Mathematics 5 — Course Syllabus

MATATAG Curriculum · Key Stage 2 · 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. Those competencies are unchanged — only their container moved. §4 keeps the CG's quarter attribution visible on every row, and §5 maps the four quarters onto the three terms.

1. Course Description

Mathematics 5 is the year the learner stops treating a fraction and a decimal as two unrelated things. Grade 4 established both separately: fractions as parts of a whole, decimals as a way of writing tenths and hundredths. Grade 5 puts them in the same sentence — multiply them, divide them, order them, and by Term 3 apply three or more operations to a mixed expression under the GMDAS rules.

Two ideas make this year hard in a way Grade 4 was not, and both deserve to be named in advance:

• Multiplication can make a number smaller. Four years of whole-number work teach the opposite. ½ × ½ = ¼ contradicts it directly, and no amount of procedural fluency repairs the intuition. It has to be seen, on an area model, before it is computed.
• Division by a fraction gives a larger answer. 3 ÷ ½ = 6 reads as a mistake to a learner who has only ever divided into equal shares. Reframing division as "how many halves fit?" is the whole lesson.

Measurement moves from perimeter into area by formula — parallelogram, triangle, trapezoid — where the recurring difficulty is not the formula but the height: learners reliably measure a slanted side instead of the perpendicular. Geometry then leaves the plane entirely for prisms, pyramids, nets and surface area. Data work reaches two data sets at once — double bar and double line graphs — which is where comparison, not just reading, becomes the skill. Probability appears for the first time in the learner's schooling.

Learning stays contextualised: the fare matrix on the jeepney, a recipe scaled for a fiesta, the tarpaulin cut for a barangay event, the rainfall recorded over two seasons.

2. Grade Level Standard

Quoted verbatim from the MATATAG Mathematics Curriculum Guide (DepEd, August 2023), page 22.

GRADE 5 — The learner demonstrates knowledge, skills, and understanding in relation to the curriculum content domains Number and Algebra (the GMDAS rules for operations with numbers; multiplication and division of fractions; decimal numbers with decimal parts up to ten thousandths; addition and subtraction of decimal numbers; divisibility rules; prime and composite numbers; multiplication and division of decimal numbers; GMDAS rules when performing three or more operations with fractions and decimals); Measurement and Geometry (12- and 24-hour time, and world time zones; area of a parallelogram, triangle, and trapezoid; prisms and pyramids; surface area of solid figures; cubes and rectangular prisms; rotation about a point given an angle); and Data and Probability (double bar graphs and double line graphs; theoretical probability). 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.

⚠️ A discrepancy inside the curriculum guide itself, left as found. The grade level standard above and the CG Quarter 2 content standard both say decimal parts up to ten thousandths. Every Quarter 2 competency that operationalises it says thousandths — place value to thousandths (Q2 · 4), reading and writing to thousandths (Q2 · 5), comparing and ordering to thousandths (Q2 · 7), rounding to the nearest thousandth (Q2 · 8). This syllabus teaches to the competencies, because those are what an examination is written from, and flags the gap rather than silently resolving it. A class that is comfortable at thousandths extends to ten thousandths in a single session; the reverse is not true.

3. Content Domains

What Grade 5 does not cover, though it is easy to assume: percentage (Grade 6), ratio and proportion (Grade 6), volume by formula (Grade 5 estimates volume with non-standard units only — the formula is Grade 6), and area of a circle (Grade 6). Grade 5 geometry finds surface area of solids, not volume.

Where the domains sit. Quarter 1 and Quarter 4 each pair Number and Algebra with Measurement and Geometry. Quarter 2 is Number and Algebra alone — the only single-domain quarter in the grade. Quarter 3 opens the year's only Data and Probability block and closes with decimals.

4. Content Map

Every entry below is quoted or closely transcribed from the official curriculum guide (DepEd, August 2023, pages 44–47), committed to this repository at docs/research/source/. Competency numbers are the CG's own and are quarter-relative.

Performance tasks are this syllabus's suggestions, not CG content — they are marked as such.

CG Quarter 1 — Time, Time Zones, Multiplying Fractions, and Area

Taught in Term 1, weeks 1–9

CG Quarter 2 — Dividing Fractions, Decimals, and Divisibility

Opens in Term 1 (weeks 10–11); completed in Term 2 (weeks 12–17)

CG Quarter 3 — Double Graphs, Probability, and Multiplying and Dividing Decimals

Opens in Term 2 (weeks 18–22); completed in Term 3 (weeks 23–26)

CG Quarter 4 — GMDAS with Fractions and Decimals, Solids, and Rotation

Taught in Term 3, weeks 27–33

A note on Quarter 4 competency 11. It asks for volume estimated in non-standard units — filling the solid with bottle caps or centimetre cubes and counting. It does not ask for length × width × height. That formula is Grade 6. Teaching it early here is the single most common way this competency is over-delivered, and it removes the exploration the Grade 6 lesson depends on.

5. Term-by-Term Scope and Sequence

Thirty-three instructional weeks, eleven per term — an even split this repository chose, not one DO 009 specifies. Assessment, remediation and reporting sit in each term's end-of-term block rather than consuming a teaching week.

⚠️ The real terms are not equal. DO No. 009, s. 2026 is reported as 54 instructional days in Term 1, 55 in Term 2 and 61 in Term 3, each with a 10-day end-of-term block, across 201 class days — roughly 34 teaching weeks split 11 / 11 / 12. The even grid below is therefore slightly tight in Term 3. The Budget of Work is what should settle it, and it remains unobtained. If you are pacing a real class, give Term 3 the slack.

Every one of the 49 CG competencies appears exactly once. Grade 5 carries substantially more competencies per available week than Grade 4 did, so fourteen weeks pair naturally adjacent competencies — marked ⊕ — rather than dropping content.

What is authoritative here and what is not. The CG assigns content to quarters. DepEd's Budget of Work assigns it to weeks. This repository has neither the Grade 5 Budget of Work nor the DO 009 implementing annexes — both are behind a network block (source-catalogue.md). The term boundaries and week numbers below are this repository's proposal, derived from the CG's own listing order. A school's approved budget of work may order it differently. Adjust freely.

Term 1 — June to September

CG Quarter 1 complete, then the opening of CG Quarter 2.

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

Term 2 — September to December

The rest of CG Quarter 2, then the opening of CG Quarter 3.

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

Term 3 — January to April

The rest of CG Quarter 3, then CG Quarter 4 complete.

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

Coverage check

All 49 CG competencies are placed. None is taught twice, and none is dropped.

6. Assessment and Grading

Per DO No. 015, s. 2026. Mathematics is a Key Stage 2 core learning area:

Transmutation is being withdrawn, and this school year sits in the middle of that.

Any spreadsheet built from this syllabus needs a year switch, not a fixed table. class-record.html implements exactly this.

⚠️ Reported, not verified. DO No. 015, s. 2026 could not be downloaded in the environment these artifacts were built in — see source-catalogue.md. Two independent search passes returned the same 20 / 50 / 30 split and the same examination subdivision, attributed to the Key Stage 2–3 core learning areas. Two passes agreeing is not the order itself. Confirm before computing a real grade.

Formative assessment used weekly

Formative work is not graded — it steers instruction.

• Exit tickets — one question at the end of each session
• The area-model check — for any fraction product, learners must be able to shade it before they compute it. A learner who can compute ⅔ × ¾ but cannot shade it has a procedure, not an idea, and Term 2's division work will collapse on it
• The game's Teacher Panel — per-round accuracy against the week's competency
• Error hunts — learners find and correct a planted mistake

7. Learner Support

8. Materials

No-cost / recycled — the default. The course is designed to run on these alone.

• Squared paper, or a hand-ruled 10 × 10 grid, for area models
• Strips of cut paper for fraction folding
• Bottle caps or tamarind seeds as counters and as non-standard volume units
• Flattened grocery cartons — the source of every net and solid model in Quarter 4
• Old newspapers for decimal hunts in prices and sports tables
• Chalk and the board

If available.

• One projector or television for the slide deck
• Any device with a browser for the game
• A world time zone map for Quarter 1 (a printed one is sufficient; the wall chart substitutes)

9. Curriculum Verification — Completed

This syllabus has been checked against the official curriculum guide, committed to this repository:

• docs/research/source/MATATAG-Mathematics-CG-2023-Grades1-10.pdf — MATATAG K to 10 Curriculum of the K to 12 Program: Mathematics, Grades 1–10, Department of Education, August 2023, 73 pages.

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