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MATATAG Key Stage 3 Term 1 · Week 7 · Number & Algebra

Grade 8 Mathematics

Factoring polynomials completely — CG competency 8. A complete, classroom-ready artifact set, verified against the official curriculum guide. Everything here runs offline.

Focus competency
Completely factor polynomials — common monomial factor, difference of two squares, quadratic and perfect square trinomials (CG 8)
Session length
45 minutes
Content domain
Number and Algebra
Needs internet?
No — not at any point
The idea this week has to establish Asked to factor 2x² − 8, a class produces three answers: 2(x² − 4), (2x − 4)(x + 2), and 2(x − 2)(x + 2). All three are correct — every one expands back. Only the last is finished. Day 1 teaches no factoring technique at all; it exists so that learners have a reason to look at their own answer a second time.

For the teacher — six documents

Planning, assessing and recording. Two lesson plan formats, because they do different jobs.

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1Syllabus

Full-year syllabus — grade level standard, the three content domains, all four CG quarters, all 51 competencies across 33 weeks, grading weights and a verification checklist. Flags that the CG puts a financial competency inside the geometry quarter, says it is not a pedagogical pairing, and suggests where to move it.

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2aLesson Plan — ILAW

The whole week, in the format you file. Five days: what "completely" means, then common monomial factor, difference of two squares, trinomials and perfect squares, then choosing the method. Includes the decision routine as it goes on the board.

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2bLesson Plan — Lesson Exemplar

Day 1, at teaching depth. Timed to the minute. Seven anticipated misconceptions — including the dangerous one where a learner decides that incomplete means wrong and starts abandoning correct intermediate steps.

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+Assessment Pack

A Table of Specifications, three complete papers with answer keys and marking notes, a weekly check, and four performance-task rubrics. Factoring takes 22.5% of the term paper for one week of teaching — the heaviest single-week weighting in this repository, and the marking notes say why.

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3.3Offline Activities

Three individual options and two group options, including cardboard algebra tiles — a trinomial factors when its tiles form a rectangle, and the sides are the factors. The final activity has teams set factoring traps for each other.

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+Class Record

Enter raw scores, get the grade. Written Works 20 · Performance Tasks 50 · Examinations 30, with the examination component split ST1/ST2/TE. Carries the SY 2026–2027 adjusted transmutation and the SY 2027–2028 zero-based rule as a switch. Saves nothing, sends nothing.

For the class — four materials

What the learners see, use and hold.

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3.1Slide Presentation

15 slides timed to the lesson plan. The three candidate answers are shown at identical size and weight — giving any of them visual priority would answer the question the slide is asking. Green means finished, amber means correct but unfinished; nothing is marked red, because nothing here is wrong.

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3.2Interactive Game

Look Again — three rounds: judge whether a factorisation is finished, factor completely, then reason about how many moves it needs. Every question is built by multiplying known factors and asking for them back, so the game cannot present an answer that fails to expand to its own question.

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+Learner Worksheet

The one artifact a learner actually holds. Printable A4. Section A asks only for a judgement — no factoring at all — because telling finished from unfinished is the competency and can be assessed on its own. Two of its rows are already complete, and one of those looks as if it should not be.

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+Wall Chart

A printable A4 landscape reference — the five-step routine, the three answers to 2x² − 8, all four factoring patterns with worked examples, the two-steppers where marks are lost, and four polynomials that do not factor, because "it stops here" is a complete answer. Also as PDF and HTML.

Verified against the official CG

Standards and competencies are quoted from the official MATATAG Mathematics Curriculum Guide (DepEd, August 2023) — Grade 8 sits on pages 23 and 56–59. Every factorisation in every artifact was verified by expanding it back with a script, and every "does not factor" claim was checked for integer roots.

How the week fits together Day 1 runs the lesson plan with the slides — or The Complete Check (I-1) if there is no projector, since Day 1 needs no factoring at all. Day 2 is the common monomial factor. Day 3 is difference of two squares, with The Factor Wall. Day 4 is trinomials, with algebra tiles and the game's Round 2. Day 5 is The Expansion Relay, then the weekly check.