ILAW Lesson Plan — Mathematics 7
Term 1 · Week 7 · Number and Algebra · five sessions × 45 minutes
| Learning Area | Mathematics |
| Grade Level | Grade 7 |
| Term / Week | Term 1, Week 7 |
| CG source | Quarter 1, competency 7 (p. 52) |
| Week Title | Percent of What? — Percentage Increase and Decrease |
| 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. 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. 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. 52):
Content standard. The learners should have knowledge and understanding of the application of percentages.
Performance standard. By the end of the quarter, the learners are able to use percentages in different contexts.
Competency covered this week — quoted verbatim:
7. solve problems involving: a. percentage increase, and b. percentage decrease.
Assumed from Grade 6 (Quarter 2, competency 8): the relationships between percentages, fractions and decimals.
✅ 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 | Show that a 20% increase followed by a 20% decrease does not return to the start, and say why | 7a, 7b |
| 2 | Find a percentage increase two ways — add the part, or multiply by the multiplier | 7a |
| 3 | Find a percentage decrease two ways, and choose the faster one | 7b |
| 4 | Handle successive changes by multiplying multipliers, and express a change as a percentage | 7a, 7b |
| 5 | Solve percentage problems in real contexts and state what the percentage was taken of | 7a, 7b |
The multiplier is not introduced on Day 1. A class given ×1.2 on Monday will compute correctly all week without ever noticing that the second 20% is a different size from the first. Day 1 works entirely in pesos, longhand, so the two different amounts sit side by side on the board.
C. Key idea and vocabulary
A percentage is always a percentage of something.
| Term | Meaning used this week |
|---|---|
| Base | The amount the percentage is taken of. The single most important word this week |
| Percentage increase | The base plus a part of the base |
| Percentage decrease | The base minus a part of the base |
| Multiplier | The single number you multiply by — 1.2 for +20%, 0.8 for −20% |
| Successive change | Two changes one after the other, where the second base is the first answer |
The class sentence, repeated all week until it is automatic: "Percent of what? Change the what, and you change the amount."
D. Integration
| Strand | How it appears |
|---|---|
| EPP / TLE · Entrepreneurship | Mark-up, discount and the difference between them |
| Araling Panlipunan | Inflation described as a repeated percentage increase |
| EsP / GMRC | Day 5 examines a real "70% OFF" claim. Being able to check a price is treated as self-protection, not cynicism |
| English | Of as the word that names the base — and how advertising hides it |
| 21st-century skills | Numerical scepticism: checking a claim rather than accepting it |
L — LEARNING EXPERIENCES
Every session is 45 minutes and runs complete with chalk alone. Digital artifacts are listed where they help; none is required. No calculators this week — see §W.
Day 1 · Up 20%, down 20%
Full teaching script:
lesson-plan.md. Summary only here.
| Phase | Min | What happens |
|---|---|---|
| Activating prior knowledge | 5 | Find 10% of 200, 10% of 350, 20% of 200, 5% of 200. Quick, oral, and note who is dividing rather than reasoning. |
| Establishing purpose | 6 | Board: *"A shirt costs ₱100. The price goes up 20%. Then it goes down 20%. What does it cost now?"* Hands up for ₱100. Most of the class will say ₱100. Write the count on the board. |
| Developing understanding | 22 | Work it longhand, in two columns. Up: 20% of 100 = 20, so ₱120. Down: 20% of 120 = 24, so ₱96. Put 20 and 24 side by side and circle them. "Same percentage. Different amount. Why?" Repeat with ₱500 → ₱550 → ₱495, and ₱1 200 → ₱1 500 → ₱1 125. |
| Making generalisations | 7 | Land the sentence. The second percentage is taken of a bigger base, so it is a bigger amount, so you come out below where you started. Ask: "Does it work the other way round — down first, then up?" Try it: 100 → 80 → 96. Same answer. |
| Evaluating | 5 | Exit ticket: ₱500 up 10%, then down 10%. Predict first, then compute. |
Independent practice, without devices:
| Start | Change | Then | Result |
|---|---|---|---|
| ₱100 | up 20% | down 20% | ₱96 |
| ₱500 | up 10% | down 10% | ₱495 |
| ₱1 200 | up 25% | down 25% | ₱1 125 |
| ₱800 | down 15% | up 15% | ₱782 |
| ₱240 | up 50% | down 50% | ₱180 |
Row 4 reverses the order and still loses. Row 5 loses a quarter of its value from two 50% moves. Both are worth putting on the board at the end — the effect is not a rounding quirk, it grows with the size of the percentage.
Day 2 · Percentage increase, two ways
| Phase | Min | What happens |
|---|---|---|
| Recall | 5 | Yesterday's five rows, from memory where possible. |
| Purpose | 5 | Board: "₱250 increased by 12%." "Two ways to do this. One is shorter." |
| Developing | 24 | Method A — find the part, then add. 10% of 250 = 25; 1% = 2.5; so 12% = 25 + 5 = 30. Answer ₱280. Method B — the multiplier. An increase of 12% leaves 112% of the original, and 112% = 1.12. So 250 × 1.12 = ₱280. Practise both on four more, then ask which they prefer and why. |
| Generalising | 6 | Build the rule: +p% means × (1 + p/100). Check it against Day 1: +20% is ×1.2. |
| Evaluating | 5 | Exit ticket: ₱800 increased by 15%, by either method, showing the working. |
Worked set (teacher's copy):
| Problem | Method A | Method B | Answer |
|---|---|---|---|
| ₱250 + 12% | 25 + 5 = 30 | 250 × 1.12 | ₱280 |
| ₱800 + 15% | 80 + 40 = 120 | 800 × 1.15 | ₱920 |
| ₱60 + 5% | 3 | 60 × 1.05 | ₱63 |
| ₱1 500 + 8% | 120 | 1500 × 1.08 | ₱1 620 |
| ₱45 + 20% | 9 | 45 × 1.2 | ₱54 |
Digital support: slides.html slides 9–11.
game.html Round 1 is single increases and decreases.
Day 3 · Percentage decrease, and choosing a method
| Phase | Min | What happens |
|---|---|---|
| Recall | 5 | Three increases, timed. |
| Purpose | 5 | Board: "₱250 decreased by 12%." Same two methods, mirrored. |
| Developing | 23 | A: 12% of 250 = 30, so 250 − 30 = ₱220. B: a 12% decrease leaves 88%, so ×0.88 → ₱220. Then four more. Then the discrimination task: which method is faster here? For 25% off, halving twice beats any multiplier. For 17% off, the multiplier wins. Learners must justify the choice, not just get the answer. |
| Generalising | 7 | −p% means × (1 − p/100). Put the two rules side by side. Then return to Day 1 with the multipliers: 1.2 × 0.8 = 0.96 — and 0.96 is 96%, which is exactly the ₱96. The whole of Day 1 in one line. |
| Evaluating | 5 | Exit ticket: ₱1 200 decreased by 35%, with the method named and justified. |
Worked set (teacher's copy):
| Problem | Multiplier | Answer | Faster method |
|---|---|---|---|
| ₱250 − 12% | 0.88 | ₱220 | multiplier |
| ₱800 − 25% | 0.75 | ₱600 | halve, halve, add — mental |
| ₱90 − 10% | 0.90 | ₱81 | find 10%, subtract |
| ₱1 200 − 35% | 0.65 | ₱780 | multiplier |
| ₱64 − 50% | 0.50 | ₱32 | halve |
Day 4 · Successive changes, and naming the change
| Phase | Min | What happens |
|---|---|---|
| Recall | 5 | Two multipliers each way, oral. |
| Purpose | 5 | Board: "50% OFF. Then 20% off the sale price. Is that 70% off?" Take a vote. |
| Developing | 23 | It is not. 0.5 × 0.8 = 0.4, so you pay 40% — a 60% discount. Work it in pesos first (₱1 000 → ₱500 → ₱400) then by multipliers. Three more successive problems. Then reverse the question: express a change as a percentage. From 80 to 100 is an increase of 20 on a base of 80 → 25%. From 100 to 80 is a decrease of 20 on a base of 100 → 20%. Same two numbers, two different percentages. |
| Generalising | 7 | Successive changes multiply; they do not add. And the percentage change depends on which end you start from, because the base changes. |
| Evaluating | 5 | Exit ticket: a price rises from ₱40 to ₱50. What percentage increase? Then it falls from ₱50 back to ₱40 — what percentage decrease? |
Worked set (teacher's copy):
| Problem | Multipliers | Result | Single equivalent |
|---|---|---|---|
| ₱1 000, 50% off then 20% off | 0.5 × 0.8 = 0.40 | ₱400 | 60% off |
| ₱450, 20% off then 10% off | 0.8 × 0.9 = 0.72 | ₱324 | 28% off |
| ₱200, up 10% then up 10% | 1.1 × 1.1 = 1.21 | ₱242 | up 21% |
| ₱600, up 30% then down 30% | 1.3 × 0.7 = 0.91 | ₱546 | down 9% |
| Change | Base | Percentage |
|---|---|---|
| 80 → 100 | 80 | increase of 25% |
| 100 → 80 | 100 | decrease of 20% |
| 40 → 50 | 40 | increase of 25% |
| 50 → 40 | 50 | decrease of 20% |
Day 5 · Real prices, and the weekly check
| Phase | Min | What happens |
|---|---|---|
| Recall | 5 | The class sentence, then two multipliers. |
| Purpose | 4 | Bring in real store flyers, receipts or photographed price tags. "Find one claim on this paper and check it." |
| Developing | 16 | Four contextual problems in pairs — a mark-up, a discount, a wage rise, a price after two changes. Every answer must be labelled with what the percentage was of. Then the flyer task: learners find a real advertised discount and verify the arithmetic. |
| 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 ______." |
Contextual problems used (answers for the teacher):
| Problem | Working | Answer |
|---|---|---|
| A ₱180 item is marked up 25% | 180 × 1.25 | ₱225 |
| A ₱1 500 phone has 30% off | 1500 × 0.70 | ₱1 050 |
| A ₱610 daily wage rises 8% | 610 × 1.08 | ₱658.80 |
| A ₱2 000 fare rises 10%, then falls 5% | 2000 × 1.1 × 0.95 | ₱2 090 |
A — ASSESSMENT
A. Formative — not graded, used to steer
| Day | Evidence gathered | What it tells you |
|---|---|---|
| 1 | The vote count for ₱100, kept on the board | How widespread the additive assumption is in this class |
| 1 | Exit ticket — ₱500 up 10%, down 10% | Whether the base idea transferred to a new number |
| 2 | Exit ticket — ₱800 + 15%, working shown | Which method the learner reaches for, and whether they can do either |
| 3 | Exit ticket — ₱1 200 − 35%, method justified | Whether method choice is reasoned or habitual |
| 4 | Exit ticket — 40 → 50 and 50 → 40 | The single best diagnostic of the week. A learner who gives 25% both times has not understood the base |
| 5 | The flyer check | Whether the skill survives contact with a real, badly-worded advertisement |
The single most useful check all week is asking "percent of what?" of any answer, right or wrong. It takes five seconds and it is the whole competency.
Also available all week: the Teacher Panel in game.html reports per-round
accuracy per learner in under a minute.
B. Summative — graded, per DO No. 015, s. 2026
Mathematics is a Key Stage 3 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 Sari-Sari Store Books (term task) | Performance Tasks | rubric in assessment.md §7 |
This week's content is examined in Summative Test 2, covering Weeks 6–10; Summative Test 1 was sat at the end of Week 5.
Recording and transmutation: class-record.html.
C. Success criteria for the week
The week has succeeded if a learner can:
- Increase or decrease any amount by any percentage, by a method they can justify
- Say, for any percentage in a problem, what it is a percentage of
- Handle two successive changes by multiplying, and explain why they do not add
- Express a change as a percentage, and get a different answer depending on the direction
Criterion 4 is the one that predicts Week 8. Discount, commission and simple interest all turn on identifying the base correctly, and a learner who is loose about it will get plausible wrong answers all term.
W — WAYS FORWARD
A. Remediation — for learners who could not justify the Day 1 exit ticket
Do not re-teach the multiplier. Re-teach 10% and 1%, concretely:
- 10% is one tenth — move the digits. 1% is one hundredth. Every other percentage is built from those two by adding and halving. A learner who owns 10% and 1% can find 17.5% with no formula at all.
- Work only in round pesos — 100, 200, 500 — until the of is secure.
- 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
- "Find a pair of successive percentage changes that do return exactly to the start." (An increase of p% is undone by a decrease of 100p/(100+p)% — up 25% then down 20%.)
- "Why does up 30% then down 30% lose 9%, whatever the starting amount?" (1.3 × 0.7 = 0.91, and the starting amount cancels out.)
- Compound interest as repeated multiplication, one year at a time — Grade 10's content arriving as a natural extension rather than a new topic.
- Game Round 3 from Day 2.
C. Differentiation held all week
| Group | Adjustment | Same competency? |
|---|---|---|
| Below level | Round amounts and friendly percentages — 10%, 20%, 50% only. 10%-and-1% building blocks on the desk | Yes — arithmetic load reduced, reasoning identical |
| On level | As written | Yes |
| Above level | The inverse task, the 0.91 proof, compound interest, Round 3 from Day 2 | Yes — extended by depth |
| Language support | Of is named as the word that identifies the base, and contrasted with its everyday use | Yes |
| Additional needs | Enlarged number lines; verbal exit ticket; peer scribe; a printed 10%/1% reference strip | Yes |
No calculators this week, and this is a deliberate cost. A calculator turns every problem in this week into "type 250 × 1.12", which is precisely the step that hides the base. From Week 8, when the arithmetic gets uglier and the concept is settled, bring them back.
D. Teacher's reflection
To be completed after Day 5.
| Learners meeting the week's intentions | ______ of ______ |
| How many said ₱100 on Day 1? | ______ of ______ |
| Named for remediation | |
| Did anyone spot that down-then-up gives the same answer? | Names. That is the multiplier idea arriving unprompted |
| Which day ran over, and what was cut | |
| Did the flyer task work, or were the advertisements too vague to check? | If vague, collect better ones next cycle — that difficulty is itself worth discussing |
| Who gave 25% both ways on the Day 4 ticket? | Those learners have the arithmetic and not the idea |
E. Next week
Week 8 pairs competencies 8 and 9 — money problems with percentages (discount, commission, sales tax, simple interest) and creating a financial plan. Every one of those is this week's skill applied to a named base, so if §C criterion 2 is not met for most of the class, spend Day 1 of Week 8 on bases before touching commission. Week 9's rate work then depends on Week 8 rather than on this week.
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