The week numbers are this repository’s proposal, not DepEd’s. A school’s approved Budget of Work replaces every one of them. The competency text and the quarter it belongs to are the guide’s own.
The performance task sits in each term’s end-of-term block rather than in a numbered week, so no week below is marked as one.
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Term 1 June – September
Quarter 1 — what this quarter is driving toward
Content standards
1. simple geometric concepts and notations; 2. perpendicular and parallel lines, and angles formed by parallel lines cut by a transversal; 3. relations and functions; 4. graphs of linear functions, and the identification of domain and range, slope, intercepts, and zeros.
Performance standard
By the end of the quarter, the learners are able to: illustrate and describe points, lines, rays, line segments, angles, and planes (MG); construct perpendicular and parallel lines (MG); determine the measure of the angles formed by parallel lines cut by a transversal (MG); identify relations and functions (NA); graph a linear function and identify the domain and range, intercepts, slope, and zeros (NA).
Performance task (suggested by this repository)
*What Does the Number Mean?* — find two real linear relationships in the barangay with different units (a fare per kilometre, a wage per hour, water lost per minute). For each: build a table, write the equation, draw the graph, and state the slope with its unit and the zero with its meaning — including saying plainly when the zero has no meaning in context.
1Week
Point, line, ray, segment, angle and plane, with geometric notation
Quarter 1Q1 · 1
Curriculum guide competency
1. illustrate and describe point, line, ray, line segment, angle, and plane using models and geometric notations
Competency placed; teaching materials not built
2Week
Constructing perpendicular and parallel lines
Quarter 1Q1 · 2
Curriculum guide competency
2. construct perpendicular and parallel lines
Competency placed; teaching materials not built
3Week
Angles formed by parallel lines cut by a transversal
Quarter 1Q1 · 3
Curriculum guide competency
3. identify the relationships between angles formed by parallel lines cut by a transversal
Competency placed; teaching materials not built
4Week
Determining angle measures with angle pairs and transversals
Quarter 1Q1 · 4
Curriculum guide competency
4. determine angle measures involving angle pairs, parallel and perpendicular lines, and parallel lines cut by a transversal
Competency placed; teaching materials not built
5Week
Relations that are functions and domain and range
Quarter 1Q1 · 5–6
Curriculum guide competencies
5. identify relations that are functions based on the definitions of relations and functions
6. determine the domain and the range of a function expressed in different representations
Competency placed; teaching materials not built
6Week
Expressing a relationship between two variables as a function
Quarter 1Q1 · 7
Curriculum guide competency
7. express the relationship between two variables as a function
Competency placed; teaching materials not built
7Week
Slope as a rate of change, and zeros — from graphs, equations and tables
Quarter 1Q1 · 8
Curriculum guide competency
8. determine the slopes (as rate of change) and the zeros of linear functions represented in (a) graphs, (b) equations, and (c) tables of values
Graphing a linear function with its domain, range, intercepts and slope and representing real-life linear relationships and solving problems
Quarter 1Q1 · 9–11
Curriculum guide competencies
9. graph a linear function and determine its (a) domain, (b) range, (c) intercepts, and (d) slope
10. represent linear relationships found in real-life situations using different representations
11. solve problems involving linear functions
Competency placed; teaching materials not built
Quarter 2 — what this quarter is driving toward
Content standards
1. parallelism and perpendicularity of lines; 2. different quadrilaterals and their properties; 3. congruence of triangles; 4. congruence proofs.
Performance standard
Determine the conditions for lines to be parallel or perpendicular (MG); use geometric properties to find unknown sides and angles of quadrilaterals (MG); apply the triangle congruence postulates and theorems (MG); construct and justify the construction of segments, angles, and triangles (MG); construct proofs of the congruence of triangles (MG).
Performance task (suggested by this repository)
*Prove It Twice* — take one property of a parallelogram. Establish it inductively by measuring five different parallelograms and tabulating the results, then prove it deductively in a two-column proof. Write a paragraph on what the second one gives you that the first cannot.
9Week
Conditions that guarantee parallelism and perpendicularity
Quarter 2Q2 · 1
Curriculum guide competency
1. determine conditions that guarantee parallelism and perpendicularity of lines
Competency placed; teaching materials not built
10Week
Classifying quadrilaterals by formal definition
Quarter 2Q2 · 2
Curriculum guide competency
2. classify quadrilaterals based on formal definitions
Competency placed; teaching materials not built
11Week
Using the properties of parallelograms to find measures
Quarter 2Q2 · 3
Curriculum guide competency
3. use properties of parallelograms to find measures of angles, sides, perpendicular height, and diagonals
Competency placed; teaching materials not built
Term 2 September – December
Quarter 2 — what this quarter is driving toward
Content standards
1. parallelism and perpendicularity of lines; 2. different quadrilaterals and their properties; 3. congruence of triangles; 4. congruence proofs.
Performance standard
Determine the conditions for lines to be parallel or perpendicular (MG); use geometric properties to find unknown sides and angles of quadrilaterals (MG); apply the triangle congruence postulates and theorems (MG); construct and justify the construction of segments, angles, and triangles (MG); construct proofs of the congruence of triangles (MG).
Performance task (suggested by this repository)
*Prove It Twice* — take one property of a parallelogram. Establish it inductively by measuring five different parallelograms and tabulating the results, then prove it deductively in a two-column proof. Write a paragraph on what the second one gives you that the first cannot.
12Week
Problems involving parallelograms, rectangles, squares and rhombuses
Quarter 2Q2 · 4
Curriculum guide competency
4. solve problems involving parallelograms, rectangles, squares, or rhombuses by applying their different properties
Competency placed; teaching materials not built
13Week
Proving properties of parallelograms
Quarter 2Q2 · 5
Curriculum guide competency
5. prove properties of parallelograms by applying the relevant theorems
Competency placed; teaching materials not built
14Week
Deriving the properties of trapezoids and kites and solving problems with them
Quarter 2Q2 · 6–7
Curriculum guide competencies
6. derive the properties of trapezoids and kites by exploring the relationship between their parts and secondary parts
7. solve problems on trapezoids and kites by applying their properties
Competency placed; teaching materials not built
15Week
Inductive versus deductive reasoning and postulates, theorems and proofs
Quarter 2Q2 · 8–9
Curriculum guide competencies
8. distinguish inductive and deductive reasoning for establishing proofs
9. state postulates and theorems about defined and undefined terms in geometry, and formulate proofs involving them
Competency placed; teaching materials not built
16Week
Triangle congruence postulates and CPCTC and problems with the congruence theorems
Quarter 2Q2 · 10–11
Curriculum guide competencies
10. use the triangle congruence postulates and theorems to illustrate congruence of triangles, including CPCTC
11. solve problems involving right triangle congruence theorems, isosceles triangle theorem, perpendicular bisector theorem, and midline theorem
Competency placed; teaching materials not built
17Week
Constructions justified by congruence and two-column congruence proofs
Quarter 2Q2 · 12–13
Curriculum guide competencies
12. construct and justify the construction of segments, angles and triangles, including the triangle's secondary parts and centers, using the triangle congruence postulates and theorems
13. construct congruence proofs involving triangles or corresponding parts of triangles using a two-column proof
Competency placed; teaching materials not built
Quarter 3 — what this quarter is driving toward
Content standards
1. quadratic equations and graphs of quadratic functions; 2. the solution of quadratic equations; 3. similarity of polygons; 4. special triangles; 5. direct and inverse variation.
Performance standard
Represent quadratic relationships (NA); interpret features of a parabola (NA); express quadratic functions in different forms (NA); sketch the graph of a quadratic function (NA); solve quadratic equations (NA); illustrate and apply similarity of polygons, including triangles (MG); apply direct and inverse variation (NA).
Performance task (suggested by this repository)
*The Shape of a Throw* — photograph or trace the path of a thrown ball against a gridded background. Fit a quadratic to three measured points, identify the vertex and both zeros, and state what each one means physically. Then say what the model gets wrong.
18Week
Real-life situations modelled by quadratic relationships
Quarter 3Q3 · 1
Curriculum guide competency
1. represent real-life situations that can be modelled using quadratic relationships
Competency placed; teaching materials not built
19Week
Graphing y = ax², y = ax² + b and y = a(x − b)²
Quarter 3Q3 · 2
Curriculum guide competency
2. graph equations in two variables to represent quadratic relationships, such as y = ax², y = ax² + b, y = a(x − b)²
Competency placed; teaching materials not built
20Week
Features of a parabola — vertex, axis, intercepts, maximum and minimum
Quarter 3Q3 · 3
Curriculum guide competency
3. interpret features of a parabola such as vertex, axis of symmetry, x-intercepts, opening direction, minimum or maximum value, zeros, and increasing and decreasing intervals
Competency placed; teaching materials not built
21Week
Transforming to vertex form and back and sketching from an equation
Quarter 3Q3 · 4–5
Curriculum guide competencies
4. transform the quadratic functions y = ax², y = ax² + b, y = a(x − b)² and y = ax² + bx + c into the form y = a(x − h)² + k, and vice versa
5. sketch the graph of quadratic functions expressed in equation form
Competency placed; teaching materials not built
22Week
The effect of changing the parameters of y = a(x − h)² + k
Quarter 3Q3 · 6
Curriculum guide competency
6. analyze the effect of changing the values of the parameters on the behavior of its graph and on the properties of the quadratic function y = a(x − h)² + k
Competency placed; teaching materials not built
Term 3 January – April
Quarter 3 — what this quarter is driving toward
Content standards
1. quadratic equations and graphs of quadratic functions; 2. the solution of quadratic equations; 3. similarity of polygons; 4. special triangles; 5. direct and inverse variation.
Performance standard
Represent quadratic relationships (NA); interpret features of a parabola (NA); express quadratic functions in different forms (NA); sketch the graph of a quadratic function (NA); solve quadratic equations (NA); illustrate and apply similarity of polygons, including triangles (MG); apply direct and inverse variation (NA).
Performance task (suggested by this repository)
*The Shape of a Throw* — photograph or trace the path of a thrown ball against a gridded background. Fit a quadratic to three measured points, identify the vertex and both zeros, and state what each one means physically. Then say what the model gets wrong.
23Week
Finding the zeros of a quadratic, graphically and algebraically
Quarter 3Q3 · 7
Curriculum guide competency
7. find the zeros of quadratic functions in factored and standard form, graphically and algebraically
Competency placed; teaching materials not built
24Week
Solving quadratic equations — square roots, factoring, and the formula
Quarter 3Q3 · 8
Curriculum guide competency
8. solve quadratic equations by (a) extracting square roots, (b) factoring, and (c) using the quadratic formula
Competency placed; teaching materials not built
25Week
Problems with quadratic functions and equations and similarity of polygons
Quarter 3Q3 · 9–10
Curriculum guide competencies
9. solve problems involving quadratic functions and equations
10. illustrate similarity of polygons
Competency placed; teaching materials not built
26Week
Triangle similarity theorems and problems involving triangle similarity
Quarter 3Q3 · 11–12
Curriculum guide competencies
11. illustrate and apply triangle similarity theorems in different situations
12. solve problems involving triangle similarity
Competency placed; teaching materials not built
27Week
Special triangles — 30-60-90 and 45-45-90 and direct and inverse variation
Quarter 3Q3 · 13–16
Curriculum guide competencies
13. solve problems involving measures of sides and angles of special triangles (30-60-90, 45-45-90)
14. illustrate real-life situations that involve direct variation and real-life situations that involve inverse variation
15. translate a relationship between two quantities into a variation statement and/or a mathematical equation, given a table of values or a graph
16. solve problems involving variation
Competency placed; teaching materials not built
Quarter 4 — what this quarter is driving toward
Content standards
1. triangle theorems and triangle inequality theorems; 2. the trigonometric ratios and their application; 3. interpretation and analysis of data to assess whether the data may be misleading; 4. probabilities of simple and compound events.
Performance standard
Apply triangle theorems and triangle inequality theorems (MG); apply trigonometric ratios to solve right triangles (MG); interpret and analyze data to assess whether the data may be misleading (DP); determine the probabilities of simple and compound events (DP).
Performance task (suggested by this repository)
*How Tall Is It?* — measure the height of something you cannot climb — a coconut tree, a flagpole, the school building — using an angle of elevation and a measured distance. Do it twice from different distances, compare the two answers, and account for the difference.
28Week
Perpendicular bisector, isosceles, equilateral and midline theorems and triangle inequalities
Quarter 4Q4 · 1–2
Curriculum guide competencies
1. solve problems involving the perpendicular bisector theorem, isosceles triangle theorem, theorems on equilateral triangles, and the midline theorem
2. explain theorems on triangle inequalities and apply these theorems in comparing measures in a triangle
Competency placed; teaching materials not built
29Week
Sine, cosine and tangent of the special angles and of any acute angle
Quarter 4Q4 · 3–4
Curriculum guide competencies
3. determine the values of the sine, cosine, and tangent trigonometric ratios corresponding to the angles of the special triangles
4. find the values of the sine, cosine, and tangent ratios of any acute angle
Competency placed; teaching materials not built
30Week
Using the trigonometric ratios to solve right triangles
Quarter 4Q4 · 5
Curriculum guide competency
5. use the trigonometric ratios in solving right triangles
Competency placed; teaching materials not built
31Week
Angles of elevation and depression and real-life right-triangle problems
Quarter 4Q4 · 6–7
Curriculum guide competencies
6. illustrate angles of elevation and angles of depression
7. solve real-life problems involving right triangles through the application of the trigonometric ratios
Competency placed; teaching materials not built
32Week
Misleading data in digital media and illustrating simple and compound events
Quarter 4Q4 · 8–9
Curriculum guide competencies
8. interpret and analyze data from the digital media that are in tabular or graphical form to assess whether the data may be misleading
9. illustrate simple and compound events
Competency placed; teaching materials not built
33Week
Probabilities of simple and compound events and problems involving them
Quarter 4Q4 · 10–11
Curriculum guide competencies
10. determine the probabilities of simple and compound events
11. solve problems involving probabilities of simple and compound events