Mathematics 10 — Course Syllabus

MATATAG Curriculum · Key Stage 3 · School Year 2026–2027

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.

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 10 is the last year of the K–10 curriculum, and it closes threads rather than opening them.

Trigonometry stops being about right triangles. Grade 9 could only solve a triangle that contained a 90° angle. The laws of sines and cosines remove that restriction in the first two weeks of the year, and with them arrives the ambiguous case — the first situation in ten years of schooling where correct working can produce two valid answers and the learner must report both.

A solution stops being a set of numbers. Every inequality before this grade produced marks on a number line. Quarter 1 asks for the solution of an inequality in two variables, and the answer is a region of the plane — infinitely many points, not one of which can be listed. The syllabus gives that shift a full week, because the method that survives it is not algebraic at all: you find the boundary, then you test a point.

The circle finally gets its algebra and its geometry in the same year. Quarter 3 puts the circle on the Cartesian plane as an equation; Quarter 4 returns to it as a figure full of angles and chords. They are never connected by the CG, and a teacher who connects them gets both for less than the price of two.

Probability becomes conditional. Quarter 3 closes the Data and Probability strand for the whole of basic education with dependent events and conditional probability — restricted by the CG to contingency tables and Venn diagrams, which is a sensible restriction and worth honouring.

The very last competency in the K–10 Mathematics curriculum is Quarter 4 competency 12: solve problems involving area of a sector of a circle, segment of a circle, and shaded regions in other figures that involve sectors or segments. It is a good place to finish — every technique in it was built somewhere earlier.

Contexts stay local: a fishing boat's bearing, the reach of a barangay wifi antenna, a sari-sari store's takings, interest on a cooperative loan, the arc of a bamboo fence.

2. Grade Level Standard

Quoted verbatim from the MATATAG Mathematics Curriculum Guide (DepEd, August 2023), page 24.

GRADE 10 — The learner demonstrates knowledge, skills, and understanding in relation to the curriculum content domains Number and Algebra (quadratic inequalities in one variable and in two variables; absolute value equations and inequalities in one variable, and their graphs; radical expressions; the roots of a quadratic equation; quadratic functions; equations reducible to quadratic equations; equation of a circle and the graph of a circle; compound interest and depreciation); Measurement and Geometry (the laws of sines and the laws of cosines; translations, reflections, and rotations, in the Cartesian plane; central angles, inscribed angles, and angles and lengths formed by intersecting chords, secants, and tangents of a circle; sectors and segments of a circle, and their areas); and Data and Probability (box-and-whisker plots, and cumulative frequency histograms and polygons; quartiles, deciles, and percentiles; interquartile range, and outliers; evaluation of statistical reports; union and intersection of events, dependent and independent events, and complementary events). This knowledge, skills, and understanding is applied, in association with the use of technology, in the processes within Mathematics of critical thinking, problem solving, communicating, reasoning, and making connections between topic areas.

⚠️ A discrepancy inside the CG, recorded rather than resolved. The grade-level standard above lists "compound interest and depreciation". Quarter 4's content standard 1 lists "simple interest, compound interest, and depreciation", and competency 1 asks learners to explore the relationship between simple and compound interest. Simple interest is therefore in the quarter but not in the grade-level standard. Nothing turns on it — you cannot teach compound interest without simple interest anyway — but a teacher checking one document against the other should know the mismatch is the CG's, not a transcription error here.

3. Content Domains

What Grade 10 does not cover: systems of inequalities (there is only ever one inequality at a time), conic sections other than the circle, the unit circle or radian measure, normal distributions, and permutations and combinations — counting is never formalised anywhere in K–10. Conditional probability is deliberately limited by the CG to contingency tables and Venn diagrams; the formula P(A|B) = P(A ∩ B) ÷ P(B) is not required.

Where the domains sit. Quarter 1 pairs Measurement and Geometry with Number and Algebra. Quarter 2 pairs Data and Probability with Number and Algebra. Quarter 3 does the same in the opposite order. Quarter 4 pairs Number and Algebra with Measurement and Geometry. No quarter in this grade is single-domain — the only grade in Key Stage 3 of which that is true.

4. Content Map

Every entry below is quoted or closely transcribed from the official curriculum guide (DepEd, August 2023, pages 65–69), 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 — Oblique Triangles, Transformations, and Inequalities

Taught in Term 1, weeks 1–8

CG Quarter 2 — Measures of Position, Radicals, and Quadratic Functions

Opens in Term 1 (weeks 9–11); completed in Term 2 (weeks 12–18)

CG Quarter 3 — Circles on the Plane, Statistical Reports, and Probability

Opens in Term 2 (weeks 19–22); completed in Term 3 (weeks 23–24)

CG Quarter 4 — Compound Interest, and the Circle as a Figure

Taught in Term 3, weeks 25–33

Competency 4 · 8 is the densest single competency in the whole K–10 curriculum. It carries six distinct angle relationships — central, inscribed, two chords, two secants, two tangents, and a secant with a tangent — under one number. Every published week-by-week plan this repository could find treats it as one week. It is not one week's work. §5 gives it its own week anyway and says plainly that the week is under-resourced; if Term 3's reported extra week exists, this is where it should go. Competency 10 has the same problem in miniature with three length relationships.

Competency 3 · 9 is the other one to watch. Three sub-parts, including conditional probability. The CG limits the solution method to contingency tables or Venn diagrams, and that limit is a gift — take it. Teaching the conditional probability formula here buys nothing and costs the week.

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; §4 says exactly where it should land.

Every one of the 46 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 10 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

End-of-term block — performance task, Term 1 examination, remediation, reporting.

Term 2 — September to December

End-of-term block — performance task, Term 2 examination, remediation, reporting.

Term 3 — January to April

End-of-term block — performance task, Term 3 examination, closing activities, reporting.

Coverage check

All 46 CG competencies are placed. None is taught twice, and none is dropped.

Three weeks in this grade are under-resourced, and all three are named here rather than hidden.

Week 18 carries three competencies. Two of them — equations reducible to quadratic, and radical equations — are the same skill in different clothes, so the pairing is defensible; the third, problems involving quadratic functions, is not, and is the one to move if you can.

Week 31 carries a single competency with six sub-cases (Q4 · 8 a–f). It is the worst week in this grade and, by sub-case count, in this repository. Two weeks is the honest allocation. This is where Term 3's reported extra week should go.

Week 24 carries a single competency with three sub-parts including conditional probability. It is survivable only because Week 23 does the groundwork on mutually exclusive and complementary events first — do not reverse that order.

Quarter 3 gets six weeks for nine competencies and is the smallest quarter in the grade. If a week has to be taken from somewhere to give to Week 31, take it from Week 21 (problems with geometric figures on the plane), which revisits Grade 9 distance and midpoint work and can be compressed.

Two connections the CG does not make, and both are free

The circle appears twice in this grade and is never joined up. Quarter 3 puts it on the Cartesian plane as (x − h)² + (y − k)² = r². Quarter 4 returns to it as a figure with chords, tangents and inscribed angles, with no coordinates in sight. A tangent line is perpendicular to the radius at the point of contact — that is a Quarter 4 property and a Quarter 3 slope calculation, and a class that meets both facts as one fact remembers both.

Week 7's test point is Week 21's test point. Deciding which side of a boundary a region lies on, and deciding whether a point is inside or outside a circle, are the same act: substitute and compare. Say so in Week 19 and Week 7 pays for itself twice.

6. Assessment and Grading

Per DO No. 015, s. 2026. Mathematics is a Key Stage 3 core learning area:

The Examinations component divides further:

⚠️ The weights are reported, and the Key Stage 3 attribution is an inference. DO No. 015, s. 2026 is reported for "Key Stages 2–3 core learning areas". Grades 4–6 are Key Stage 2 and Grades 7–10 are Key Stage 3, so the same model is applied here — but this repository has not obtained the order itself. See source-catalogue.md. Confirm the weights before computing a real grade. Everything else in this syllabus stands on the CG, which is held.

Transmutation. SY 2026–2027 uses the adjusted table, in which a raw score of 70 transmutes to a final grade of 75. From SY 2027–2028 the table is zero-based and 75 raw is the passing floor. class-record.html carries both as a switch and refuses to interpolate below the one anchor this repository actually holds.

A summative test may not exceed half the term examination's item count. See assessment.md for the Table of Specifications and three complete papers.

7. Verification Checklist

Part of the E-turo MATATAG artifact set. Companion files: lesson-plan.md · lesson-plan-ilaw.md · assessment.md · offline-activities.md · class-record.html · worksheet.html