Mathematics 7 — Course Syllabus
MATATAG Curriculum · Key Stage 3 · School Year 2026–2027
| Learning Area | Mathematics |
| Grade Level | Grade 7 |
| Key Stage | Key Stage 3 (Grades 7–10) — entry year |
| Time Allotment | 45 minutes daily · 5 days a week · 3 terms |
| Prerequisite | Mathematics 6 (Key Stage 2 exit standard) |
| 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. 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 7 opens Key Stage 3, and it is the year mathematics stops being only about quantities you can count.
Three doors open, in this order:
- Numbers below zero. Integers arrive in Quarter 3. Learners who have spent six years being told you cannot take 7 from 3 now have to. The difficulty is never the arithmetic — it is believing the answer.
- Numbers that are not fractions. √2 appears in Quarter 2, and with it the discovery that the number line has points no fraction reaches. Most Grade 7 classes meet this in a single sentence and move on; it deserves longer.
- Letters standing for numbers. Quarter 4 introduces the variable. Everything before it in the year is preparation, and the syllabus is sequenced so that arrives last, after integers and after operations are secure.
Alongside those, Quarter 1 does something unusual for a mathematics curriculum: it asks learners to create a financial plan (CG Q1 · 9). That competency is not decoration. Percentage increase, discount, commission, sales tax and simple interest are all in the same quarter, and they are the arithmetic of a payslip and a loan. This syllabus treats them as the practical core of Term 1 rather than as a word-problem topic.
Geometry begins from drawing — polygons constructed with a ruler and protractor before any angle formula is stated — because a learner who has drawn a regular decagon knows something about its angles that no formula delivers.
Context stays local throughout: sari-sari store mark-ups, jeepney fares per kilometre, a tricycle driver's daily takings, remittance charges, the barangay's rainfall records.
2. Grade Level Standard
Quoted verbatim from the MATATAG Mathematics Curriculum Guide (DepEd, August 2023), page 23.
GRADE 7 — The learner demonstrates knowledge, skills, and understanding in relation to the curriculum content domains Number and Algebra (application of percentages; use of rates; rational numbers; square roots of perfect squares, cube roots of perfect cubes, and irrational numbers; sets and subsets, and the union and intersection of sets; Venn diagrams; the set of integers, and comparing and ordering integers; the four operations with integers; simplification of numerical expressions involving integers; absolute value of an integer; the solution of simple equations; the evaluation of algebraic expressions following substitution; the rearrangement of a formula to make a different variable the subject of the formula; operations using scientific notation); Measurement and Geometry (regular and irregular polygons and their features/properties; determination of measures of angles and number of sides of polygons; conversion of units of measure; volume of square and rectangular pyramids, and cylinders); and Data and Probability (data collection and sampling techniques, and the presentation of data in appropriate tables and graphs; interpretation of statistical graphs; outcomes from experiments). 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 7 coverage |
|---|---|
| Number and Algebra (NA) | Percentages applied. Rates. Rational numbers. Square roots of perfect squares, cube roots of perfect cubes, irrational numbers. Sets, subsets, union, intersection, Venn diagrams. Integers, their order and the four operations. Simplifying expressions with integers; absolute value. Simple equations; evaluating algebraic expressions; rearranging a formula. Scientific notation. |
| Measurement and Geometry (MG) | Regular and irregular polygons and their properties. Measures of angles and numbers of sides. Conversion of units within and across systems. Volume of square and rectangular pyramids, and of cylinders. |
| Data and Probability (DP) | Data collection and sampling. Frequency distribution tables. Pie, bar, line and stem-and-leaf graphs. Interpreting statistical graphs. Outcomes from experiments. |
What Grade 7 does not cover, though it is easy to assume: operations with algebraic expressions — Grade 7 evaluates expressions and rearranges formulas, but multiplying out and factoring polynomials is Grade 8. Also not here: linear equations in two variables and their graphs (Grade 8), the Cartesian plane (Grade 8), theoretical probability as a calculation (Grade 7 collects experimental outcomes; Grade 8 formalises it), and measures of central tendency (Grade 8).
Where the domains sit. Every quarter mixes at least two domains. Quarter 1 pairs Measurement and Geometry with Number and Algebra; Quarter 2 does the same in the other order; Quarters 3 and 4 both pair Data and Probability with Number and Algebra.
4. Content Map
Every entry below is quoted or closely transcribed from the official curriculum guide
(DepEd, August 2023, pages 52–55), 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 — Polygons, Percentages, Rates, and Rational Numbers
Taught in Term 1, weeks 1–9
| Domains | Measurement and Geometry (MG) · Number and Algebra (NA) |
| Content standards | 1. regular and irregular polygons and their features/properties; 2. determination of measures of angles and number of sides of polygons; 3. application of percentages; 4. use of rates; 5. rational numbers. |
| Learning competencies | 1. draw and describe regular and irregular polygons with 5, 6, 8, or 10 sides, based on measurements of sides and angles, using a ruler and protractor. 2. draw triangles, quadrilaterals, and regular polygons (5, 6, 8, or 10 sides) with given angle measures. 3. describe and explain the relationships between angle pairs based on their measures. 4. classify polygons according to the number of sides, whether they are regular or irregular, and whether they are convex or non-convex. 5. deduce the relationship between the exterior angle and adjacent interior angle of a polygon. 6. determine the measures of angles and the number of sides of polygons. 7. solve problems involving (a) percentage increase, and (b) percentage decrease. 8. solve money problems involving percentages (e.g., discount, commission, sales tax, simple interest). 9. create a financial plan. 10. identify and explain the uses of rates. 11. solve problems involving rates (e.g., speed). 12. describe given rational numbers as fractions, decimals, or percentages. 13. order rational numbers on a number line. 14. perform operations on rational numbers. |
| Performance standards | By the end of the quarter, the learners are able to: draw, and describe the features/properties of, regular and irregular polygons (MG); use percentages in different contexts (NA); identify and use rates (NA); create a financial plan (NA); describe, order, and perform operations on, rational numbers (NA). |
| Performance task (suggested) | The Sari-Sari Store Books — take or construct one week of a small store's takings. Compute the mark-up percentage on five goods, the effect of a 10% supplier price rise on each, and the discount needed to clear slow stock without selling below cost. Then build a one-page financial plan for the following month with a stated savings target. |
CG Quarter 2 — Roots, Unit Conversion, Volume, and Sets
Opens in Term 1 (weeks 10–11); completed in Term 2 (weeks 12–17)
| Domains | Number and Algebra (NA) · Measurement and Geometry (MG) |
| Content standards | 1. square roots of perfect squares, cube roots of perfect cubes, and irrational numbers; 2. conversion of units of measure; 3. volume of square and rectangular pyramids, and cylinders; 4. sets and subsets, and the union and intersection of sets using Venn diagrams; 5. subsets of real numbers. |
| Learning competencies | 1. determine the square roots of perfect squares and the cube roots of perfect cubes. 2. identify irrational numbers involving square roots and cube roots, and their locations on the number line. 3. convert units of measure within the International System of Units (SI) and across different systems of measure. 4. explain inductively the volume of a cylinder using the area of a circle, leading to the identification of the formula. 5. find the volume of a cylinder. 6. solve problems involving the volumes of cylinders. 7. explore inductively the volume of square and rectangular pyramids using rectangular prisms, leading to the identification of the formula. 8. estimate volumes of square and rectangular pyramids. 9. solve problems involving volumes of square or rectangular pyramids. 10. describe sets and their subsets, the union of sets, and the intersection of sets. 11. illustrate sets and their subsets, the union of sets, and the intersection of sets, through the use of Venn diagrams. 12. illustrate the different subsets of real numbers. |
| Performance standards | Determine square roots of perfect squares and cube roots of perfect cubes, and identify irrational numbers (NA); convert units of measure from different systems of measure (MG); find the volume of square and rectangular pyramids, and the volume of cylinders (MG); describe sets and their subsets, and the union and intersection of sets (NA); illustrate sets and subsets, and union and intersection of sets, using Venn diagrams (NA). |
| Performance task (suggested) | What Fits in the Drum — measure a real cylindrical container (a water drum, a tin, a bucket). Compute its volume, convert it to litres, and check the answer by filling it. Report the difference between the computed and the measured value as a percentage, and account for it. |
CG Quarter 3 — Data, and the Integers
Opens in Term 2 (weeks 18–22); completed in Term 3 (weeks 23–26)
| Domains | Data and Probability (DP) · Number and Algebra (NA) |
| Content standards | 1. data collection and sampling techniques, and the presentation of data in appropriate tables and graphs; 2. interpretation of statistical graphs; 3. the set of integers, and comparing and ordering integers; 4. the four operations with integers; 5. simplification of numerical expressions involving integers; 6. absolute value of an integer. |
| Learning competencies | 1. investigate different data collection and sampling techniques. 2. organize statistical data in a frequency distribution table. 3. use appropriate graphs to represent organized data: pie graph, bar graph, line graph, and stem-and-leaf plot. 4. interpret statistical graphs. 5. describe the set of integers. 6. use positive and negative numbers to describe directions or opposites in real-life situations. 7. locate integers on the number line. 8. compare and order integers. 9. add and subtract integers, using concrete models (e.g., counters, integer chips), pictorial models (e.g., bar models, number lines), and with integers written as numerals. 10. multiply and divide integers. 11. simplify numerical expressions involving integers using number properties and the order of operations (GEMDAS). 12. identify the absolute value of an integer, and its meaning on the number line. |
| Performance standards | Collect data, and organize data in a frequency distribution table (DP); represent and interpret data in different types of graphs (DP); compare and order integers, including through the use of the number line (NA); perform the four operations with integers (NA); simplify numerical expressions involving integers (NA); identify the absolute value of an integer (NA). |
| Performance task (suggested) | Above and Below — collect a real data set that genuinely goes both ways: daily temperature against a monthly average, a small business's profit and loss by day, elevations above and below sea level. Present it in a frequency table and a suitable graph, and answer three questions that require adding and subtracting negatives. |
CG Quarter 4 — Equations, Expressions, Experiments, and Scientific Notation
Taught in Term 3, weeks 27–33
| Domains | Number and Algebra (NA) · Data and Probability (DP) |
| Content standards | 1. the solution of simple equations; 2. the evaluation of algebraic expressions following substitution; 3. the rearrangement of a formula to make a different variable the subject of the formula; 4. outcomes from experiments; 5. operations using scientific notation. |
| Learning competencies | 1. solve simple equations represented by bar models to find unknowns. 2. distinguish a variable from a constant in an algebraic expression. 3. evaluate algebraic expressions given the value/s of the variable/s. 4. translate verbal phrases into algebraic expressions. 5. illustrate the properties of equality. 6. solve one variable in terms of the other variables in a formula. 7. write equations in algebraic form. 8. find the value of an unknown in an equation where the unknown is non-negative. 9. solve problems involving algebraic expressions and formulas. 10. collect data from experiments (e.g., number of heads obtained when tossing a coin a number of times, number of prime numbers obtained when rolling a die a number of times). 11. express outcomes in words and/or symbols, and represent outcomes in tables and/or graphs. 12. solve problems using the outcomes of experiments. 13. write numbers in scientific notation to represent very large or very small numbers, and vice versa. 14. perform operations on numbers expressed in scientific notation. |
| Performance standards | Solve simple equations (NA); substitute into an algebraic expression to evaluate the expression (NA); rearrange a formula to make a different variable the subject of the formula (NA); gather data from experiments and represent the data in different forms (DP); write numbers in scientific notation and perform operations on numbers written in scientific notation (NA). |
| Performance task (suggested) | Is the Coin Fair? — toss one coin 200 times in pairs, recording every outcome. Tabulate, graph the running proportion of heads, and write a paragraph on whether the evidence supports the coin being fair. Then state what a different result would have had to look like to change the conclusion. |
A note on Quarter 4 competency 8. It restricts the unknown to non-negative values — even though the class has just spent Quarter 3 on integers. That is a deliberate narrowing in the CG, not an oversight to correct: negative solutions arrive in Grade 8 with linear equations. Setting a Grade 7 equation whose answer is −3 goes beyond the competency.
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, which is where Quarter 4's fourteen competencies land. 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 52 CG competencies appears exactly once. Seventeen 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 7 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.
| Week | Focus | CG source | Artifacts in this repo |
|---|---|---|---|
| 1 | Drawing and describing regular and irregular polygons | Q1 · 1 | — |
| 2 | Drawing triangles, quadrilaterals and regular polygons to given angles | Q1 · 2 | — |
| 3 ⊕ | Relationships between angle pairs and classifying polygons | Q1 · 3–4 | — |
| 4 ⊕ | The exterior angle and its adjacent interior angle and finding angles and sides | Q1 · 5–6 | — |
| 5 ⊕ | Rational numbers as fractions, decimals or percentages and ordering them | Q1 · 12–13 | — |
| 6 | Operations on rational numbers | Q1 · 14 | — |
| 7 | Percentage increase and percentage decrease | Q1 · 7 | ✔ Full set — both lesson plans, slides, game, offline activities, worksheet, wall chart |
| 8 ⊕ | Money problems — discount, commission, sales tax, simple interest and the financial plan | Q1 · 8–9 | — |
| 9 ⊕ | Identifying and explaining rates and solving problems involving rates | Q1 · 10–11 | — |
| 10 ⊕ | Square roots and cube roots and identifying irrational numbers on the number line | Q2 · 1–2 | — |
| 11 | Converting units within SI and across systems | Q2 · 3 | — |
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.
| Week | Focus | CG source |
|---|---|---|
| 12 ⊕ | The volume of a cylinder, deduced from the area of a circle and finding it | Q2 · 4–5 |
| 13 | Problems involving the volume of cylinders | Q2 · 6 |
| 14 ⊕ | The volume of pyramids, explored from prisms and estimating them | Q2 · 7–8 |
| 15 | Problems involving the volume of pyramids | Q2 · 9 |
| 16 ⊕ | Sets, subsets, union and intersection and Venn diagrams | Q2 · 10–11 |
| 17 | The subsets of the real numbers | Q2 · 12 |
| 18 | Data collection and sampling techniques | Q3 · 1 |
| 19 | Frequency distribution tables | Q3 · 2 |
| 20 | Choosing the graph — pie, bar, line, stem-and-leaf | Q3 · 3 |
| 21 | Interpreting statistical graphs | Q3 · 4 |
| 22 ⊕ | Describing the set of integers and using signed numbers for direction | Q3 · 5–6 |
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.
| Week | Focus | CG source |
|---|---|---|
| 23 ⊕ | Locating integers on the number line and comparing and ordering them | Q3 · 7–8 |
| 24 | Adding and subtracting integers with concrete and pictorial models | Q3 · 9 |
| 25 ⊕ | Multiplying and dividing integers and GEMDAS with integers | Q3 · 10–11 |
| 26 | Absolute value and its meaning on the number line | Q3 · 12 |
| 27 ⊕ | Simple equations from bar models and variable versus constant | Q4 · 1–2 |
| 28 ⊕ | Evaluating algebraic expressions and translating verbal phrases | Q4 · 3–4 |
| 29 ⊕ | The properties of equality and writing equations in algebraic form | Q4 · 5, 7 |
| 30 ⊕ | Making a different variable the subject and problems with expressions and formulas | Q4 · 6, 9 |
| 31 | Finding the value of a non-negative unknown | Q4 · 8 |
| 32 ⊕ | Collecting data from experiments, expressing outcomes and solving problems with them | Q4 · 10–12 |
| 33 ⊕ | Scientific notation and operations in scientific notation | Q4 · 13–14 |
End-of-term block — performance task, Term 3 examination, closing activities, reporting.
Coverage check
| CG quarter | Competencies | Weeks allotted | Where |
|---|---|---|---|
| Quarter 1 | 14 | 9 | Term 1, weeks 1–9 |
| Quarter 2 | 12 | 8 | Term 1 weeks 10–11; Term 2 weeks 12–17 |
| Quarter 3 | 12 | 9 | Term 2 weeks 18–22; Term 3 weeks 23–26 |
| Quarter 4 | 14 | 7 | Term 3, weeks 27–33 |
| Total | 52 | 33 |
All 52 CG competencies are placed. None is taught twice, and none is dropped.
Quarter 4 is the pinch point of this grade: fourteen competencies in seven weeks. It contains the learner's first encounter with a variable, and it is the worst possible content to rush. Two things make it survivable. First, Quarter 4 competencies 1–9 are tightly sequenced — each is a small step from the last — so merged weeks are natural rather than forced. Second, DO 009's reported day counts give Term 3 the extra week. Use it here.
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, the game's Teacher Panel record |
| 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, but on an adjusted table: a raw grade of 70 transmutes to a passing 75 |
| 2027–2028 onward | Transmutation removed. Zero-based — a raw 75 is a term grade of 75, and that raw 75 is the absolute minimum pass |
Any spreadsheet built from this syllabus needs a year switch, not a fixed table.
class-record.html implements exactly this.
⚠️ Reported, not verified — and note the key stage. 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. Key Stage 3 is Grades 7–10 and Mathematics is a core area throughout, so the same weights are applied here as in Grades 4–6. Two passes agreeing is not the order itself, and the Key Stage 3 attribution is one inference further than the Key Stage 2 one. 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 "percent of what?" check — for any percentage answer, ask what the percentage was taken of. This single question catches the dominant Grade 7 percentage error and takes five seconds
- 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
| Provision | What it looks like |
|---|---|
| Below-level | Percentages anchored on 10% and 1% as building blocks, so any percentage can be assembled without a formula. A number line stays on the desk all year — it is the single most useful object in Grade 7, for rationals, for integers and for absolute value alike. |
| On-level | Standard task with a required written justification. |
| Above-level | Extension by depth — "find a pair of successive percentage changes that do return to the start", not ten more mark-up problems. |
| Language | All materials are in English. Key terms are introduced orally before they are read, and mathematical of is distinguished explicitly from everyday of. |
| Learners with additional needs | Enlarged print, extended time, verbal instead of written response, a peer scribe. Protractor work has an alternative: pre-drawn angle templates cut from card. All digital artifacts are keyboard-operable and screen-reader labelled. |
| Absence and catch-up | Every digital artifact is a single file that copies to a phone or USB stick and runs offline at home, with no account and no data connection. |
8. Materials
No-cost / recycled — the default. The course is designed to run on these alone.
- A ruler and a protractor per pair — the one genuinely required purchase in Grade 7, and a paper protractor printed or traced from a master works
- Bottle caps in two colours, or caps and seeds, as integer chips for Quarter 3
- String, tins, bottles and a measuring jug for Quarter 2's volume work
- Old receipts, price tags and store flyers — the raw material for the whole of Week 7 and Week 8
- Squared paper for graphs
- Chalk and the board
If available.
- One projector or television for the slide deck
- Any device with a browser for the game
- A calculator per pair for Quarter 1's money work. Not for the percentage lesson itself — Week 7 is about what a percentage means, and a calculator hides exactly the step that matters
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.
| Item | Source | Status |
|---|---|---|
| Grade level standard (§2) | CG p. 23 | ✅ Verbatim |
| Content domains (§3) | CG p. 23 | ✅ Verified |
| Quarter 1 content, competencies, performance standards (§4) | CG p. 52 | ✅ Verbatim |
| Quarter 2 (§4) | CG p. 53 | ✅ Verbatim |
| Quarter 3 (§4) | CG p. 54 | ✅ Verbatim |
| Quarter 4 (§4) | CG p. 55 | ✅ Verbatim |
| The non-negative restriction on Q4 · 8 (§4 note) | CG p. 55 | ✅ Verified as written |
| Week-by-week sequence (§5) | Derived from CG ordering | ⚠️ School decision — see §5 note |
| Three-term calendar (header, §5) | DO No. 009, s. 2026 | ⚠️ Adopted, but from reporting — the order itself is unread |
| Term boundaries and week numbers (§5) | This repository | ⚠️ Proposal — the Budget of Work that would settle it is unobtained |
| Assessment weights (§6) | DO No. 015, s. 2026 | ⚠️ Adopted, from reporting, and the Key Stage 3 attribution is an inference — see §6 |
| 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