Mathematics

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner… STANDARDS M4ME-IIIi-51  BEAM LG Gr.4 Module 18 The learner… The learner… M4ME-IIIi-52 – Perimeter M4ME-IIIj-53Grade 4- FOURTH QUARTER 61. finds the perimeter of triangles, M4ME-IIIj-54  DLP Gr. 4 Module 82, 83, squares, rectangles, parallelograms, M4ME-IVa-55 86 and trapezoids. M4ME-IVa-56 M4ME-IVb-57  Lesson Guide in Elem. 62. solves routine and non-routine Math Gr. 4 p.302, 305 problems in real-life situations M4ME-IVb-58 involving perimeter of squares and  BEAM LG Gr.4 Module 18 rectangles, triangles, parallelograms, – Perimeter and trapezoids.  Lesson Guide in Elem. 63. differentiates perimeter from area. Math Gr. 4 p.309 64. converts sq. cm to sq. m and vice  BEAM LG Gr.4 Module 13 versa. – Area 65. finds the area of irregular figures made  DLP Gr. 4 Module 85 up of squares and rectangles using sq.  Lesson Guide in Elem. cm and sq. m. Math Gr. 4 p.315, 317, 66. estimates the area of irregular plane 321, 325 figures made up of squares and  BEAM LG Gr.4 Module 13 rectangles. – Area, Gr. 5 Module 14 – Area 67. derives the formulas for the area of  DLP Gr. 4 Module 48, Gr. 5 triangles, parallelograms, and Module 47, 50 trapezoids.  Lesson Guide in Elem. Math Gr. 5 p.372, 377, Gr. 68. finds the area of triangles, 6 p. 373, 378 parallelograms and trapezoids using sq.  MISOSA Module Gr.5 – cm and sq. m. Page 50 of 109K to 12 Mathematics Curriculum Guide December 2013

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner… STANDARDS M4ME-IVc-59 Area of a Trapezoid M4ME-IVc-60  BEAM LG Gr.4 Module 13 The learner… The learner… – Area M4ME-IVd-61  Lesson Guide in Elem. 69. estimates the area of triangles, Math Gr. 5 p.386 parallelograms, and trapezoids M4ME-IVd-62 M4ME-IVe-63  BEAM LG Gr.4 Module 14 70. solves routine and non-routine M4ME-IVe-64 – Volume problems involving squares, M4ME-IVf-65 rectangles, triangles, parallelograms, M4ME-IVf-66  DLP Gr. 4 Module 87 and trapezoids. M4SP-IVg-1.4  Lesson Guide in Elem. M4SP-IVg-2.4 71. creates problems(with reasonable M4SP-IVg-3.4 Math Gr. 5 p.328 answers) involving perimeter and area  Lesson Guide in Elem. involving squares, rectangles, triangles, parallelograms, and Math Gr. 6 p.391 trapezoids.  Lesson Guide in Elem. 72. visualizes the volume of solid figures in Math Gr. 4 p.331, 337 different situations using non-standard (e.g. marbles, etc.) and standard units. Page 51 of 109Statistics and demonstrates is able to create and 73. derives the formula for the volume ofProbability understanding of the interpret simple rectangular prisms. concepts of bar graphs representations of data and simple experiments. (tables and bar graphs) and 74. finds the volume of a rectangular prism describe outcomes in using cu. cm and cu. m. simple experiments. 75. solves routine and non-routine problems involving the volume of a rectangular prism. 76. creates problems(with reasonable answers) involving volume of rectangular prism. 77. collects data on two variables using any source. 78. organizes data in tabular form and presents them in a single/double horizontal or vertical bar graph. 79. interprets data presented in different kinds of bar graphs (vertical/horizontal, single/double bars).K to 12 Mathematics Curriculum Guide December 2013

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner… STANDARDS M4SP-IVh-4.4 M4SP-IVh-5.4 The learner… The learner… M4SP-IVi-9 80. solves routine and non-routine problems using data presented in a M4SP-IVi-10 single or double-bar graph. M4SP-IVi-11 M4SP-IVj-12 81. draws inferences based on data M4SP-IVj-13 presented in a double-bar graph. 82. records favorable outcomes in a simple experiment (e.g. tossing a coin, spinning a wheel, etc.) 83. expresses the outcome in a simple experiment in words, symbols, tables, or graphs. 84. explains the outcomes in an experiment. 85. solves routine and non-routine problems involving a simple experiment. 86. creates problems involving a simple experiment.K to 12 Mathematics Curriculum Guide December 2013 Page 52 of 109

K to 12 BASIC EDUCATION CURRICULUM GRADE 5CONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner… STANDARDS The learner… The learner…Grade 5- FIRST QUARTERNumbers and 1. demonstrates 1. is able to recognize 1. visualizes numbers up to 10 000 000 M5NS-Ia-1.5  DLP Gr. 3 Module 1, Gr. 4Number understanding of and represent whole with emphasis on numbers 100 001 – Module 1Sense whole numbers up to numbers up to 10 000 10 000 000. M5NS-Ia-9.5 10 000 000. 000 in various forms  BEAM LG Gr. 4 Module 1- and contexts. 2. reads and writes numbers up to M5NS-Ia-15.3 Whole Numbers 2. demonstrates 10 000 000 in symbols and in words. M5NS-Ib-58.1 understanding of 2. is able to apply M5NS-Ib-58.2  Lesson Guide in Elem. divisibility, order of divisibility, order of M5NS-Ib-58.3 Math Gr. 4 p. 1 operations, factors operations, factors and and multiples, and the multiples, and the four  MISOSA Gr. 4 Module – four fundamental fundamental operations Numbers through Billions operations involving involving fractions in fractions mathematical problems  DLP Gr. 3 Module 3, Gr. 4 and real-life situations. Module 3 3. rounds numbers to the nearest  BEAM LG Gr. 4 Module 1- hundred thousand and million. Whole Numbers, Gr. 5 Module 1 4. uses divisibility rules for 2, 5, and 10 to find the common factors of  Lesson Guide in Elem. numbers. Math Gr. 4 p. 7, Gr. 5 p. 1 5. uses divisibility rules for 3, 6, and 9 to  DLP Gr. 3 Module 6, Gr. 5 find common factors. Module 4 6. uses divisibility rules for 4, 8, 12, and  BEAM LG Gr. 4 Module – 11 to find common factors. Rounding Off Numbers  Lesson Guide in Elem. Math Gr. 4 p. 13  MISOSA Gr. 4 Module – Rounding Numbers  DLP Gr. 4 Module 4, Gr. 5 Module 1, 12  Lesson Guide in Elem. Math Gr. 5 p.48  DLP Gr. 5 Module 1, 12  Lesson Guide in Elem. Math Gr. 5 p.51, 57  DLP Gr. 5 Module 1, 12K to 12 Mathematics Curriculum Guide December 2013 Page 53 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner… STANDARDS M5NS-Ic-59  Lesson Guide in Elem. M5NS-Ic-60 The learner… The learner… M5NS-Ic-61.2 Math Gr. 5 p.57 M5NS-Id-62.2 7. solves routine and non-routine M5NS-Id-68.2  DLP Gr. 5 Module 9 problems involving factors, multiples,  BEAM LG Gr. 6 – Number and divisibility rules for M5NS-Id-69.2 2,3,4,5,6,8,9,10,11, and 12. M5NS-Ie-70.2 Theory M5NS-Ie-71.2  Lesson Guide in Elem. 8. creates problems(with reasonable answers) involving factors, multiples Math Gr. 5 p.33, Gr. 6 p. and divisibility rules. 148  DLP Gr. 5 Module 11 9. states, explains, and interprets  BEAM LG Gr. 6 – Number Parenthesis, Multiplication, Division, Theory Addition, Subtraction (PMDAS) or  Lesson Guide in Elem. Grouping, Multiplication, Division, Math Gr. 5 p.44, Gr. 6 p. Addition, Subtraction (GMDAS) rule. 151 10. simplifies a series of operations on Page 54 of 109 whole numbers involving more than two operations using the PMDAS or GMDAS rule. 11. finds the common factors and the GCF of 2–4 numbers using continuous division. 12. finds the common multiples and LCM of 2–4 numbers using continuous division. 13. solves real-life problems involving GCF and LCM of 2-3 given numbers. 14. creates problems(with reasonable answers)involving GCF and LCM of 2-3 given numbers.K to 12 Mathematics Curriculum Guide December 2013

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner… STANDARDS The learner… The learner… 15. adds fractions and mixed fractions M5NS-Ie-84  DLP Gr. 5 Module 16, 22 without and with regrouping. M5NS-If-85  Lesson Guide in Elem. M5NS-If-87.2 16. subtracts fractions and mixed fractions Math Gr. 5 p. 99 – 107 without and with regrouping.  MISOSA Gr. 5 Modules on 17. solves routine and non-routine Addition of Fractions and problems involving addition and/or Mixed Forms subtraction of fractions using appropriate problem solving strategies  BEAM LG Gr. 5 Module 4 – and tools. Subtraction of Dissimilar Fractions 18. creates problems (with reasonable answers) involving addition and/or  Lesson Guide in Elem. subtraction of fractions using Math Gr. 5 p. 140-166 appropriate problem solving strategies.  MISOSA Gr. 5 Modules on 19. visualizes multiplication of fractions Subtraction of Fractions using models. and Mixed Forms  BEAM LG Gr. 5 Module 7 – Application of Subtraction of Fraction  Lesson Guide in Elem. Math Gr. 5 p. 119, 172,176  MISOSA Gr. 5 Modules on Addition and Subtraction of Word problems involving Fractions M5NS-If-88.2 M5NS-Ig-89  DLP Gr. 4 Module 69  BEAM LG Gr. 4 Module 10K to 12 Mathematics Curriculum Guide December 2013 – Multiplication of Fractions  Lesson Guide in Elem. Math Gr. 4 p. 250, Gr. 5 p.180  MISOSA Gr. 5 Module – Visualization of Multiplication of Fractions Page 55 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner… STANDARDS M5NS-Ig-90.1  DLP Gr. 4 Module 70, Gr. 5 The learner… The learner… Module 25 M5NS-Ig-91 20. multiplies a fraction and a whole M5NS-Ih-92.1  BEAM LG Gr. 4 Module 10 number and another fraction. – Multiplication of Fractions M5NS-Ih-93.1 21. multiplies mentally proper fractions M5NS-Ih-94  Lesson Guide in Elem. with denominators up to 10. M5NS-Ii-95 Math Gr. 4 p. 254, 261, Gr. M5NS-Ii-96.1 5 p.187, 196, 200 22. solves routine or non-routine problems M5NS-Ij-97.1 involving multiplication without or with  MISOSA Gr. 5 Modules – addition or subtraction of fractions and Multiplication of Fractions whole numbers using appropriate problem solving strategies and tools.  DLP Gr. 4 Module 71  BEAM LG Gr. 4 Module 10 23. creates problems (with reasonable answers) involving multiplication of – Multiplication of Fractions fractions.  Lesson Guide in Elem. 24. shows that multiplying a fraction by its Math Gr. 4 p.264, 269 reciprocal is equal to 1.  MISOSA Gr. 5 Modules – 25. visualizes division of fractions. Word problems on 26. divides Multiplication of Fractions - simple fractions  DLP Gr. 6 Module 38 - whole numbers by a fraction and  MISOSA Modules Gr.6 – vice versa Division of Fractions 27. solves routine or non-routine problems involving division without or with any of the other operations of fractions and whole numbers using appropriate problem solving strategies and tools .K to 12 Mathematics Curriculum Guide December 2013 Page 56 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner… STANDARDS The learner… The learner… 28. creates problems (with reasonable M5NS-Ij-98.1 answers) involving division or with any of the other operations of fractions and whole numbers.Grade 5- SECOND QUARTERNumbers and 1. demonstrates 1. is able to recognize 29. gives the place value and the value of M5NS-IIa-101.2  DLP Gr. 6 Module 5Number understanding of and represent a digit of a given decimal number  Lesson Guide in Elem.Sense decimals. decimals in various through ten thousandths. forms and contexts. Math Gr. 5 p.237, Gr. 6 p. 2. demonstrates understanding of 2. is able to apply the 38 the four  MISOSA Module Gr.6 – fundamental operations involving Place Value of Decimals decimals and ratio and proportion. four fundamental  DLP Gr. 4 Module 47, Grade 5 Module 30, Gr. 6 operations involving Module 6 decimals and ratio and  BEAM LG Gr. 5 Decimals, proportion in Gr. 6 Module 2 mathematical 30. reads and writes decimal numbers M5NS-IIa-102.2  Lesson Guide in Elem. problems and real-life through ten thousandths. Math Gr. 5 p.241, Gr. 6 situations. p.43  MISOSA Module Gr.6 – Read and Write Decimals 31. rounds decimal numbers to the nearest M5NS-IIa-103.2  DLP Gr. 4 Module 49, hundredth and thousandth. Grade 5 Module 31, Gr. 6 Module 8K to 12 Mathematics Curriculum Guide December 2013  BEAM LG Gr. 5 Decimals, Gr. 6 Module 2  Lesson Guide in Elem. Math Gr. 5 p.247, Gr. 6 p.49  MISOSA Gr. 5 and 6 Modules –Rounding Decimals Page 57 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner… STANDARDS The learner… The learner… 32. compares and arranges decimal M5NS-IIb-104.2  DLP Gr. 6 Module 7 numbers.  BEAM LG Gr. 6 Module 2  Lesson Guide in Elem. Math Gr. 6 p. 46  MISOSA Module Gr.6 – Compare and Order Decimals 33. visualizes addition and subtraction of M5NS-IIb-105 decimals. 34. adds and subtracts decimal numbers M5NS-IIb-106.1  DLP Gr. 4 Module 50, 51, through thousandths without and with M5NS-IIc-107 52, 53, Grade 5 Module 32, regrouping. 34 35. estimates the sum or difference of  BEAM LG Gr. 4 Module 7 – decimal numbers with reasonable Addition and Subtraction of results. Decimals, Gr. 5 Module 7 36. solves routine or non-routine problems  Lesson Guide in Elem. involving addition and subtraction of Math Gr. 5 p.117, 251, decimal numbers including money 254, 257, 264 using appropriate problem solving strategies and tools.  MISOSA Gr. 4 and Gr. 5 Modules – Addition and Subtraction of Decimals  DLP Gr. 6 Module 9 M5NS-IIc-108.1  DLP Gr. 4 Module 54, 55, 56, Grade 5 Module 35K to 12 Mathematics Curriculum Guide December 2013  BEAM LG Gr. 4 Module 7 – Addition and Subtraction of Decimals, Gr. 5 Module 7  Lesson Guide in Elem. Math Gr. 5 p.271  MISOSA Gr. 4 Modules – Word Problems on Addition and Subtraction of Decimals Page 58 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner… STANDARDS The learner… The learner… 37. creates problems (with reasonable M5NS-IIc-109.1 answers) involving addition and/or subtraction of decimal numbers M5NS-IId-110  Lesson Guide in Elem. including money. M5NS-IId-111.1 Math Gr. 5 p.274 M5NS-IId-111.2 38. visualizes multiplication of decimal M5NS-IIe-112  MISOSA Gr. 5 Module – numbers using pictorial models. Multiplication of Decimals M5NS-IIe-113.1 and Whole Numbers 39. multiplies decimals up to 2 decimal places by 1- to 2-digit whole numbers.  Lesson Guide in Elem. Math Gr. 5 p.279, 282 40. multiplies decimals with factors up to 2 decimal places.  MISOSA Gr. 5 Module – Multiplication of Decimals 41. estimates the products of decimal through Hundredths numbers with reasonable results.  DLP Gr. 6 Module 13 42. solves routine and non-routine  MISOSA Module Gr.6 – problems involving multiplication without or with addition or subtraction Estimating Quotients of of decimals and whole numbers Decimals including money using appropriate problem solving strategies and tools.  MISOSA Gr. 5 Module – Word Problems on 43. visualizes division of decimal numbers Multiplication of Decimals using pictorial models. M5NS-IIf-115  Lesson Guide in Elem. 44. divides decimals with up to 2 decimal Math Gr. 5 p.305 places. M5NS-IIf-116.1  DLP Grade 5 Module 42 45. divides whole numbers with quotients M5NS-IIf-116.2  BEAM LG Gr. 5 Module 13 in decimal form. M5NS-IIg-117  Lesson Guide in Elem. 46. estimates the quotients of decimal Math Gr. 5 p.314 numbers with reasonable results.  MISOSA Gr. 5 Module – Division of Decimals  Lesson Guide in Elem. Math Gr. 6 p.109  DLP Gr. 6 Module 18K to 12 Mathematics Curriculum Guide December 2013 Page 59 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner… STANDARDS M5NS-IIg-120.1  DLP Grade 5 Module 43 M5NS-IIg-121.1  BEAM LG Gr. 5 Module 13 The learner… The learner… M5NS-IIh-122  MISOSA Gr. 5 Module – 47. solves routine and non-routine Word Problems on Division problems involving division without or of Decimals with any of the other operations of decimals and whole numbers including  MISOSA Gr. 5 Module – money using appropriate problem Visualization of Ratio solving strategies and tools. 48. creates problems (with reasonable answers) involving multiplication and/or division or with any of the other operations of decimals and whole numbers including money. 49. visualizes the ratio of 2 given numbers. 50. expresses ratio using either the colon M5NS-IIh-123  DLP Gr. 6 Module 42 (:) or fraction.  BEAM LG Gr. 5 Module 9, M5NS-IIi-124 51. identifies and writes equivalent ratios. Gr. 6 Module 11 M5NS-IIi-125  Lesson Guide in Elem. 52. expresses ratios in their simplest forms. M5NS-IIi-126 53. finds the missing term in a pair of M5NS-IIj-127 Math Gr. 5 p.218 M5NS-IIj-128  MISOSA Gr. 5 Module – equivalent ratios. 54. defines and describes a proportion. Expressing Ratio 55. recognizes when two quantities are in  DLP Grade 5 Module 29  BEAM LG Gr. 5 Module 9 direct proportion.  Lesson Guide in Elem.K to 12 Mathematics Curriculum Guide December 2013 Math Gr. 5 p.227  MISOSA Gr. 5 Module – Proportion  Lesson Guide in Elem. Math Gr. 5 p.222  MISOSA Gr. 5 Module – Ratio in its Simplest Form  DLP Gr. 6 Module 43 Page 60 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner… STANDARDS M5NS-IIIa-136  DLP Gr. 5 Module 44 The learner… The learner…  BEAM LG Gr. 5 Module 14 M5NS-IIIa-137  Lesson Guide in Elem.Grade 5- THIRD QUARTER M5NS-IIIa-138 M5NS-IIIb-139 Math Gr. 5 p.321, 325, demonstrates is able to apply percent in 56. visualizes percent and its relationship to M5NS-IIIb-140 330, 334 understanding of percent. mathematical problems and fractions, ratios, and decimal numbers M5NS-IIIb-141  MISOSA Gr. 5 Modules– real-life situations using models. M5GE-IIIc-19 Percent, Fraction, Ratio M5GE-IIIc-20 and Decimal 57. defines percentage, rate or percent, M5GE-IIIc-21  DLP Gr. 6 Module 45 and base. M5GE-IIId-22  BEAM LG Gr. 6 Module 17 M5GE-IIId-23.1  Lesson Guide in Elem. 58. identifies the base, percentage, and Math Gr. 6 p.311 rate in a problem.  DLP Gr. 6 Module 45  Lesson Guide in Elem.Geometry demonstrates is able to construct and 59. finds the percentage in a given Math Gr. 5 p.339 understanding of describe polygons, circles, problem.  DLP Gr. 6 Module 46 polygons, circles, and solid and solid figures .  BEAM LG Gr. 6 Module 17 figures. 60. solves routine and non-routine  Lesson Guide in Elem. problems involving percentage using Math Gr. 5 p.345 appropriate strategies and tools.  BEAM LG Gr. 6 Module 17 61. creates problems involving percentage,  DLP Gr. 4 Module 72 with reasonable answers.  Lesson Guide in Elem. 62. visualizes, names, and describes Math Gr. 5 p.350, 354 polygons with 5 or more sides.  DLP Gr. 5 Module 46 63. describes and compares properties of  BEAM LG Gr. 5 Geometry polygons (regular and irregular polygons). 64. draws polygons with 5 or more sides. 65. visualizes congruent polygons. 66. visualizes and describes a circle.K to 12 Mathematics Curriculum Guide December 2013 Page 61 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner… STANDARDS The learner… The learner…Patterns and demonstrates 1. is able to apply the 67. identifies the terms related to a circle. M5GE-IIId-23.2Algebra understanding of the knowledge of sequence M5GE-IIIe-24 concept of sequence and in various situations. 68. draws circles with different radii using a M5GE-IIIe-25 solving simple equations. compass. M5GE-IIIe-26 2. is able to use different problem solving 69. visualizes and describes solid figures. M5AL-IIIf-6 strategies. 70. makes models of different solid figures: cube, prism, pyramid, cylinder, cone, and sphere using plane figures. 71. formulates the rule in finding the next term in a sequence. e.g. 1, 3, 7,15, (15 x 2+1) Possible answers: (x 2 + 1) (+2, +4, +8, +16) 72. uses different strategies (looking for a M5AL-IIIf-14 pattern, working backwards, etc.) to solve for the unknown in simple equations involving one or more operations on whole numbers and fractions. e.g. 3 x _ + 1 = 10 (the unknown is solved by working backwards)Measurement demonstrates is able to apply knowledge 73. measures time using a 12-hour and a M5ME-IIIg-14 understanding of time and of time and circumference 24-hour clock. M5ME-IIIg-15 circumference. in mathematical problems and real-life situations. 74. calculates time in the different world time zones in relation to the Philippines.K to 12 Mathematics Curriculum Guide December 2013 Page 62 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner… STANDARDS The learner… The learner… 75. solves problems involving time. M5ME-IIIg-16 M5ME-IIIh-67 76. visualizes circumference of a circle. M5ME-IIIh-68  BEAM LG Gr. 5 Module 2 - 77. measures circumference of a circle M5ME-IIIi-69 Circumference using appropriate tools. M5ME-IIIi-70  BEAM LG Gr. 5 Module 2 – Circumference 78. derives a formula in finding the M5ME-IIIj-71 circumference of a circle.  Lesson Guide in Elem. M5ME-IVa-72 Math Gr. 5 p.362 79. finds the circumference of a circle. M5ME-IVa-73  DLP Gr. 5 Module 52 80. solves routine and non-routine M5ME-IVa-74  BEAM LG Gr. 5 Module 2 – problems involving circumference of a circle. Circumference  Lesson Guide in Elem.Grade 5- FOURTH QUARTER Math Gr. 5 p.366Measurement demonstrates is able to apply knowledge 81. visualizes area of a circle.  MISOSA Gr. 5 Module – understanding of area, of area, volume and volume and temperature. temperature in 82. derives a formula in finding the area of Circumference of a Circle mathematical problems and a circle .  BEAM LG Gr. 5 Module 2 – real-life situations. Circumference 83. finds the area of a given circle.  Lesson Guide in Elem.K to 12 Mathematics Curriculum Guide December 2013 Math Gr. 5 p.369  MISOSA Gr. 5 Module – Word Problems on Circumference  BEAM LG Gr. 5 Module 14 - Area  DLP Gr. 5 Module 49  BEAM LG Gr. 5 Module 14 – Area  Lesson Guide in Elem. Math Gr. 5 p.382  MISOSA Gr. 5 Module – Area of a Circle  DLP Gr. 5 Module 53  BEAM LG Gr. 5 Module 14 - Area Page 63 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner… STANDARDS The learner… The learner… 84. solves routine and non-routine M5ME-IVb-75 problems involving the area of a circle. M5ME-IVb-76 M5ME-IVc-77 85. creates problems involving a circle, M5ME-IVc-78 with reasonable answers. M5ME-IVc-79 86. visualizes the volume of a cube and M5ME-IVd-80  Lesson Guide in Elem. rectangular prism. Math Gr. 5 p. 389, Gr. 6 p. M5ME-IVd-81 384 87. names the appropriate unit of measure M5ME-IVd-82 used for measuring the volume of a  Lesson Guide in Elem. cube and a rectangle prism. Math Gr. 6 p.391 88. derives the formula in finding the  DLP Gr. 6 Module 57 volume of a cube and a rectangular  Lesson Guide in Elem. prism using cubic cm and cubic m. Math Gr. 5 p.392, Gr. 6 p. 89. converts cu. cm to cu. m and vice 388 versa; cu.cm to L and vice versa.  DLP Gr. 5 Module 54  BEAM LG Gr. 5 Module 18 90. finds the volume of a given cube and – Volume rectangular prism using cu. cm and cu.  Lesson Guide in Elem. m. Math Gr. 5 p.395  MISOSA Gr. 5 Module – 91. estimates and uses appropriate units of Volume of a Rectangular measure for volume. Prism 92. solves routine and non-routine  DLP Gr. 5 Module 55 problems involving volume of a cube  BEAM LG Gr. 5 Module 18 and rectangular prism in real-life situations using appropriate strategies – Volume and tools.  Lesson Guide in Elem. 93. creates problems (with reasonable Math Gr. 5 p.399 answers) involving volume of a cube M5ME-IVe-83 M5ME-IVe-84  DLP Gr. 5 Module 56  BEAM LG Gr. 5 Module 19K to 12 Mathematics Curriculum Guide December 2013 Page 64 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner… STANDARDS M5ME-IVf-85 – Temperature The learner… The learner…  Lesson Guide in Elem. M5ME-IVf-86 and rectangular prism in real-life Math Gr. 5 p.305 situations. M5ME-IVf-87 M5ME-IVg-88  DLP Gr. 5 Module 57 94. reads and measures temperature using M5SP-IVg-1.5  BEAM LG Gr. 5 Module 19 thermometer (alcohol and/or digital) in degree Celsius. M5SP-IVg-2.5 – Temperature M5SP-IVh-3.5  Lesson Guide in Elem. 95. estimates the temperature(e.g. inside M5SP-IVh-4.5 the classroom). M5SP-IVh-5.5 Math Gr. 5 p.409  MISOSA Gr. 5 Module – 96. solves routine and non-routine problems involving temperature in real- Temperature life situations.  BEAM LG Gr. 5 Module 20 97. creates problems involving – Line Graph temperature, with reasonable answers.  Lesson Guide in Elem.Statistics and demonstrates is able to create and 98. collects data on one to two variables Math Gr. 5 p.417Probability understanding of line interpret representations of using any source. graphs and experimental data (tables and line  MISOSA Gr. 5 Module – probability. graphs) and apply 99. organizes data in tabular form and Line Graph experimental probability in presents them in a line graph. mathematical problems and  DLP Gr. 5 Module 58, 59 real-life situations.  BEAM LG Gr. 5 Module 20 100. interprets data presented in different – Line Graph kinds of line graphs (single to double-  Lesson Guide in Elem. line graph). Math Gr. 5 p.412 101. solves routine and non-routine problems using data presented in a line Page 65 of 109 graph. 102. draws inferences based on data presented in a line graph.K to 12 Mathematics Curriculum Guide December 2013

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner… STANDARDS M5SP-IVi-14 M5SP-IVi-15 The learner… The learner… M5SP-IVi-16 103. describes experimental probability. M5SP-IVj-17 M5SP-IVj-18 104. performs an experimental probability and records result by listing. 105. analyzes data obtained from chance using experiments involving letter cards (A to Z) and number cards (0 to 20). 106. solves routine and non-routine problems involving experimental probability. 107. creates routine and non-routine problems involving experimental probability.K to 12 Mathematics Curriculum Guide December 2013 Page 66 of 109

K to 12 BASIC EDUCATION CURRICULUM GRADE 6CONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner… STANDARDS The learner… The learner…Grade 6- FIRST QUARTERNumbers and demonstrates is able to apply the four 1. adds and subtracts simple fractions and  Lesson Guide in Elem.Number understanding of the four fundamental operations mixed numbers without or with Math Gr. 6 p. 203, 207,Sense fundamental operations involving fractions and regrouping. 212, 216, 219, 223 involving fractions and decimals in mathematical decimals. problems and real-life M6NS-Ia-86  DLP Gr. 6 Module 31, 32 situations.  BEAM LG Gr. 6 Module 8A  MISOSA Modules Gr.5 and 6– Subtraction of Mixed Numbers 2. solves routine and non-routine M6NS-Ia-87.3  Lesson Guide in Elem. problems involving addition and/or Math Gr. 6 p.232 subtraction of fractions using appropriate problem solving strategies  BEAM LG Gr. 6 Module 8B and tools.  MISOSA Module Gr.6 – Word Problems on Subtraction of Fractions 3. creates problems (with reasonable M6NS-Ia-88.3 answers) involving addition and/or subtraction of fractions. M6NS-Ib-90.2  Lesson Guide in Elem. Math Gr. 5 p.203, 209, Gr. 4. multiplies simple fractions and mixed fractions. 6 p. 237, 250  DLP Gr. 5 Module 24, 26, Gr. 6 Module 35  BEAM LG Gr. 5 Module 9, Gr. 6 Module 9  MISOSA Module Gr.5 and 6– Multiplication of Mixed Numbers and FractionsK to 12 Mathematics Curriculum Guide December 2013 Page 67 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner… STANDARDS The learner… The learner… 5. solves routine or non-routine problems M6NS-Ib-92.2  Lesson Guide in Elem. involving multiplication without or with Math Gr. 5 p.213, Gr. 6 p. addition or subtraction of fractions and 262 mixed fractions using appropriate problem solving strategies and tools.  DLP Gr. 5 Module 27, 28, Gr. 6 Module 36, 37 6. creates problems (with reasonable answers) involving multiplication  BEAM LG Gr. 5 Module 9, without or with addition or subtraction Gr. 6 Module 9 of fractions and mixed fractions.  MISOSA Module Gr.6 – 7. divides simple fractions and mixed Word Problems on fractions. Multiplication of Fractions 8. solves routine or non-routine problems involving division without or with any of M6NS-Ib-93.2 the other operations of fractions and mixed fractions using appropriate M6NS-Ic-96.2  Lesson Guide in Elem. problem solving strategies and tools. M6NS-Ic-97.2 Math Gr. 6 p.273, 277 9. creates problems (with reasonable  BEAM LG Gr. 6 Module 10 answers) involving division without or  MISOSA Module Gr.6 – with any of the other operations of fractions and mixed fractions. Division of Mixed Numbers  Lesson Guide in Elem. Math Gr. 6 p.282, 286  DLP Gr. 6 Module 40, 41  BEAM LG Gr. 6 Module 10 M6NS-Ic-98.2 10. adds and subtracts decimals and mixed M6NS-Id-106.2  Lesson Guide in Elem. decimals through ten thousandths Math Gr. 6 p.54, 56, 60, 62 without or with regrouping.  DLP Gr. 6 Module 10, 11K to 12 Mathematics Curriculum Guide December 2013  BEAM LG Gr. 6 Module on Addition and Subtraction of Decimals  MISOSA Modules Gr.5 – Addition and Subtraction of Mixed Decimals Page 68 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner… STANDARDS The learner… The learner… 11. solves 1 or more steps routine and M6NS-Id-108.2  MISOSA Module Gr.6 – non-routine problems involving addition Subtraction of Mixed and/or subtraction of decimals and Decimals mixed decimals using appropriate problem solving strategies and tools.  Lesson Guide in Elem. Math Gr. 6 p.68 12. creates problems (with reasonable answers) involving addition and/or  DLP Gr. 6 Module 12, 17 subtraction of decimals and mixed  BEAM LG Gr. 6 Module on decimals. Addition and Subtraction of 13. multiplies decimals and mixed decimals Decimals with factors up to 2 decimal places.  MISOSA Module Gr.5 – Word problems on Addition and Subtraction of Decimals M6NS-Id-109.2 14. multiplies mentally decimals up to 2 M6NS-Ie-111.3  Lesson Guide in Elem. decimals places by 0.1, 0.01,10, and M6NS-Ie-111.4 Math Gr. 5 p. 289, Gr. 6 100. p.73, 76, 80, 83  DLP Gr. 5 Module 37, 38, Gr. 6 Module 15  MISOSA Module Gr.5 and 6 –Multiplication of Mixed Decimals; Decimals through Hundredths  Lesson Guide in Elem. Math Gr. 5 p. 293, Gr. 6 p.86  DLP Gr. 5 Module 40  BEAM LG Gr. 6 Module 4  MISOSA Modules Gr.5 – Multiplication of Decimals by 10 and 100, by 0.1, 0.01, and 0.001K to 12 Mathematics Curriculum Guide December 2013 Page 69 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner… STANDARDS The learner… The learner… 15. solves routine and non-routine M6NS-Ie-113.2  Lesson Guide in Elem. problems involving multiplication of M6NS-If-113.3 Math Gr. 5 p.301, Gr. 6 decimals and mixed decimals including p.93 money using appropriate problem solving strategies.  DLP Gr. 6 Module 41  BEAM LG Gr. 5 Module 12 16. solves multi-step problems involving multiplication and addition or  Lesson Guide in Elem. subtraction of decimals, mixed decimals Math Gr. 6 p.96 and whole numbers including money using appropriate problem solving M6NS-If-114 strategies and tools. 17. creates problems (with reasonable answers) involving multiplication without or with addition or subtraction of decimals, mixed decimals and whole numbers including money. 18. divides whole numbers by decimals up M6NS-Ig-116.3  Lesson Guide in Elem. to 2 decimal places and vice versa. Math Gr.5 p.310, Gr. 6 p.103, 105, 117  DLP Gr. 6 Module 19  BEAM LG Gr. 6 Module 5- Division of Decimals  MISOSA Module Gr.5 and 6 –Division of Decimals by Whole Numbers 19. divides decimals/mixed decimals up to M6NS-Ig-116.4  Lesson Guide in Elem. 2 decimal places. M6NS-Ih-116.5 Math Gr. 6 p.121 20. divides decimals up to 4 decimal places  DLP Gr. 6 Module 20 by 0.1, 0.01, and 0.001.  BEAM LG Gr. 6 Module 5- Division of Decimals  Lesson Guide in Elem. Math Gr. 6 p.127  BEAM LG Gr. 6 Module 5- Division of DecimalsK to 12 Mathematics Curriculum Guide December 2013 Page 70 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner… STANDARDS The learner… The learner… 21. divides decimals up to 2 decimal M6NS-Ih-118  Lesson Guide in Elem. places by 10, 100, and 1 000 mentally. M6NS-Ii-119 Math Gr. 6 p.125 M6NS-Ii-120.2 22. differentiates terminating from  BEAM LG Gr. 6 Module 5- Division of Decimals repeating, non-terminating decimal quotients.  Lesson Guide in Elem. Math Gr. 6 p.111 23. solves routine and non-routine problems involving division of decimals,  MISOSA Module Gr.6 – mixed decimals, and whole numbers Repeating and Terminating including money using appropriate Decimals problem solving strategies and tools.  Lesson Guide in Elem. 24. solves multi-step routine and non- Math Gr. 5 p. 318, Gr. 6 routine problems involving division and p.130 any of the other operations of decimals, mixed decimals, and whole  DLP Gr. 6 Module 21 numbers including money using  BEAM LG Gr. 6 Module 5- appropriate problem solving strategies and tools. Division of Decimals 25. creates problems (with reasonable  Lesson Guide in Elem. answers) involving division without or Math Gr. 6 p.133 with any of the other operations of decimals, mixed decimals and whole M6NS-Ij-120.3 numbers including money. M6NS-Ij-121.2Grade 6- SECOND QUARTER M6NS-IIa-129Numbers and demonstrates is able to apply knowledge 26. expresses one value as a fraction of M6NS-IIa-130Number understanding of order of of order of operations, ratio another given their ratio and viceSense operations, ratio and and proportion, percent, versa. proportion, percent, exponents, and integers in exponents, and integers. mathematical problems and 27. finds how many times one value is as real-life situations. large as another given their ratio and vice versa.K to 12 Mathematics Curriculum Guide December 2013 Page 71 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner… STANDARDS The learner… The learner… 28. defines and illustrates the meaning of M6NS-IIb-131 ratio and proportion using concrete or pictorial models. M6NS-IIb-132 29. sets up proportions for groups of objects or numbers and for given situations. 30. finds a missing term in a proportion M6NS-IIb-133  Lesson Guide in Elem. (direct, inverse, and partitive). Math Gr. 6 p.301, 304, 307  BEAM LG Gr. 6 Module 11  MISOSA Module Gr.6 – Word Problems on Direct, Partitive and Inverse Proportion 31. solves problems involving direct M6NS-IIc-134 proportion, partitive proportion, and inverse proportion in different contexts M6NS-IIc-135 such as distance, rate, and time using M6NS-IId-142 appropriate strategies and tools. M6NS-IId-143 32. creates problems involving ratio and proportion, with reasonable answers. 33. finds the percentage or rate or percent  Lesson Guide in Elem. in a given problem. Math Gr. 6 p.316, 320, 323 34. solves routine and non-routine  DLP Gr. 6 Module 47, 48, problems involving finding the 49 percentage, rate and base using appropriate strategies and tools.  MISOSA Module Gr.6 – Finding the Percentage, 35. solves percent problems such as Rate and Base percent of increase/decrease (discounts, original price, rate of  MISOSA Module Gr.6 – discount, sale price, marked-up price), Word Problems on commission, sales tax, and simple Percentage interest. M6NS-IIe-144  Lesson Guide in Elem. Math Gr. 6 p.332, 336,K to 12 Mathematics Curriculum Guide December 2013 340, 344  DLP Gr. 6 Module 50, 51, 52  BEAM LG Gr. 6 Module 17 Page 72 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner… STANDARDS The learner… The learner… 36. creates problems involving percent, M6NS-IIe-145 with reasonable answers. M6NS-IIf-146 37. describes the exponent and the base in M6NS-IIf-147  Lesson Guide in Elem. a number expressed in exponential M6NS-IIf-148 Math Gr. 6 p.6 notation.  DLP Gr. 6 Module 1 38. gives the value of numbers expressed  MISOSA Module Gr.6 – in exponential notation. Exponents 39. interprets and explains the Grouping, Exponent, Multiplication, Division,  Lesson Guide in Elem. Addition, Subtraction (GEMDAS) rule. Math Gr. 6 p.9 40. performs two or more different  DLP Gr.4 Module 32 operations on whole numbers with or  MISOSA Module Gr.6 – without exponents and grouping symbols. Expressions involving Exponents 41. identifies real-life situations that make use of integers.  DLP Gr. 6 Module 2 42. describes the set of integers. M6NS-IIf-149  Lesson Guide in Elem. 43. compares integers with other numbers M6NS-IIg-150 Math Gr. 6 p.13, 17, 21, such as whole numbers, fractions, and 25, 28 decimals.  BEAM LG Gr. 6 Module 1 – 44. represents integers on the number line. Order of Operations 45. compares and arranges integers.  MISOSA Modules Gr.6 – Evaluating Expressions M6NS-IIg-151 M6NS-IIg-152 M6NS-IIh-153  Lesson Guide in Elem. M6NS-IIh-154 Math Gr. 6 p.353K to 12 Mathematics Curriculum Guide December 2013  Lesson Guide in Elem. Math Gr. 6 p.356, 358  DLP Gr. 6 Module 68, 69  BEAM LG Gr. 6 Module 18 – Expression and Integers Page 73 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner… STANDARDS The learner… The learner… 46. describes and interprets the basic M6NS-IIh-155 operations on integers using materials M6NS-IIi-156 such as algebra tiles, counters, chips, and cards. M6NS-IIj-157 47. performs the basic operations on integers. 48. solves routine and non-routine problems involving basic operations of integers using appropriate strategies and tools.Grade 6- THIRD QUARTERGeometry demonstrates is able to construct and 49. visualizes and describes the different M6GE-IIIa-27  Lesson Guide in Elem. understanding of solid describe the different solid solid figures: cube, prism, pyramid, Math Gr. 6 p.360, 363 figures. figures: cube, prism, cylinder, cone, and sphere. pyramid, cylinder, cone, and sphere. 50. differentiates solid figures from plane M6GE-IIIa-28 figures. 51. illustrates the different solid figures M6GE-IIIb-29 using various concrete and pictorial M6GE-IIIb-30 models.  DLP Gr. 6 Module 54 52. identifies the faces of a solid figure. 53. visualizes and describes the different  BEAM LG Gr. 6 Module 15 solid figures: cube, prism, pyramid, cylinder, cone, and sphere. M6GE-IIIc-31 54. identifies the nets of the following M6GE-IIIc-32 space figures: cube, prism, pyramid, cylinder, cone, and sphere using plane figures.K to 12 Mathematics Curriculum Guide December 2013 Page 74 of 109

K to 12 BASIC EDUCATION CURRICULUM CONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS STANDARDSPatterns and The learner…Algebra The learner… The learner… demonstrates understanding of sequence is able to apply knowledge 55. formulates the rule in finding the nth M6AL-IIId-7 in forming rules, of sequence, expressions, term using different strategies expressions and equations. and equations in (looking for a pattern, guessing and mathematical problems and checking, working backwards) real-life situations. e.g. 4,7,13,16,…n (the nth term is 3n+1) 56. differentiates expression from M6AL-IIId-15  Lesson Guide in Elem. equation. M6AL-IIIe-16 Math Gr. 6 p.1, 3  BEAM LG Gr. 6 Module 18 – Expression and Integers 57. gives the translation of real-life verbal M6AL-IIIe-17 expressions and equations into letters or symbols and vice versa. M6AL-IIIe-18  DLP Gr. 6 Module 70, 71 M6AL-IIIf-19 58. defines a variable in an algebraicMeasurement demonstrates is able to apply knowledge expression and equation. M6AL-IIIf-20 understanding of rate of speed, area, and surface M6ME-IIIg-17 and speed, and of area area of plane and 59. represents quantities in real-life M6ME-IIIg-18 and surface area of solid/space figures in situations using algebraic expressions plane and solid/space mathematical problems and and equations. M6ME-IIIh-89 figures. real-life situations 60. solves routine and non-routine problems involving different types of numerical expressions and equations such as 7+ 9 =___ + 6. 61. creates routine and non-routine problems involving numerical expressions and equations. 62. calculates speed, distance, and time. 63. solves problems involving average rate and speed. 64. finds the area of composite figures formed by any two or more of the following: triangle, square, rectangle, circle, and semi-circle.K to 12 Mathematics Curriculum Guide December 2013 Page 75 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner… STANDARDS The learner… The learner… 65. solves routine and non-routine M6ME-IIIh-90 problems involving area of composite figures formed by any two or more of M6ME-IIIi-91  Lesson Guide in Elem. the following: triangle, square, Math Gr. 6 p.371 rectangle, circle, and semi-circle. 66. visualizes and describes surface area and names the unit of measure used for measuring the surface area of solid/space figures. 67. derives a formula for finding the M6ME-IIIi-92  Lesson Guide in Elem. surface area of cubes, prisms, M6ME-IIIi-93 Math Gr. 6 p.369, 381 pyramids, cylinders, cones, and M6ME-IIIj-94 spheres.  DLP Gr. 6 Module 55  BEAM LG Gr. 6 Module 16 68. finds the surface area of cubes, prisms, pyramids, cylinders, cones, – Surface Area and spheres.  BEAM LG Gr. 6 Module 16 69. solves word problems involving – Surface Area measurement of surface area.  MISOSA Module Gr.6 – Surface Area on Cube, Rectangular Prism, Pyramid and Cylinder  DLP Gr. 6 Module 56  BEAM LG Gr. 6 Module 17 – Surface AreaGrade 6- FOURTH QUARTERMeasurement demonstrates is able to apply knowledge 70. determines the relationship of the understanding of volume of volume of solid figures volume between of solid figures and and meter reading in M6ME-IVa-95 meter reading. mathematical problems and 70.1 a rectangular prism and a real-life situations. pyramid; 70.2 a cylinder and a cone; 70.3 and a cylinder and sphere. 71. derives the formula for finding the M6ME-IVa-96  DLP Gr. 6 Module 58 volume of cylinders, pyramids, cones,  BEAM LG Gr. 6 Module 18 and spheres. – VolumeK to 12 Mathematics Curriculum Guide December 2013 Page 76 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner… STANDARDS The learner… The learner… 72. finds the volume of cylinders, M6ME-IVb-97  Lesson Guide in Elem. pyramids, cones, and spheres. Math Gr. 6 p.394, 398  BEAM LG Gr. 6 Module 18 – Volume  MISOSA Module Gr.6 – Volume of Rectangular Prism, Pyramid and Cylinder 73. solves routine and non-routine M6ME-IVc-98  Lesson Guide in Elem. problems involving volumes of solids. Math Gr. 6 p.402  DLP Gr. 6 Module 59  BEAM LG Gr. 6 Module 19 – Volume 74. creates problems involving surface M6ME-IVc-99 area and volume of solid/space figures, with reasonable answers. M6ME-IVd-100  Lesson Guide in Elem. Math Gr. 6 p.406, 409 75. reads and interprets electric and water meter readings.  DLP Gr. 6 Module 60, 61  BEAM LG Gr. 6 Module 20 – Meter Reading 76. solves routine and non-routine M6ME-IVd-101  Lesson Guide in Elem. problems involving electric and water Math Gr. 6 p.412, 415 consumption.  DLP Gr. 6 Module 62  BEAM LG Gr. 6 Module 20 – Meter Reading 77. creates problems involving electric M6ME-IVd-102 and water consumption, with reasonable answers.K to 12 Mathematics Curriculum Guide December 2013 Page 77 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner… STANDARDS M6SP-IVe-1.6  Lesson Guide in Elem. The learner… The learner… M6SP-IVe-2.6 Math Gr. 6 p.426Statistics and demonstrates is able to create and 78. collects data on one or two variables M6SP-IVf-3.6  DLP Gr. 6 Module 65Probability understanding of pie interpret representations using any source. M6SP-IVf-4.6  BEAM LG Gr. 6 Module 21 graphs and experimental of data (tables and pie M6SP-IVg-6 probability. graphs) and apply 79. constructs a pie graph based on a M6SP-IVg-19 – Circle Graphs experimental probability given set of data. M6SP-IVh-20  MISOSA Module Gr.6 – in mathematical problems M6SP-IVh-21 Constructing Circle Graph and real-life situations.  Lesson Guide in Elem. 80. interprets data presented in a pie Math Gr. 6 p.422 graph.  DLP Gr. 6 Module 64  BEAM LG Gr. 6 Module 21 81. solves routine and non-routine problems using data presented in a – Circle Graphs pie graph.  MISOSA Module Gr.6 – 82. creates problems that can be Interpreting Circle Graph answered using information presented in a pie graph.  Lesson Guide in Elem. Math Gr. 6 p.349 83. describes the meaning of probability such as 50% chance of rain and one  BEAM LG Gr. 6 Module 17 in a million chance of winning. – Prediction and Outcome Page 78 of 109 84. quantifies the phrases “most likely to happen” and “unlikely to happen”. 85. performs experiments and records outcomes.K to 12 Mathematics Curriculum Guide December 2013

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner… STANDARDS The learner… The learner… 86. makes listings and diagrams of M6SP-IVi-22  BEAM LG Gr. 6 Module 17 outcomes and tells the number of – Prediction and Outcome favorable outcomes and chances using these listings and diagrams. 87. makes simple predictions of events M6SP-IVi-23  Lesson Guide in Elem. based on the results of experiments. M6SP-IVj-24 Math Gr. 6 p.347  DLP Gr. 6 Module 67  BEAM LG Gr. 6 Module 17 – Prediction and Outcome 88. solves routine and non-routine M6SP-IVj-25 problems involving experimental and theoretical probability. 89. creates problems involving experimental and theoretical probability.K to 12 Mathematics Curriculum Guide December 2013 Page 79 of 109

K to 12 BASIC EDUCATION CURRICULUM GRADE 7CONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS STANDARDS The learner... Page 80 of 109 The learner...Grade 7- FIRST QUARTER The learner...Numbers and demonstrates is able to formulate 1. describes well-defined sets, subsets, M7NS-Ia-1 universal sets, and the null set andNumber understanding of key challenging situations cardinality of sets. M7NS-Ia-2Sense concepts of sets and the involving sets and real M7NS-Ib-1 2. illustrates the union and intersection M7NS-Ib-2 real number system. numbers and solve these in of sets and the difference of two sets. a variety of strategies. M7NS-Ic-1 3. uses Venn Diagrams to represent sets, subsets, and set operations. M7NS-Ic-d-1 M7NS-Id-2 4. solves problems involving sets. M7NS-Ie-1 M7NS-Ie-2 5. represents the absolute value of a M7NS-If-1 number on a number line as the M7NS-Ig-1 distance of a number from 0. M7NS-Ig-2 6. performs fundamental operations on integers. 7. illustrates the different properties of operations on the set of integers. 8. expresses rational numbers from fraction form to decimal form and vice versa. 9. arranges rational numbers on a number line. 10. performs operations on rational numbers 11. describes principal roots and tells whether they are rational or irrational. 12. determines between what two integers the square root of a number is.K to 12 Mathematics Curriculum Guide December 2013

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner... STANDARDS M7NS-Ig-3 The learner... The learner... M7NS-Ig-4 M7NS-Ih-1 13. estimates the square root of a M7NS-Ih-2 whole number to the nearest M7NS-Ii-1 hundredth. M7NS-Ii-2 M7NS-Ij-1 14. plots irrational numbers (up to square roots) on a number line.*** M7ME-IIa-1 M7ME-IIa-2 15. illustrates the different subsets of real numbers. M7ME-IIa-3 16. arranges real numbers in increasing M7ME-IIb-1 or decreasing order. M7ME-IIb-2 17. writes numbers in scientific notation and vice versa. 18. represents real-life situations which involve real numbers. 19. solves problems involving real numbers.Grade 7- SECOND QUARTERMeasurement demonstrates is able to formulate real-life 1. illustrates what it means to measure. understanding of the key problems involving 2. describes the development of concepts of measurement. measurements and solve these using a variety of measurement from the primitive to strategies. the present international system of units. 3. approximates the measures of quantities particularly length , weight/mass, volume, time, angle and temperature and rate. 4. converts measurements from one unit to another in both Metric and English systems.*** 5. solves problems involving conversion of units of measurement.***K to 12 Mathematics Curriculum Guide December 2013 Page 81 of 109

K to 12 BASIC EDUCATION CURRICULUM CONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALSPatterns and STANDARDS Page 82 of 109Algebra M7AL-IIc-1 The learner... The learner... The learner... M7AL-IIc-2 The learner … M7AL-IIc-3 M7AL-IIc-4 demonstrates is able to model situations 6. translates English phrases to M7AL-IId-1 understanding of key using oral, written, mathematical phrases and vice versa. M7AL-IId-2 M7AL-IId-e-1 concepts of algebraic graphical, and algebraic 7. interprets the meaning of an where M7AL-IIe-2 expressions, the properties methods in solving problems n is a positive integer. M7AL-IIe-g-1 of real numbers as applied involving algebraic 8. differentiates between constants and M7AL-IIg-2 in linear equations, and expressions, linear variables in a given algebraic M7AL-IIh-1 inequalities in one variable. equations, and inequalities expression. M7AL-IIh-2 in one variable. 9. evaluates algebraic expressions for given values of the variables. 10. classifies algebraic expressions which are polynomials according to degree and number of terms. 11. adds and subtracts polynomials. 12. derives the laws of exponent. 13. multiplies and divides polynomials. 14. uses models and algebraic methods to find the: (a) product of two binomials; (b) product of the sum and difference of two terms; (c) square of a binomial; (d) cube of a binomial; (e) product of a binomial and a trinomial.*** 15. solves problems involving algebraic expressions. 16. differentiates between algebraic expressions and equations. 17. translates English sentences to mathematical sentences and vice versa.K to 12 Mathematics Curriculum Guide December 2013

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner... STANDARDS M7AL-IIh-3 Page 83 of 109 M7AL-IIh-4 The learner... The learner... M7AL-IIi-1 M7AL-IIi-j-1 18. differentiates between equations and M7AL-IIj-2 inequalities. M7GE-IIIa-1 M7GE-IIIa-2 19. illustrates linear equation and M7GE-IIIa-3 inequality in one variable. M7GE-IIIb-1 20. finds the solution of linear equation or inequality in one variable. M7GE-IIIc-1 21. solves linear equation or inequality in M7GE-IIId-e-1 one variable involving absolute value by: (a) graphing; and (b) algebraic methods. 22. solves problems involving equations and inequalities in one variable.Grade 7- THIRD QUARTERGeometry demonstrates is able to create models of 23. represents point, line and plane using understanding of key plane figures and formulate concrete and pictorial models. concepts of geometry of and solve accurately shapes and sizes, and authentic problems involving 24. illustrates subsets of a line. geometric relationships. sides and angles of a polygon 25. classifies the different kinds of angles. 26. derives relationships of geometric figures using measurements and by inductive reasoning; supplementary angles, complementary angles, congruent angles, vertical angles, adjacent angles, linear pairs, perpendicular lines, and parallel lines.*** 27. derives relationships among angles formed by parallel lines cut by a transversal using measurement and by inductive reasoning. 28. uses a compass and straightedge to bisect line segments and angles and construct perpendiculars and parallels.K to 12 Mathematics Curriculum Guide December 2013

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner... STANDARDS Page 84 of 109 M7GE-IIIe-2 The learner... The learner... M7GE-IIIf-1 29. illustrates polygons: (a) convexity; M7GE-IIIg-1 (b) angles; and (c) sides. M7GE-IIIh-i-1 M7GE-IIIj-1 30. derives inductively the relationship of exterior and interior angles of a M7SP-IVa-1 convex polygon. M7SP-IVa-2 31. illustrates a circle and the terms M7SP-IVa-3 related to it: radius, diameter chord, M7SP-IVb-1 center, arc, chord, central angle, and M7SP-IVc-1 inscribed angle. M7SP-IVd-e-1 32. constructs triangles, squares, M7SP-IVf-1 rectangles, regular pentagons, and regular hexagons. 33. solves problems involving sides and angles of a polygon.Grade 7- FOURTH QUARTERStatistics and demonstrates is able to collect and The learner …Probability understanding of key organize data systematically concepts, uses and and compute accurately 34. explains the importance of Statistics. importance of Statistics, measures of central 35. poses problems that can be solved data collection/gathering tendency and variability and and the different forms of apply these appropriately in using Statistics. data representation, data analysis and measures of central interpretation in different 36. formulates simple statistical tendency, measures of fields. instruments. variability, and probability. 37. gathers statistical data. 38. organizes data in a frequency distribution table. 39. uses appropriate graphs to represent organized data: pie chart, bar graph, line graph, histogram, and ogive.*** 40. illustrates the measures of central tendency (mean, median, and mode) of a statistical data.K to 12 Mathematics Curriculum Guide December 2013

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner... STANDARDS M7SP-IVf-g-1 M7SP-IVh-1 The learner... The learner... M7SP-IVh-i-1 41. calculates the measures of central M7SP-IVj-1 tendency of ungrouped and grouped M7SP-IVj-2 data. 42. illustrates the measures of variability (range, average deviation, variance, standard deviation) of a statistical data. 43. calculates the measures of variability of grouped and ungrouped data. 44. uses appropriate statistical measures in analyzing and interpreting statistical data. 45. draws conclusions from graphic and tabular data and measures of central tendency and variability.*** Suggestion for ICT enhanced lesson when available and where appropriateK to 12 Mathematics Curriculum Guide December 2013 Page 85 of 109

K to 12 BASIC EDUCATION CURRICULUM GRADE 8CONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS STANDARDS The learner... The learner...Grade 8- FIRST QUARTER The learner...Patterns and demonstrates is able to formulate real-life 1. factors completely different typesAlgebra understanding of key problems involving factors of of polynomials (polynomials with common monomial factor, concepts of factors of polynomials, rational difference of two squares, sum and M8AL-Ia-b-1 polynomials, rational algebraic expressions, linear difference of two cubes, perfect algebraic expressions, equations and inequalities in square trinomials, and general M8AL-Ib-2 linear equations and two variables, systems of trinomials). inequalities in two linear equations and M8AL-Ic-1 variables, systems of linear inequalities in two variables 2. solves problems involving factors M8AL-Ic-2 equations and inequalities and linear functions, and of polynomials. M8AL-Ic-d-1 in two variables and linear solve these problems M8AL-Id-2 functions. accurately using a variety of 3. illustrates rational algebraic M8AL-Ie-1 strategies. expressions. M8AL-Ie-3 4. simplifies rational algebraic M8AL-Ie-4 expressions. M8AL-Ie-5 5. performs operations on rational algebraic expressions. 6. solves problems involving rational algebraic expressions. 7. illustrates the rectangular coordinate system and its uses.*** 8. illustrates linear equations in two variables. 9. illustrates the slope of a line. 10. finds the slope of a line given two points, equation, and graph.K to 12 Mathematics Curriculum Guide December 2013 Page 86 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner... STANDARDS M8AL-If-1 The learner... The learner... M8AL-If-2 11. writes the linear equation M8AL-If-3 M8AL-Ig-1 ax  by  c in the form M8AL-Ig-2 y  mx  b and vice versa. M8AL-Ih-1 M8AL-Ih-2 12. graphs a linear equation given (a) M8AL-Ih-3 any two points; (b) the x – and y M8AL-Ii-j-1 – intercepts; (c) the slope and a point on the line.*** 13. describes the graph of a linear equation in terms of its intercepts and slope.*** 14. finds the equation of a line given (a) two points; (b) the slope and a point; (c) the slope and its intercepts. 15. solves problems involving linear equations in two variables. 16. illustrates a system of linear equations in two variables. 17. graphs a system of linear equations in two variables.*** 18. categorizes when a given system of linear equations in two variables has graphs that are parallel, intersecting, and coinciding. 19. solves a system of linear equations in two variables by (a) graphing; (b) substitution; (c) elimination.***K to 12 Mathematics Curriculum Guide December 2013 Page 87 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner... STANDARDS Page 88 of 109 M8AL-Ij-2 The learner... The learner... M8AL-IIa-1 20. solves problems involving systems of linear equations in two M8AL-IIa-2 variables. M8AL-IIa-3Grade 8- SECOND QUARTER M8AL-IIa-4 M8AL-IIb-1Patterns and demonstrates key is able to formulate and 21. illustrates linear inequalities in two M8AL-IIb-2Algebra concepts of linear solve accurately real-life variables. M8AL-IIc-1 inequalities in two problems involving linear M8AL-IIc-2 variables, systems of linear inequalities in two variables, 22. differentiates linear inequalities in M8AL-IIc-3 inequalities in two systems of linear inequalities two variables from linear equations M8AL-IId-1 variables and linear in two variables, and linear in two variables. M8AL-IId-2 functions. functions. M8AL-IId-e-1 23. graphs linear inequalities in two variables. 24. solves problems involving linear inequalities in two variables. 25. solves a system of linear inequalities in two variables.*** 26. solves problems involving systems of linear inequalities in two variables. 27. illustrates a relation and a function. 28. verifies if a given relation is a function. 29. determines dependent and independent variables. 30. finds the domain and range of a function. 31. illustrates a linear function. 32. graphs a linear function’s (a) domain; (b) range; (c) table ofK to 12 Mathematics Curriculum Guide December 2013

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner... STANDARDS Page 89 of 109 M8AL-IIe-2 The learner... The learner... M8GE-IIf-1 values; (d) intercepts; and (e) M8GE-IIf-2 slope. M8GE-IIg-1 M8GE-IIg-2 33. solves problems involving linear M8GE-IIh-1 functions. M8GE-IIi-j-1 M8GE-IIIa-1Geometry demonstrates is able to communicate 34. determines the relationship understanding of key mathematical thinking with between the hypothesis and the M8GE-IIIa-c-1 concepts of logic and coherence and clarity in conclusion of an if-then statement. reasoning. formulating and analyzing arguments. 35. transforms a statement into an equivalent if-then statement. 36. determines the inverse, converse, and contrapositive of an if-then statement. 37. illustrates the equivalences of: (a) the statement and its contrapositive; and (b) the converse and inverse of a statement. 38. uses inductive or deductive reasoning in an argument. 39. writes a proof (both direct and indirect).Grade 8- THIRD QUARTERGeometry demonstrates 1. is able to formulate 40. describes a mathematical system. understanding of key an organized plan to concepts of axiomatic handle a real-life 41. illustrates the need for an axiomatic structure of geometry and situation. structure of a mathematical system triangle congruence. in general, and in Geometry in particular: (a) defined terms; (b) undefined terms; (c) postulates; and (d) theorems.K to 12 Mathematics Curriculum Guide December 2013

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner... STANDARDS M8GE-IIId-1 M8GE-IIId-e-1 The learner... The learner... M8GE-IIIf-1 42. illustrates triangle congruence.*** M8GE-IIIg-1 2. is able to 43. illustrates the SAS, ASA and SSS M8GE-IIIh-1 communicate mathematical congruence postulates.*** M8GE-IIIi-j-1 thinking with 44. solves corresponding parts of coherence and clarity in congruent triangles formulating, investigating, 45. proves two triangles are congruent. analyzing, and solving real-life 46. proves statements on triangle problems involving congruence. congruent triangles using appropriate 47. applies triangle congruence to and accurate construct perpendicular lines and representations. angle bisectors.Grade 8- FOURTH QUARTERGeometry demonstrates is able to communicate 48. illustrates theorems on triangle understanding of key mathematical thinking with inequalities (Exterior Angle Inequality concepts of inequalities in a coherence and clarity in Theorem, Triangle Inequality M8GE-IVa-1 triangle, and parallel and formulating, investigating, Theorem, Hinge Theorem).*** perpendicular lines. analyzing, and solving real- M8GE-IVb-1 life problems involving 49. applies theorems on triangle M8GE-IVc-1 triangle inequalities, and inequalities. M8GE-IVd-1 parallelism and perpendicularity of lines 50. proves inequalities in a triangle. using appropriate and accurate representations. 51. proves properties of parallel lines cut by a transversal.***K to 12 Mathematics Curriculum Guide December 2013 Page 90 of 109

K to 12 BASIC EDUCATION CURRICULUM CONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner... STANDARDSStatistics and M8GE-IVe-1Probability demonstrates The learner... The learner... M8GE-IVf-1 understanding of key M8GE-IVf-g-1 concepts of probability. is able to formulate and 52. determines the conditions under solve practical problems which lines and segments are parallel M8GE-IVh-1 involving probability of or perpendicular. M8GE-IVi-1 simple events. M8GE-IVi-j-1 53. illustrates an experiment, outcome, sample space and event.*** 54. counts the number of occurrences of an outcome in an experiment: (a) table; (b) tree diagram; (c) systematic listing; and (d) fundamental counting principle.*** 55. finds the probability of a simple event. 56. illustrates an experimental probability and a theoretical probability. 57. solves problems involving probabilities of simple events.*** Suggestion for ICT enhanced lesson when available and where appropriateK to 12 Mathematics Curriculum Guide December 2013 Page 91 of 109

K to 12 BASIC EDUCATION CURRICULUM GRADE 9CONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING STANDARDS The learner... M9AL-Ia-1 MATERIALS The learner... M9AL-Ia-b-1Grade 9- FIRST QUARTER The learner... 1. illustrates quadratic equations. M9AL-Ic-1  BEAM Second Year M9AL-Ic-2  Module 4 (TG)Patterns and demonstrates is able to investigate 2. solves quadratic equations by: (a)  EASE Module Second YearAlgebra understanding of key thoroughly mathematical extracting square roots; (b) factoring; concepts of quadratic (c) completing the square; and (d) Quadratic Equations equations, inequalities and relationships in various using the quadratic formula.  Module 3 functions, and rational situations, formulate real-  Chapter 2 algebraic equations. life problems involving 3. characterizes the roots of a quadratic  Quadratic Equations pp.44- quadratic equations, equation using the discriminant. inequalities and functions, 46 (LM) and rational algebraic 4. describes the relationship between the equations and solve them coefficients and the roots of a  BEAM Second Year using a variety of quadratic equation.  Module 4 (TG) strategies.  EASE Module Second Year Quadratic Equations, Module 3  Chapter 2Quadratic Equations pp.47-53(LM)  BEAM Second Year, Module 4 (TG)  EASE Module Second Year Quadratic Equations, Module 3  Chapter 2  Quadratic Equations pp.53- 59 (LM)  BEAM Second Year  Module 4 (TG)  EASE Module Second Year Quadratic Equations, Module 3 Chapter 2  Quadratic Equations pp.53- 59 (LM)K to 12 Mathematics Curriculum Guide December 2013 Page 92 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING The learner... STANDARDS MATERIALS M9AL-Ic-d-1 The learner... The learner...  BEAM Second Year M9AL-Ie-1  Module 4 (TG) 5. solves equations transformable to M9AL-If-1  LM quadratic equations (including M9AL-If-2  EASE Module Second Year rational algebraic equations). M9AL-If-g-1 M9AL-Ig-2 Quadratic Equations, 6. solves problems involving quadratic M9AL-Ig-3 Module 3 equations and rational algebraic  Chapter 2 equations.  Quadratic Equations pp.53- 59 (LM) 7. illustrates quadratic inequalities  BEAM Second Year  Module 4 (TG) 8. solves quadratic inequalities.  EASE Module Second Year Quadratic Equations, 9. solves problems involving quadratic Module 3 inequalities.  Chapter 2  Quadratic Equations pp.61- 10. models real-life situations using 64 (LM) quadratic functions.  11. represents a quadratic function using: (a) table of values; (b) graph;  APEX Chapter 3 and (c) equation.  Quadratic Functions  Lessons 18-19 pp.203-217K to 12 Mathematics Curriculum Guide December 2013 (LM)  APEX Chapter 3  Quadratic Functions  Lessons 18-19 pp.203-217 (LM)  BEAM Fourth Year, Module 3  BEAM Fourth Year  Module 3 (TG)  EASE Module Fourth Year Quadratic Equations, Module 1 (LM) Page 93 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING The learner... STANDARDS M9AL-Ih-1 MATERIALS M9AL-Ig-h-i-1 The learner... The learner... M9AL-Ii-2  BEAM Fourth Year M9AL-Ij-1  Module 3 12. transforms the quadratic function  Math IV: Advanced defined byy = ax2+ bx + cinto the Algrebra, Trigonometry formy = a(x – h)2 + k. and Statistics (Lesson Plans) 2002 BEC (Week 8) 13. graphs a quadratic function: (a) pp.31-32 (TG) domain; (b) range; (c) intercepts;  EASE Module Fourth Year (d) axis of symmetry; (e) vertex; Quadratic Equations, (f) direction of the opening of the Module 1 parabola.  APEX Chapter 3  Quadratic Functions 14. analyzes the effects of changing  Lesson 2 pp.101-105 (LM) the values of a, h and k in the  BEAM Fourth Year, Module equation y = a(x – h)2 + k of a 3 (TG) quadratic function on its graph.***  EASE Module Fourth Year Quadratic Equations, 15. determines the equation of a Module 1 (LM) quadratic function given: (a) a  BEAM Fourth Year table of values; (b) graph; (c)  Math IV: Advanced zeros. Algebra, Trigonometry, and Statistics (LessonK to 12 Mathematics Curriculum Guide December 2013 Plans) 2002 BEC (Week 8- 9) pp.37-41 (TG)  EASE Module Fourth Year, Module 2  APEX Chapter 3  Quadratic Functions  Lesson 2 pp.120-125 (LM)  EASE Module Fourth Year  Quadratic Functions, Modules 3 and 4  APEX Chapter 3  Quadratic Functions  Lesson 1 pp.92-100  Lesson 13 pp.165-171(LM) Page 94 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING The learner... STANDARDS MATERIALS The learner... The learner... 16. solves problems involving M9AL-Ii-j-2  Math IV: Advanced quadratic functions. Algebra, Trigonometry, M9AL-IIa-1 and Statistics (LessonGrade 9- SECOND QUARTER M9AL-IIa-b-1 Plans) 2002 BEC (Week 8- M9AL-IIb-c-1 9) pp.37-41 (TG)Patterns and demonstrates is able to formulate andAlgebra understanding of key solve accurately problems  EASE Module Fourth Year concepts of variation and involving radicals.  Quadratic Functions, radicals. 17.illustrates situations that involve the following variations: (a) direct; (b) Modules 3 and 4 inverse; (c) joint; (d) combined.  APEX Chapter 3  Quadratic Functions 18.translates into variation statement a  Lesson 14 pp.172-183 relationship between two quantities (LM) given by: (a) a table of values; (b) a  BEAM Second Year, mathematical equation; (c) a graph, Module 8 (TG) and vice versa.  EASE Module Second Year 19.solves problems involving variation.  Variations  Modules 1-3  Chapter 4 Variation pp.102-121 (LM)  BEAM Second Year, Module 8 (TG)  EASE Module Second Year  Variations, Modules 1-3  Chapter 4 Variation pp.102-121 (LM)  BEAM Second Year, Module 8 (TG)  EASE Module Second Year  Variations, Modules 1-3  Chapter 4 Variation pp.102-(LM)K to 12 Mathematics Curriculum Guide December 2013 Page 95 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING The learner... STANDARDS M9AL-IId-1 MATERIALS The learner... The learner...  BEAM Second Year, Module 9 (TG) 20.applies the laws involving positive integral exponents to zero and  Ease Module Second Year negative integral exponents.  Integral Exponents, Modules 2  Chapter 5 Integral Exponents pp.122-135 (LM) 21.illustrates expressions with rational M9AL-IId-2  BEAM Second Year, exponents. Module 9 (TG) M9AL-IIe-1 22.simplifies expressions with rational M9AL-IIf-1  Ease Module Second Year exponents. M9AL-IIf-2  Integral Exponents, 23.writes expressions with rational Module 2 exponents as radicals and vice versa.  Chapter 6 Radical 24.derives the laws of radicals. Expressions pp.149 (LM)K to 12 Mathematics Curriculum Guide December 2013  BEAM Second Year, Module 9 & 10 (TG)  EASE Module Second Year  Radical Expressions, Module 2  Chapter 6 Radical Expressions pp.149-150 (LM)  BEAM Second Year, Module 10 Chapter 6 Radical Expressions pp.150-151 (TG)  BEAM Second Year, Module 10 (TG)  EASE Module Second Year  Radical Expressions, Module 3 (LM) Page 96 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING The learner... STANDARDS M9AL-IIg-1 MATERIALS M9AL-IIh-1 The learner... The learner... M9AL-IIi-1  BEAM Second Year, M9AL-IIj-1 Module 10 (TG) 25.simplifies radical expressions using the laws of radicals.  EASE Module Second Year  Radical Expressions, 26.performs operations on radical expressions.*** Module 3  Chapter 6 Radical 27.solves equations involving radical expressions.*** Expressions pp.152-156 (LM) 28. solves problems involving radicals.  BEAM Second Year, Module 11 (TG)  EASE Module Second Year  Radical Expressions  Modules 4-5  Chapter 6 Radical Expressions pp.157-166 (Lm)  BEAM Second Year  Module 11 (TG)  EASE Module Second Year  Radical Expressions  Module 6  Chapter 6 Radical Expressions pp.167-170 (LM)  BEAM Second Year  Module 11 (TG)  EASE Module Second Year  Radical Expressions  Module 6  Chapter 6 Radical Expressions pp.171 (LM)K to 12 Mathematics Curriculum Guide December 2013 Page 97 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING STANDARDS MATERIALS The learner... The learner... The learner...Grade 9- THIRD QUARTERGeometry demonstrates is able to investigate,  BEAM Third Year understanding of key analyze, and solve concepts of quadrilaterals problems involving 29. identifies quadrilaterals that are M9GE-IIIa-1  Module 12 (TG) (parallelograms, quadrilaterals parallelograms. trapezoids, kites) and M9GE-IIIa-2  APEX Lesson 1-7 triangle similarity. (parallelograms, trapezoids, M9GE-IIIb-1 kites) and triangle similarity  Quadrilaterals through appropriate and accurate representation.  Geometry Chapter 1 Geometry of Shape and 30. determines the conditions that Size guarantee a quadrilateral a parallelogram.  Quadrilaterals p.17 Chapter 4 Quadrilaterals 31. uses properties to find measures of angles, sides and other quantities  4.1.3 The Parallelogram involving parallelograms. and its properties p.124 (LM) 32. proves theorems on the different kinds of parallelogram (rectangle, rhombus,  BEAM Third Year square).  Module 12 (TG) 33. proves the Midline Theorem.  Geometry Chapter 4 Quadrilaterals  4.2. Conditions which guarantee that a quadrilateral is a parallelogram p.132 (LM)  EASE Module Third Year  Properties of Quadrilaterals  Module 1 (LM) M9GE-IIIc-1 M9GE-IIId-1K to 12 Mathematics Curriculum Guide December 2013 Page 98 of 109