATICS / QUARTER 2 / GRADE 7 I. CURRICULUM CONTENT, STANDARDS, AND LESSON COMPETENCIES A. Content The learners should have knowledge and understanding of square roots of perfect squares, cube roots of perfect Standards cubes, and irrational numbers. B. Performance By the end of the quarter, the learners are able to determine square roots of perfect squares and cube roots of perfect Standards cubes, and identify irrational numbers. (NA) C. Learning The learners determine the square roots of perfect squares and the cube roots of perfect cubes. Competencies 1. The learners define perfect square and perfect cube. and Objectives 2. The learners identify perfect squares and perfect cubes. 3. The learners define square root and cube root. 4. The learners determine the square roots of perfect squares. 5. The learners determine the cube roots of perfect cubes. The learners identify irrational numbers involving square roots and cube roots, and their locations on the number line. 1. The learners define irrational numbers. 2. The learners identify irrational numbers involving square roots and cube roots. 3. The learners determine the location of irrational numbers involving square roots and cube roots by plotting them on a number line. D. Content Perfect square and perfect cube Square root and cube root Irrational numbers (involving square root and cube root) E. Integration II. LEARNING RESOURCES Department of Education. (2020). Alternative Delivery Mode. Quarter 1-Module 7: Principal Roots and Irrational Numbers. Department of Education. (2020). Alternative Delivery Mode. Quarter 1-Module 8: Estimating Square Roots of Whole Numbers and Plotting Irrational Numbers Sipnayan. (2020, October 10). How to Plot Irrational Numbers on the Number Line Part 1 [with English subtitles] [Video]. YouTube. https://www.youtube.com/watch?v=ESGkaZnrwrI 1 III. TEACHING AND LEARNING PROCEDURE NOTES TO TEACHERS A. Activating Prior DAY 1 (10 minutes) Knowledge 1. Short Review Lead the students to the Compute the area of each square. concept that the area of the Square sxs Area square is obtained by multiplying a number (length of 1x1 _______________________ the side of the square) to itself. s=1 Follow up by reviewing the 2x2 lesson on exponents. _______________________ s=2 _____ x _____ _______________________ s=3 _____ x _____ _______________________ s=4 Find the volume of each cube. Cube sxsxs Volume Lead the students to the 1x1x1 concept that the volume of the s=1 _______________________ cube is obtained by multiplying the number (length of the side of the cube) to itself three 2x2x2 times. Follow up by reviewing _______________________ s=2 the lesson on exponents. 2  s=3 ___ x ___ x ___ _______________________ s=4 ___ x ___ x ___ _______________________ 2. Feedback (Optional) B. Establishing 1. Lesson Purpose (15 minutes) Lesson Purpose Perfect square and cube 1. Can you form a square with the given unit squares? This activity may be explored a. using manipulatives (physical # of unit squares: ________ or virtual). Can you form a square? _______ b. This may also be given as a whole class activity or # of unit squares: ________ discussion as the teacher Can you form a square? _______ presents the figure through c. slides presentation. # of unit squares: ________ Can you form a square? _______ d. # of unit squares: ________ Can you form a square? _______ Which of the four given figures formed a square? ________________________ Observe the # of unit squares in a, b, and d. What can you say about the numbers? ______________________________________________________________ 2. Can you form a cube with the given unit cubes? 3  a. # of unit cubes: ________ Can you form a cube? _______ b. # of unit cubes: ________ Can you form a cube? _______ c. # of unit cubes: ________ Can you form a cube? _______ d. # of unit cubes: ________ Can you form a cube? _______ Which of the four given figures formed a cube? __________________________ Observe the # of unit cubes in b and d. What can you say about the numbers? _____________________________________________________________ 3. How can you find the length of the sides of a square if its area is given? _________________________________________________________________________ 4. How can you find the length of the sides of a cube if its volume is given? _________________________________________________________________________ 2. Unlocking Content Area Vocabulary Questions 3 and 4 maybe given The number of square units that can form a square is called a perfect as a whole class discussion. square. The number of cube units that can form a cube is called a perfect cube. The square root of the area of the square (perfect square) is the length of the side of the square. (5 minutes) The cube root of the volume of a cube (perfect cube) is the length of each side of the cube. 4 C. Developing and SUB-TOPIC 1: Perfect Square and Square Root (20 minutes) Deepening 1. Explicitation Understanding When a number n is multiplied by itself, such as when we compute the area of a square, we write 𝑛2 and read it “n squared”. The result is called the square of n. That is, if 𝑛2 = 𝑚, then m is a square of n and m is a perfect square. 2. Worked Example Example: Complete the following table to show the squares of the whole All the given activities here may numbers. be done individually or Number 0 1 2 3 4 5 6 7 8 9 10 11 12 collaboratively, depending on Square 0 1 16 81 the type of students the teacher has. The numbers in the second row are called perfect square numbers. What can you say about the square of negative numbers? Sometimes, we will need to look at the relationship between numbers and their squares in reverse. For example: Because 102 = 100, we say 100 is the square of 10. We also say that 10 is the square root of 100. A number whose square is m is called a square root of m. The symbol, √𝑚, is read “the square root of m”, where m is called the radicand, and √⬚ is called the radical sign. 3. Lesson Activity A. Complete the table below. Perfect Exponential Form Square (a number that when multiplied by itself, the Square answer is the number in column one) Root 9 3x3 3 36 6x6 6 49 7x7 81 121 625 4/25 5 DAY 2 B. Perfect Square and Square Root. Place each number in its appropriate column: 0, 25, 40, 49, 121, 625, 8, 18/2, ¼, 27 Begin Day 2 with recalling Perfect Square Number Not Perfect Square Number concepts covered in the previous day. (10 minutes) for review Square Root of Perfect Square Numbers (10 minutes) for the activity Questions for discussion: 1. How did you decide which column the given number should be placed in? 2. Were all your answers correct? If not, why do you think some of your answers were not correct? What will you do to avoid this error next time? 3. How did you compute the square roots of the perfect square numbers? Let the students discuss their SUB-TOPIC 2: Perfect Cube and Cube Root answers. 1. Explicitation A perfect cube is a number that is obtained by multiplying the same integer three times. For example, multiplying the number 2 three times results in 8. Therefore, 8 is a perfect cube. When a number is cubed, we write 𝑛3 and read it “n cubed”. The result is called the cube of n. That is, if 𝑛3 = 𝑚, then m is a cube of n and m is a perfect cube. 2. Worked Example Example: Complete the following table to show the cubes of the following integers. Number –5 –4 –3 –2 –1 0 1 2 3 4 Cube –125 –8 The numbers in the second row are called perfect cube numbers. When a number is cubed, it means that it is multiplied three times. Cube root is reversing the process of cubing a number. For example, when a number (15 minutes) 5 is cubed, then it is multiplied 3 times: 5 x 5 x 5, which is 125. The cube root of 125 is 5. This is because 125 is obtained when the number 5 is multiplied three times. 3 3 The symbol for cube root is √⬚. The √𝑚 is read as “cube root of m”. 6 3. Lesson Activity A. Complete the table below. Perfect Exponential Form (a number that when multiplied three times, the Cube Root Cube result is the given perfect cube) 1 1x1x1 1 –8 –2 x –2 x –2 –2 (15 minutes) 125 –216 1,000 1/8 8/27 B. Perfect Cube and Cube Root. Place each number in its appropriate column: –27, 0, 9, 64, 81, 512, 729, –1/27, 4/64 Perfect Cube Number Not Perfect Cube Number Cube Root of Perfect Cube Numbers Questions for discussion: 1. How did you decide which column the given number should be placed in? 2. Were all your answers correct? If not, why do you think some of your answers were not correct? What will you do to avoid this error next time? 3. How did you compute the cube roots of the perfect cube numbers? DAY 3 SUB-TOPIC 3: Irrational Numbers 1. Explicitation Place the following numbers in the appropriate columns: 3 3 3 3 1/2 , –3, √9, √7, √100, √17, √1, √−8, √9, √12 Rational Number Irrational Number 7  Questions for discussion: 1. Observe the numbers in the first column. What do you observe about the rational numbers? Let the students discuss their 2. Observe the numbers in the second column. What do you observe about answers. the irrational numbers? (What can you say about the number inside the radical sign?) Lead the students to the definition of irrational numbers: If the radicand of a square root is not a perfect square, then it is considered Begin Day 3 with recalling an irrational number. Likewise, if the radicand of a cube root is not a perfect concepts covered in the cube, then it is an irrational number. These numbers cannot be written as a previous day. fraction because the decimal does not end (or non-terminating) and does not (5 minutes) for review repeat a pattern (or non-repeating). (15 minutes) for the activity In plotting an irrational number involving square root or cube root on a number line, estimate first the square root or cube root of the given irrational number and to which two consecutive integers it lies in between. Let student view the video on 2. Worked Example how to plot irrational numbers For example, to locate and plot √3 on the number line, we identify two perfect involving square roots using squares nearest to the radicand 3. These are 1 and 4. So, √3 is between 1 and this link: 2 (the square roots of 1 and 4, respectively). Since, 3 is closer to 4 than to 1, √3 www.youtube.com/watch?v=ES is closer to 2. GkaZnrwrI. √3 √1 √4 (10 minutes) Locate and plot the following square roots and cube roots on a number line: a. √90 b. √27 3 c. √20 8  3 d. √75 3. Lesson Activity Irrational Numbers. A. Estimate the given square root or cube root and find the letter that corresponds to it on the number line. 3 1. √15 3. √99 5. √388 3 2. √38 4. √20 B. Plot the points on a number line. 1. Point A: √26 2. Point B: √32 3. Point C: √68 3 4. Point D: √40 3 5. Point E: √−199 D. Making 1. Learner’s Takeaways (20 minutes) Generalizations A. Define and give an example for each term: Let the students answer the Perfect square Perfect cube questions and then afterward, ask some learners to share Square root Cube root their answers. Irrational numbers (involving square root and cube root) B. Answer the following questions: 1. How do you compute the square root of a perfect square? 2. How do you compute the cube root of a perfect cube? 9  3. How do you plot irrational numbers involving square root and cube root? 2. Reflection on Learning Are there any challenges and misconceptions you encountered while studying the lesson? What are those? IV. EVALUATING LEARNING: FORMATIVE ASSESSMENT AND TEACHER’S REFLECTION NOTES TO TEACHERS A. Evaluating DAY 4 Assessment helps teachers Learning 1. Formative Assessment gauge how well students A. Find the square root if the given number is a perfect square. Find its cube understand mathematical root if it is a perfect cube. concepts and principles. It Square Root of the Number if Cube Root of the Number if it provides feedback on their Number comprehension, problem- it is a Perfect Square is a Perfect Cube solving skills, and ability to 49 apply mathematical knowledge. 121 Let students answer all items –27 here individually or collaboratively. 1/4 9/25 216 –8 324 512 400 B. Solve the following problems. 1. Mr. Agra has a square vegetable plot which has an area of 144 square meters. If Mr. Agra will put a fence around the vegetable plot, how long should be the fencing material that he will need? 2. Mrs. San Jose has two cubic containers of different sizes. The larger of the two has sides that measure 25 cm while the smaller one has sides that measure 18 cm. Will the two containers be enough for 1,000 cubic 10  centimeters of water? C. Plot the following numbers on a number line. 1. √17 3. √41 5. √100 3 3 2. √55 4. √25 2. Homework (Optional) The teacher may give homework to master the lesson. B. Teacher’s Note observations on any The teacher may take note of Effective Practices Problems Encountered Remarks of the following areas: some observations related to the effective practices and strategies explored problems encountered after utilizing the different strategies, materials used, learner materials used engagement, and other related stuff. learner engagement/ Teachers may also suggest interaction ways to improve the different activities explored/lesson others exemplar. C. Teacher’s Reflection guide or prompt can be on: Teacher’s reflection in every Reflection principles behind the teaching lesson conducted/facilitated is What principles and beliefs informed my lesson? essential and necessary to Why did I teach the lesson the way I did? improve practice. You may also consider this as an input for students the LAC/Collab sessions. What roles did my students play in my lesson? What did my students learn? How did they learn? ways forward 11 What could I have done differently? What can I explore in the next lesson? 12