ILAW Lesson Plan — Mathematics 5
Term 1 · Week 7 · Number and Algebra · five sessions × 45 minutes
| Learning Area | Mathematics |
| Grade Level | Grade 5 |
| Term / Week | Term 1, Week 7 |
| CG source | Quarter 1, competency 8, building on 7 (p. 44) |
| Week Title | A Part of a Part — Multiplying a Fraction by a Fraction |
| Duration | 5 × 45 minutes |
| Format | ILAW — Intentions · Learning Experiences · Assessment · Ways Forward |
Two formats, two jobs. This is the week, in the format DepEd prescribes for the plan a teacher files. Its companion
lesson-plan.mdis Day 1 only, in the MATATAG Lesson Exemplar format, written at the depth of a teaching script — every question, every anticipated wrong answer, every timing. Use this one to plan and to file; open that one before you teach Monday.
⚠️ The ILAW field list is reported, not read. DO No. 009, s. 2026 is understood to prescribe ILAW as the single lesson plan template for SY 2026–2027, replacing both the Daily Lesson Log and the Detailed Lesson Plan, and to bar schools, divisions and regions from requiring any other. The four section names below are consistently reported; the exact sub-fields your division expects may differ. The order itself could not be downloaded in the environment this was built in — see
source-catalogue.md§8. Check against your division's own copy before filing.
I — INTENTIONS
A. Curriculum anchor
Quoted from the MATATAG Mathematics CG (DepEd, August 2023, p. 44):
Content standard. The learners should have knowledge and understanding of multiplication of fractions.
Performance standard. By the end of the quarter, the learners are able to multiply fractions.
Competency covered this week — quoted verbatim:
8. multiply a fraction by a fraction.
Assumed from last week, and deliberately re-opened on Day 1:
7. multiply fractions using models.
✅ Verified against the curriculum guide committed at
docs/research/source/.
B. What learners will be able to do, by day
| Day | Intention — by the end of the session, at least 80% of learners can… | Competency |
|---|---|---|
| 1 | Predict, then demonstrate by folding, that a fraction of a fraction is smaller than either factor — and say why in their own words | 7 → 8 |
| 2 | Read a product off an area model on a grid, and explain what the overlap counts | 7, 8 |
| 3 | State and use the rule — numerator × numerator over denominator × denominator — and connect each part of it back to the grid | 8 |
| 4 | Simplify before multiplying and handle a whole number or mixed number by rewriting it as a fraction | 8 |
| 5 | Recognise "of" as multiplication in a word problem and solve it without a model | 8 |
The rule does not arrive until Day 3, and that is deliberate. A class taught "top times top, bottom times bottom" on Monday will have it by Tuesday and will still believe multiplication makes numbers bigger in March. Days 1 and 2 buy the meaning that Days 3–5 then run on.
C. Key idea and vocabulary
A part of a part is smaller than both parts.
| Term | Meaning used this week |
|---|---|
| Of | The word that signals multiplication. Half of a half is ½ × ½ |
| Area model | A rectangle shaded twice — once across, once down. The overlap is the product |
| Numerator | The count — how many parts we have |
| Denominator | The size — how many parts the whole was cut into |
| Simplest form | The same quantity written with the smallest possible numbers |
The class sentence, repeated all week until it is automatic: "'Of' means multiply. A part of a part is smaller than both."
D. Integration
| Strand | How it appears |
|---|---|
| EPP / TLE | Recipe scaling on Day 5 — two-thirds of a half-kilo of rice |
| Araling Panlipunan | Land use: "three-quarters of the barangay is farmland; two-thirds of that is rice" |
| EsP / GMRC | Fair sharing on Day 1 — the fold is done in pairs and both must agree before cutting |
| English | The word of as a mathematical operator, contrasted with its ordinary use |
| 21st-century skills | Learners predict before they compute, and are held to the prediction |
L — LEARNING EXPERIENCES
Every session is 45 minutes and runs complete with chalk and scrap paper alone. Digital artifacts are listed where they help; none is required.
Day 1 · A part of a part — the fold
Full teaching script:
lesson-plan.md. Summary only here.
| Phase | Min | What happens |
|---|---|---|
| Activating prior knowledge | 5 | Board: 6 × 4, 12 × 3, 20 × 5. Then the question: "When you multiply, what happens to the number?" The class will say "it gets bigger." Write MULTIPLYING MAKES IT BIGGER on the board and leave it there. |
| Establishing purpose | 6 | Board: ½ × ½. "Predict. Bigger than a half, or smaller?" Show of hands, counts recorded on the board, unresolved. Most will vote bigger. |
| Developing understanding | 22 | Each pair gets one rectangle of scrap paper. Fold in half, shade one half. Fold the other way in half, shade again with a different mark. Open it. Four parts; the doubly-shaded piece is one of four. So ½ × ½ = ¼. Repeat with ½ × ⅓, then ⅔ × ½. |
| Making generalisations | 7 | Return to the board. Cross out MULTIPLYING MAKES IT BIGGER; the learner who argued loudest for it is asked to write the replacement. Land on: "Multiplying by a number less than one makes it smaller. A part of a part is smaller than both." |
| Evaluating | 5 | Exit ticket: predict and then justify ¾ × ½ — smaller than ¾? Smaller than ½? Both? |
Independent practice, without devices — learners fold, shade, and record:
| Fold this | Then this | Product | Simplest form |
|---|---|---|---|
| ½ | ½ | 1/4 | ¼ |
| ½ | ⅓ | 1/6 | ⅙ |
| ⅔ | ½ | 2/6 | ⅓ |
| ¾ | ½ | 3/8 | ⅜ |
| ⅔ | ¾ | 6/12 | ½ |
Why the misconception is written on the board and left standing. Told they are wrong, learners file the correction beside the belief and keep both. Made to vote, then made to fold the counter-example with their own hands, they have to give the belief up. The Grade 4 place value lesson in this repository uses the same move for the same reason.
Day 2 · The area model on a grid
| Phase | Min | What happens |
|---|---|---|
| Recall | 5 | Yesterday's five products, from memory, on slates or scrap. |
| Purpose | 5 | "Folding works for halves and thirds. What about ⅗ × ¾? Fold that." Let them try and fail. Introduce the grid as the tool that scales. |
| Developing | 25 | On a 4-column, 3-row grid: shade 3 of the 4 columns for ¾. Then shade 2 of the 3 rows for ⅔, crossing the first shading. Count the doubly-shaded cells: 6. Count all cells: 12. So ⅔ × ¾ = 6/12 = ½. Repeat with ⅗ × ¾ on a 4 × 5 grid → 9/20. Then ⅖ × ⅚ on a 6 × 5 grid → 10/30 = ⅓. |
| Generalising | 5 | "Where do the 12 cells come from?" — 3 rows × 4 columns. "Where do the 6 come from?" — 2 shaded rows × 3 shaded columns. Do not state the rule yet. Let the question sit overnight. |
| Evaluating | 5 | Exit ticket: draw the grid for ½ × ⅘ and give the product. |
Digital support: slides.html slides 4–8 animate the double shading.
game.html Round 1 is grid-reading only.
Day 3 · From the grid to the rule
| Phase | Min | What happens |
|---|---|---|
| Recall | 6 | Yesterday's closing question, back on the board. Take answers. |
| Purpose | 4 | "You already know the rule. You said it yesterday. Let us write it down." |
| Developing | 22 | Build the statement from the class's own words: the number of shaded cells is numerator × numerator; the number of cells altogether is denominator × denominator. Formalise: a/b × c/d = (a × c)/(b × d). Worked: ⅜ × ⅔ = 6/24 = ¼ (I do) → ⅚ × ⅗ = 15/30 = ½ (we do) → independent set (you do). Every answer must be checked against a quick sketch for the first three. |
| Generalising | 8 | "Does the rule ever give a bigger answer?" Try 3/2 × 4/3 = 12/6 = 2. Yes — when a factor is greater than one. The Day 1 sentence is refined, not discarded. |
| Evaluating | 5 | Exit ticket: ⅖ × ⅜, and one sentence on why the denominator grew. |
Independent practice:
| Problem | Product | Simplest form |
|---|---|---|
| ⅜ × ⅔ | 6/24 | ¼ |
| ⅚ × ⅗ | 15/30 | ½ |
| ⅞ × ½ | 7/16 | 7/16 |
| ¾ × ⅘ | 12/20 | ⅗ |
| ⅗ × ½ | 3/10 | 3/10 |
Day 4 · Simplifying first, and awkward factors
| Phase | Min | What happens |
|---|---|---|
| Recall | 5 | Three products from Day 3, timed. |
| Purpose | 5 | Board: ⁸⁄₉ × ³⁄₄. Multiply first → 24/36, then simplify → ⅔. "Is there less work available?" |
| Developing | 22 | Cancelling before multiplying: the 3 and the 9 share a factor, the 8 and the 4 share a factor. Same answer, smaller numbers, fewer errors. Then whole numbers: 4 × ⅔ — rewrite 4 as 4/1 → 8/3 → 2⅔. Then mixed numbers: 1½ × ⅔ — rewrite as 3/2 × 2/3 → 6/6 → 1. |
| Generalising | 8 | "Every whole number is a fraction with a 1 underneath. Every mixed number can be made improper. So there is only ever one rule." |
| Evaluating | 5 | Exit ticket: 2¼ × ⅔ (= 9/4 × 2/3 = 18/12 = 1½). |
Watch for this on Day 4. Learners who cancel across the wrong pair — top with top, or bottom with bottom — get a wrong answer that looks tidy. Require the sketch-check on the first two items of the independent set, not the last two.
Day 5 · "Of" in the wild, and the weekly check
| Phase | Min | What happens |
|---|---|---|
| Recall | 5 | The class sentence, said together, then three quick products. |
| Purpose | 4 | Board: "Two-thirds of the class brought merienda. Half of those brought rice cakes. What fraction of the class brought rice cakes?" |
| Developing | 16 | Three more word problems, worked in pairs. The skill being taught is finding the word "of", not the arithmetic — learners underline it before they compute. Contrast one problem where of is not multiplication ("three of the twelve chairs are broken") so the cue is not applied blindly. |
| Weekly check | 15 | Ten items — assessment.md §6. Written Works. |
| Closing | 5 | Day 1 exit tickets returned. Learners write one line: "On Monday I thought ______. Now I know ______." |
Word problems used (answers for the teacher):
| Problem | Working | Answer |
|---|---|---|
| ⅔ of the class brought merienda; ½ of those brought rice cakes | ½ × ⅔ | ⅓ of the class |
| A tarpaulin is ¾ m long; ⅔ of it is printed | ⅔ × ¾ | ½ m |
| ⅘ of a ₱500 budget is spent; ¼ of that went on transport | ¼ × ⅘ = ⅕; ⅕ of 500 | ₱100 |
| A recipe needs ⅔ of a half-kilo of rice | ⅔ × ½ | ⅓ kg |
A — ASSESSMENT
A. Formative — not graded, used to steer
| Day | Evidence gathered | What it tells you |
|---|---|---|
| 1 | The vote count before the fold, kept on the board | How widespread the misconception is in this class |
| 1 | Exit ticket — predict and justify ¾ × ½ | Whether the fold changed the belief or only the answer |
| 2 | Exit ticket — grid for ½ × ⅘ | Whether the model is a tool or a picture they copy |
| 3 | Exit ticket — ⅖ × ⅜ plus one sentence | Whether the rule is attached to meaning |
| 4 | Exit ticket — 2¼ × ⅔ | Whether mixed numbers were genuinely absorbed |
| 5 | Returned Day 1 tickets and the one-line reflection | Learners see their own movement across the week |
The single most useful check all week is asking a learner who has the right answer to shade it. Correct arithmetic with no model behind it is the failure mode that Term 2's division work will expose, and it is invisible in a mark book.
Also available all week: the Teacher Panel in game.html reports per-round
accuracy per learner in under a minute, without marking a single paper.
B. Summative — graded, per DO No. 015, s. 2026
Mathematics is a Key Stage 2 core learning area: Written Works 20% · Performance Tasks 50% · Examinations 30%.
| Instrument | Component | Where |
|---|---|---|
| Worksheet §A–C, and the Day 5 weekly check | Written Works | worksheet.html · assessment.md §6 |
| Summative Test 2 — end of Week 10, 20 items | Examinations (30% of the component) | assessment.md §4 |
| Term 1 Examination — end-of-term block, 40 items | Examinations (40% of the component) | assessment.md §5 |
| Group Activity 1 and 2 | Performance Tasks | rubrics in assessment.md §7 |
| The OFW Call Schedule (term task) | Performance Tasks | rubric in assessment.md §7 |
This week's content is examined in Summative Test 2, which covers Weeks 6–10; Summative Test 1 has already been sat at the end of Week 5.
Recording and transmutation: class-record.html, which carries the
SY 2026–2027 adjusted table and the SY 2027–2028 zero-based rule as a switch.
C. Success criteria for the week
The week has succeeded if a learner can, without a grid in front of them:
- Multiply any two fractions and give the answer in simplest form
- Sketch a model that justifies the answer when asked
- Explain why the product is usually smaller than both factors, and when it is not
- Find the word of in a problem and act on it
Criterion 3 is the one that predicts next week and the one that Term 2 depends on. A class that has 1 and 4 but not 3 will meet 3 ÷ ½ = 6 in Week 10 and refuse to believe it.
W — WAYS FORWARD
A. Remediation — for learners who could not justify their Day 1 or Day 2 exit ticket
Do not re-teach the rule. Re-teach the meaning, concretely:
- Back to paper folding, halves and quarters only, until the learner can state the product before opening the sheet.
- Pre-drawn grids so the learner shades rather than draws — the drawing is not the competency and it is where the effort was going.
- Ten minutes during Day 3 and Day 4 independent work, small group, while the rest work on.
B. Enrichment — for learners secure by Day 2
- The inverse task: "Find two fractions whose product is ⅜. Now find a different pair."
- "When is a × b exactly equal to a? Prove it." (When b = 1 — and the proof is worth having.)
- Three-factor products: ½ × ⅔ × ¾, and whether the order matters.
- Game Round 3 from Day 2 rather than Day 4.
C. Differentiation held all week
| Group | Adjustment | Same competency? |
|---|---|---|
| Below level | Halves, thirds and quarters only; pre-drawn grids; fraction strips on the desk | Yes — denominators reduced, reasoning identical |
| On level | As written | Yes |
| Above level | Inverse tasks, three-factor products, Round 3 from Day 2 | Yes — extended by depth |
| Language support | Of is introduced orally and contrasted with its everyday use before it is read | Yes |
| Additional needs | Enlarged grids; verbal exit ticket; peer scribe; pre-folded paper for learners with fine-motor difficulty | Yes |
D. Teacher's reflection
To be completed after Day 5.
| Learners meeting the week's intentions | ______ of ______ |
| Named for remediation | |
| How many voted "bigger" on Day 1? | ______ of ______. Compare with next year's class |
| Did the fold change minds, or only answers? | The Day 5 one-line reflections are the evidence |
| Which day ran over, and what was cut | |
| Did holding the rule back until Day 3 work? | Or did the class need it sooner to feel secure? |
| Who could compute but not shade? | Names. They are Term 2's problem if not caught now |
E. Next week
Week 8 takes up competency 9 — multi-step problems involving multiplication of fractions, possibly combined with addition or subtraction. It assumes this week's rule is automatic, because the difficulty moves to reading the problem. If §C criterion 1 is not met for most of the class, spend Day 1 of Week 8 on fluency instead and compress the multi-step work; Week 9 merges three competencies already, so the slack is not there — take it from Term 3.
Part of the E-turo MATATAG artifact set. Companion files:
lesson-plan.md (Day 1, Lesson Exemplar format) ·
syllabus.md · assessment.md ·
worksheet.html · slides.html ·
game.html · offline-activities.md ·
class-record.html