Mathematics 9 — Course Syllabus
MATATAG Curriculum · Key Stage 3 · School Year 2026–2027
| Learning Area | Mathematics |
| Grade Level | Grade 9 |
| Key Stage | Key Stage 3 (Grades 7–10) |
| Time Allotment | 45 minutes daily · 5 days a week · 3 terms |
| Prerequisite | Mathematics 8 |
| Curriculum Basis | MATATAG K to 10 Curriculum (DepEd, 2023); DO No. 010, s. 2024 |
| Calendar Basis | DO No. 009, s. 2026 — three-term school calendar |
| Assessment Basis | DO No. 015, s. 2026 — revised classroom assessment and grading |
The three-term school year
From SY 2026–2027 the school year runs in three terms, not four quarters. Each term pairs protected instructional time with a block for assessment, remediation, and reporting.
| Term | Months | Blocks |
|---|---|---|
| Term 1 | June – September | Opening block, then instructional block |
| Term 2 | September – December | Instructional block, then end-of-term block |
| Term 3 | January – April | Instructional block, then closing activities |
The curriculum guide predates this calendar and still assigns content to four quarters. §4 keeps the CG's quarter attribution visible on every row; §5 maps the four onto the three.
1. Course Description
Mathematics 9 is where two things arrive that change what mathematics is for the learner.
The first is the function. Grade 8 graphed lines; Grade 9 asks what a line means — its domain, its range, its slope as a rate of change, its zeros. A slope stops being the number in front of x and becomes pesos per kilometre, litres per minute, degrees per hour. That shift is the most portable idea in the grade and the syllabus gives it a full week.
The second is proof. Quarter 2 asks learners to distinguish inductive from deductive reasoning and to write two-column congruence proofs. Nothing before Grade 9 has required a learner to justify every line of an argument, and nothing after it lets them stop.
Between them sits the parabola (Quarter 3, the largest quarter in the grade at sixteen competencies) and, in Quarter 4, the trigonometric ratios — the first time a ratio of two lengths is given a name and treated as a number in its own right.
Quarter 4 also contains a competency that is not really about mathematics at all: interpret and analyse data from digital media to assess whether the data may be misleading. It is the direct continuation of Grade 6's media-literacy competency and Grade 8's primary and secondary data work, and it is the one competency in the grade a learner will use every day for the rest of their life.
Contexts stay local: a tricycle fare per kilometre, a water drum draining, the parabola of a thrown ball, a roof's pitch, the shadow of a coconut tree at noon.
2. Grade Level Standard
Quoted verbatim from the MATATAG Mathematics Curriculum Guide (DepEd, August 2023), page 23.
GRADE 9 — The learner demonstrates knowledge, skills, and understanding in relation to the curriculum content domains Number and Algebra (relations and functions; graphs of linear functions, and the identification of domain and range, slope, intercepts, and zeros; quadratic equations and graphs of quadratic functions; the solution of quadratic equations; direct and inverse variation); Measurement and Geometry (simple geometric concepts and notations; perpendicular and parallel lines, and angles formed by parallel lines cut by a transversal; quadrilaterals and their properties; congruence of triangles; congruence proofs; similarity of polygons; special triangles; triangle theorems and triangle inequality theorems; the trigonometric ratios and their application); and Data and Probability (interpretation and analysis of data to assess whether the data may be misleading; probabilities of simple and compound events). This knowledge, skills, and understanding is applied, with the use of technology, to the processes within Mathematics of critical thinking, problem solving, communicating, reasoning, and making connections between topic areas.
3. Content Domains
| Domain | Grade 9 coverage |
|---|---|
| Number and Algebra (NA) | Relations and functions. Graphs of linear functions; domain, range, slope, intercepts, zeros. Quadratic equations and the graphs of quadratic functions; solving quadratics three ways. Direct and inverse variation. |
| Measurement and Geometry (MG) | Points, lines, rays, segments, angles, planes and their notation. Perpendicular and parallel lines; angles from a transversal. Quadrilaterals and their properties. Congruence of triangles and congruence proofs. Similarity of polygons; special triangles. Triangle theorems and triangle inequality theorems. The trigonometric ratios and their application. |
| Data and Probability (DP) | Assessing whether data may be misleading. Probabilities of simple and compound events. |
What Grade 9 does not cover: the laws of sines and cosines (Grade 10), circle theorems (Grade 10), quadratic inequalities (Grade 10), the equation of a circle (Grade 10), and box-and-whisker plots, quartiles and percentiles (Grade 10). Grade 9's trigonometry is confined to right triangles.
Where the domains sit. Quarter 1 pairs Measurement and Geometry with Number and Algebra. Quarter 2 is Measurement and Geometry alone. Quarter 3 mixes the two. Quarter 4 pairs Measurement and Geometry with Data and Probability.
4. Content Map
Every entry below is quoted or closely transcribed from the official curriculum guide
(DepEd, August 2023, pages 60–64), committed at
docs/research/source/. Competency numbers are the CG's own.
Performance tasks are this syllabus's suggestions, not CG content.
CG Quarter 1 — Geometric Notation, Parallel Lines, and Linear Functions
Taught in Term 1, weeks 1–8
| Domains | Measurement and Geometry (MG) · Number and Algebra (NA) |
| 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. |
| Learning competencies | 1. illustrate and describe point, line, ray, line segment, angle, and plane using models and geometric notations. 2. construct perpendicular and parallel lines. 3. identify the relationships between angles formed by parallel lines cut by a transversal. 4. determine angle measures involving angle pairs, parallel and perpendicular lines, and parallel lines cut by a transversal. 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. 7. express the relationship between two variables as a function. 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. 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. |
| Performance standards | 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) | 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. |
CG Quarter 2 — Quadrilaterals, Congruence, and Proof
Opens in Term 1 (weeks 9–11); completed in Term 2 (weeks 12–17)
| Domains | Measurement and Geometry (MG) |
| Content standards | 1. parallelism and perpendicularity of lines; 2. different quadrilaterals and their properties; 3. congruence of triangles; 4. congruence proofs. |
| Learning competencies | 1. determine conditions that guarantee parallelism and perpendicularity of lines. 2. classify quadrilaterals based on formal definitions. 3. use properties of parallelograms to find measures of angles, sides, perpendicular height, and diagonals. 4. solve problems involving parallelograms, rectangles, squares, or rhombuses by applying their different properties. 5. prove properties of parallelograms by applying the relevant theorems. 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. 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. 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. 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. |
| Performance standards | 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) | 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. |
CG Quarter 3 — Quadratics, Similarity, and Variation
Opens in Term 2 (weeks 18–22); completed in Term 3 (weeks 23–27)
| Domains | Number and Algebra (NA) · Measurement and Geometry (MG) — the largest quarter in the grade |
| 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. |
| Learning competencies | 1. represent real-life situations that can be modelled using quadratic relationships. 2. graph equations in two variables to represent quadratic relationships, such as y = ax², y = ax² + b, y = a(x − b)². 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. 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. 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. 7. find the zeros of quadratic functions in factored and standard form, graphically and algebraically. 8. solve quadratic equations by (a) extracting square roots, (b) factoring, and (c) using the quadratic formula. 9. solve problems involving quadratic functions and equations. 10. illustrate similarity of polygons. 11. illustrate and apply triangle similarity theorems in different situations. 12. solve problems involving triangle similarity. 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. |
| Performance standards | 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) | 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. |
CG Quarter 4 — Triangle Theorems, Trigonometry, Misleading Data, and Probability
Taught in Term 3, weeks 28–33
| Domains | Measurement and Geometry (MG) · Data and Probability (DP) |
| 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. |
| Learning 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. 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. 5. use the trigonometric ratios in solving right triangles. 6. illustrate angles of elevation and angles of depression. 7. solve real-life problems involving right triangles through the application of the trigonometric ratios. 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. 10. determine the probabilities of simple and compound events. 11. solve problems involving probabilities of simple and compound events. |
| Performance standards | 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) | 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. |
Competency 8 is the one to protect from being skipped. Assess whether the data may be misleading has no calculation in it, appears in a quarter otherwise full of trigonometry, and is the easiest thing in Grade 9 to leave out. It is also the direct continuation of Grade 6 Quarter 4 competency 8 and Grade 8 Quarter 4 competencies 3–4, and it is the single competency in this grade with the widest use outside school. Teach it with real charts, not invented ones.
5. Term-by-Term Scope and Sequence
Thirty-three instructional weeks, eleven per term — an even split this repository chose.
⚠️ The real terms are not equal. DO No. 009, s. 2026 is reported as 54 / 55 / 61 instructional days across 201 class days — roughly 34 teaching weeks split 11 / 11 / 12. The Budget of Work is what should settle it, and it remains unobtained. Give Term 3 the slack.
Every one of the 51 CG competencies appears exactly once. Twelve weeks pair naturally adjacent competencies — marked ⊕.
What is authoritative here and what is not. The CG assigns content to quarters; the Budget of Work assigns it to weeks, and this repository has neither the Grade 9 Budget of Work nor the DO 009 annexes (
source-catalogue.md). The grid below is this repository's proposal. Adjust freely.
Term 1 — June to September
| Week | Focus | CG source | Artifacts in this repo |
|---|---|---|---|
| 1 | Point, line, ray, segment, angle and plane, with geometric notation | Q1 · 1 | — |
| 2 | Constructing perpendicular and parallel lines | Q1 · 2 | — |
| 3 | Angles formed by parallel lines cut by a transversal | Q1 · 3 | — |
| 4 | Determining angle measures with angle pairs and transversals | Q1 · 4 | — |
| 5 ⊕ | Relations that are functions and domain and range | Q1 · 5–6 | — |
| 6 | Expressing a relationship between two variables as a function | Q1 · 7 | — |
| 7 | Slope as a rate of change, and zeros — from graphs, equations and tables | Q1 · 8 | ✔ Full set — both lesson plans, slides, game, offline activities, worksheet, wall chart |
| 8 ⊕ | Graphing a linear function with its domain, range, intercepts and slope and representing real-life linear relationships and solving problems | Q1 · 9–11 | — |
| 9 | Conditions that guarantee parallelism and perpendicularity | Q2 · 1 | — |
| 10 | Classifying quadrilaterals by formal definition | Q2 · 2 | — |
| 11 | Using the properties of parallelograms to find measures | Q2 · 3 | — |
End-of-term block — performance task, Term 1 examination, remediation, reporting.
Term 2 — September to December
| Week | Focus | CG source |
|---|---|---|
| 12 | Problems involving parallelograms, rectangles, squares and rhombuses | Q2 · 4 |
| 13 | Proving properties of parallelograms | Q2 · 5 |
| 14 ⊕ | Deriving the properties of trapezoids and kites and solving problems with them | Q2 · 6–7 |
| 15 ⊕ | Inductive versus deductive reasoning and postulates, theorems and proofs | Q2 · 8–9 |
| 16 ⊕ | Triangle congruence postulates and CPCTC and problems with the congruence theorems | Q2 · 10–11 |
| 17 ⊕ | Constructions justified by congruence and two-column congruence proofs | Q2 · 12–13 |
| 18 | Real-life situations modelled by quadratic relationships | Q3 · 1 |
| 19 | Graphing y = ax², y = ax² + b and y = a(x − b)² | Q3 · 2 |
| 20 | Features of a parabola — vertex, axis, intercepts, maximum and minimum | Q3 · 3 |
| 21 ⊕ | Transforming to vertex form and back and sketching from an equation | Q3 · 4–5 |
| 22 | The effect of changing the parameters of y = a(x − h)² + k | Q3 · 6 |
End-of-term block — performance task, Term 2 examination, remediation, reporting.
Term 3 — January to April
| Week | Focus | CG source |
|---|---|---|
| 23 | Finding the zeros of a quadratic, graphically and algebraically | Q3 · 7 |
| 24 | Solving quadratic equations — square roots, factoring, and the formula | Q3 · 8 |
| 25 ⊕ | Problems with quadratic functions and equations and similarity of polygons | Q3 · 9–10 |
| 26 ⊕ | Triangle similarity theorems and problems involving triangle similarity | Q3 · 11–12 |
| 27 ⊕ | Special triangles — 30-60-90 and 45-45-90 and direct and inverse variation | Q3 · 13–16 |
| 28 ⊕ | Perpendicular bisector, isosceles, equilateral and midline theorems and triangle inequalities | Q4 · 1–2 |
| 29 ⊕ | Sine, cosine and tangent of the special angles and of any acute angle | Q4 · 3–4 |
| 30 | Using the trigonometric ratios to solve right triangles | Q4 · 5 |
| 31 ⊕ | Angles of elevation and depression and real-life right-triangle problems | Q4 · 6–7 |
| 32 ⊕ | Misleading data in digital media and illustrating simple and compound events | Q4 · 8–9 |
| 33 ⊕ | Probabilities of simple and compound events and problems involving them | Q4 · 10–11 |
End-of-term block — performance task, Term 3 examination, closing activities, reporting.
Coverage check
| CG quarter | Competencies | Weeks allotted | Where |
|---|---|---|---|
| Quarter 1 | 11 | 8 | Term 1, weeks 1–8 |
| Quarter 2 | 13 | 9 | Term 1 weeks 9–11; Term 2 weeks 12–17 |
| Quarter 3 | 16 | 10 | Term 2 weeks 18–22; Term 3 weeks 23–27 |
| Quarter 4 | 11 | 6 | Term 3, weeks 28–33 |
| Total | 51 | 33 |
All 51 CG competencies are placed. None is taught twice, and none is dropped.
Two weeks in this grade are over-packed, and both are named here rather than hidden. Week 8 carries three competencies, and Week 27 carries four — special triangles plus the whole of direct and inverse variation. Week 27 is the worst in any grade in this repository. Variation is only loosely connected to what precedes it, so if your budget of work allows, lift competencies 14–16 out of Quarter 3 entirely and teach them wherever there is room. Failing that, Term 3's reported extra week belongs here.
Quarter 4 gets six weeks for eleven competencies, which is defensible only because five of its six weeks pair naturally. Do not let it be squeezed further: competency 8 is usually the first casualty and it is the one that matters most outside the examination.
6. Assessment and Grading
Per DO No. 015, s. 2026. Mathematics is a Key Stage 3 core learning area:
| Component | Weight | What it covers in this course |
|---|---|---|
| Written Works | 20% | Quizzes, seatwork, written problem-solving with shown reasoning |
| Performance Tasks | 50% | The three term performance tasks, group activities, oral explanations |
| Examinations | 30% | Summative Test 1 (30%), Summative Test 2 (30%), Term Examination (40%) |
Transmutation is being withdrawn, and this school year sits in the middle of that.
| School year | What applies to Grades 4–12 |
|---|---|
| 2026–2027 — this one | Transmutation continues, on an adjusted table: raw 70 → passing 75 |
| 2027–2028 onward | Transmutation removed; zero-based, raw 75 is the minimum pass |
class-record.html implements this as a year switch.
⚠️ Reported, not verified, and the Key Stage 3 attribution is an inference. See
source-catalogue.md. Confirm before computing a real grade.
Formative assessment used weekly
- Exit tickets — one question at the end of each session
- The unit check — for any slope, rate or ratio, ask for its unit. A slope without a unit is a number a learner has read off; a slope with one is a rate they understand. Five seconds
- The game's Teacher Panel — per-round accuracy against the week's competency
- Two-column discipline — from Quarter 2 on, every geometric claim gets a reason beside it
7. Learner Support
| Provision | What it looks like |
|---|---|
| Below-level | Squared paper always available; slope computed from whole-number grid steps before any formula. Contexts kept to money and time, where the units are already familiar. |
| On-level | Standard task with a required written justification. |
| Above-level | Extension by depth — "find two real relationships with the same slope and different units, and say what that means", not twenty more gradients. |
| Language | All materials in English. Rate of change, zero and intercept are introduced orally, and zero of a function is explicitly distinguished from the number zero. |
| Learners with additional needs | Enlarged pre-ruled axes; extended time; verbal response; peer scribe. Compass and straight-edge work has a string-and-pencil alternative. All digital artifacts are keyboard-operable. |
| Absence and catch-up | Every digital artifact is a single file that copies to a phone or USB stick and runs offline at home. |
8. Materials
No-cost / recycled — the default.
- Squared paper — the single most-used material in the grade
- A ruler and a protractor per pair; a compass or a loop of string for Quarter 2 constructions
- Cardboard triangles cut to 30-60-90 and 45-45-90 for Quarter 3
- A measuring tape or knotted string, and a home-made clinometer (a protractor, a straw and a weighted thread) for Quarter 4
- Real charts cut from newspapers or printed from phones — the raw material for competency 8
- Coins, dice or numbered caps for probability
- Chalk and the board
If available. A projector for the slide deck; any browser for the game; a scientific calculator per pair from Week 29 onward — not before, because Week 7's slopes are meant to be reasoned, not computed.
9. Curriculum Verification — Completed
| Item | Source | Status |
|---|---|---|
| Grade level standard (§2) | CG p. 23 | ✅ Verbatim |
| Content domains (§3) | CG p. 23 | ✅ Verified |
| Quarter 1 (§4) | CG p. 60 | ✅ Verbatim |
| Quarter 2 (§4) | CG p. 61 | ✅ Verbatim |
| Quarter 3 (§4) | CG pp. 62–63 | ✅ Verbatim — the performance standards run onto p. 63 |
| Quarter 4 (§4) | CG p. 64 | ✅ Verbatim |
| Week-by-week sequence (§5) | Derived from CG ordering | ⚠️ School decision |
| Three-term calendar (header, §5) | DO No. 009, s. 2026 | ⚠️ Adopted, from reporting |
| Term boundaries and week numbers (§5) | This repository | ⚠️ Proposal — the Budget of Work is unobtained |
| Assessment weights (§6) | DO No. 015, s. 2026 | ⚠️ Adopted, from reporting; Key Stage 3 attribution is an inference |
| Performance tasks (§4) | This syllabus | ⚠️ Suggestions, not CG content |
Part of the E-turo MATATAG artifact set. Companion files:
lesson-plan-ilaw.md · lesson-plan.md ·
assessment.md · offline-activities.md ·
slides.html · game.html ·
worksheet.html · class-record.html