ILAW Lesson Plan — Mathematics 9
Term 1 · Week 7 · Number and Algebra · five sessions × 45 minutes
| Learning Area | Mathematics |
| Grade Level | Grade 9 |
| Term / Week | Term 1, Week 7 |
| CG source | Quarter 1, competency 8 (p. 60) |
| Week Title | Twelve Pesos Per What? — Slope as a Rate of Change |
| 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 filing. Its companion
lesson-plan.mdis Day 1 only, at teaching-script depth.
⚠️ 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. The four section names are consistently reported; sub-fields may differ by division. See
source-catalogue.md§8.
I — INTENTIONS
A. Curriculum anchor
Quoted from the MATATAG Mathematics CG (DepEd, August 2023, p. 60):
Content standard. The learners demonstrate knowledge and understanding of graphs of linear functions, and the identification of domain and range, slope, intercepts, and zeros.
Performance standard. By the end of the quarter, the learners are able to graph a linear function and identify the domain and range, intercepts, slope, and zeros.
Competency covered this week — quoted verbatim:
8. determine the slopes (as rate of change) and the zeros of linear functions represented in: a. graphs, b. equations, and c. tables of values.
The CG writes "(as rate of change)" into the competency itself. That parenthesis is not decoration — it is the difference between a learner who can compute rise over run and one who knows what the answer is. This week is built around it.
✅ 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… | Representation |
|---|---|---|
| 1 | State a slope with its unit and say what the zero means in context — including when it means nothing | context |
| 2 | Find the slope from a graph, and read its sign correctly | (a) graphs |
| 3 | Find the slope and the zero from an equation | (b) equations |
| 4 | Find the slope and the zero from a table of values | (c) tables |
| 5 | Move between all three representations of the same function | a, b, c |
Day 1 is not about computation. It is about the sentence "twelve pesos per kilometre" — and specifically about the words after per. A class that starts at rise-over-run on Monday will produce correct slopes with no units all year and will not be able to interpret one in Grade 10.
C. Key idea and vocabulary
A slope is a rate. It always has a unit, and the unit tells you what it means.
| Term | Meaning used this week |
|---|---|
| Slope | How much y changes for each one of x. Written as y-units per x-unit |
| Rate of change | The same thing, said in words |
| Zero of a function | The x-value where y = 0. Not the number zero, and not the y-intercept |
| y-intercept | Where the line crosses the y-axis — the value when x = 0 |
| Positive / negative slope | Rising / falling as x increases. A steep fall is a large negative rate |
The class sentence, repeated all week: "Twelve pesos per what? Say the unit, or you have not said the slope."
D. Integration
| Strand | How it appears |
|---|---|
| Araling Panlipunan | Fare structures and how they are set |
| EPP / TLE | Wage per hour; material used per unit produced |
| Science | Litres per minute, degrees per hour — rate is the same idea in both subjects |
| English | The preposition per, and what it does grammatically |
| 21st-century skills | Reading a number in context rather than in isolation |
L — LEARNING EXPERIENCES
Every session is 45 minutes and runs complete with chalk and squared paper. No calculators this week — every number is chosen to be reasoned.
Day 1 · Twelve pesos per what?
Full teaching script:
lesson-plan.md. Summary only here.
| Phase | Min | What happens |
|---|---|---|
| Activating prior knowledge | 5 | Grade 7 rates, oral: 240 km in 3 hours; ₱180 for 3 kg; 12 km per litre. Each answer must be given with its unit. |
| Establishing purpose | 6 | Board: "A tricycle charges ₱30 to start, then ₱12 per kilometre." Build the table together for 0, 1, 2, 5 km. Then: "Which number in that table is the slope?" |
| Developing understanding | 22 | Write y = 12x + 30. The 12 is the slope; its unit is pesos per kilometre. The 30 is the y-intercept; its unit is pesos. Then the zero: 12x + 30 = 0 gives x = −2.5 km, which is meaningless — you cannot travel minus two and a half kilometres. Then the second context: a drum holds 200 L and drains at 25 L per minute, so y = 200 − 25x, slope −25 L per minute, and the zero is x = 8 minutes — the drum is empty. Meaningful. |
| Making generalisations | 7 | Land the sentence. A slope has a unit. A zero has a meaning — or it has none, and saying so is a correct answer. |
| Evaluating | 5 | Exit ticket: a candle 24 cm tall burns 3 cm per hour. Slope with unit, and the zero with its meaning. |
Independent practice, without devices:
| Context | Equation | Slope (with unit) | Zero | Meaning of the zero |
|---|---|---|---|---|
| Tricycle: ₱30 + ₱12/km | y = 12x + 30 | 12 pesos per km | −2.5 | none — negative distance |
| Drum: 200 L, drains 25 L/min | y = 200 − 25x | −25 litres per minute | 8 | empty after 8 minutes |
| Candle: 24 cm, burns 3 cm/h | y = 24 − 3x | −3 cm per hour | 8 | gone after 8 hours |
| Load: ₱150, ₱2.50 per minute | y = 150 − 2.5x | −2.50 pesos per minute | 60 | used up after 60 minutes |
| Wage: ₱80 per hour | y = 80x | 80 pesos per hour | 0 | no hours worked, no pay |
The first row is the one to dwell on. Its zero is a perfectly good number and a nonsense answer. Learners trained to always "interpret the zero" will invent a meaning for −2.5 km. The correct response is "the zero of this function is −2.5, and it has no meaning here."
Day 2 · Slope from a graph
| Phase | Min | What happens |
|---|---|---|
| Recall | 5 | Yesterday's five slopes, with units, from memory. |
| Purpose | 5 | A line drawn on squared paper through (0, 1) and (4, 9). "No equation. No table. Find the rate." |
| Developing | 23 | Rise over run, counted on the grid: up 8, across 4, so 2. Then the sign: a line through (0, 6) and (3, 0) falls — rise is −6, run is 3, slope −2. Then a gentle one, (1, 2) to (5, 4): slope ½. Then a horizontal line: slope 0. Then a vertical line: undefined, and why — the run is zero and you cannot divide by it. |
| Generalising | 7 | Steepness is the size of the slope; direction is its sign. A slope of −5 is steeper than a slope of +2. Reading the zero off a graph is easier than any other representation: it is where the line crosses the x-axis. |
| Evaluating | 5 | Exit ticket: from a given graph, slope and zero. |
Worked set (teacher's copy):
| Through | Rise | Run | Slope | Zero (x-intercept) |
|---|---|---|---|---|
| (0, 1) and (4, 9) | 8 | 4 | 2 | −0.5 |
| (0, 6) and (3, 0) | −6 | 3 | −2 | 3 |
| (1, 2) and (5, 4) | 2 | 4 | ½ | −3 |
| (2, 7) and (6, 7) | 0 | 4 | 0 | none — the line never meets the x-axis |
| (3, 1) and (3, 8) | 7 | 0 | undefined | 3 — but this is not a function |
The last row is worth the two minutes it costs. A vertical line has no slope and is not a function — it fails the definition the class met in Week 5. Both facts are the same fact.
Day 3 · Slope from an equation
| Phase | Min | What happens |
|---|---|---|
| Recall | 5 | Three slopes from graphs, timed. |
| Purpose | 5 | Board: y = 3x − 5. "Where is the slope? How do you know?" |
| Developing | 23 | y = mx + b: m is the slope, b the y-intercept. Read off four. Then the ones that are not in that form: y = 7 − 4x (slope −4, not 7 — the order does not matter, the coefficient of x does) and 2y = 6x + 10 (divide first: y = 3x + 5). Then zeros: set y = 0 and solve. |
| Generalising | 7 | The slope is the coefficient of x once y is alone. The zero is where the line crosses the x-axis, found by putting y = 0 — and the y-intercept is found by putting x = 0. The two are opposite substitutions, and confusing them is the commonest error of the week. |
| Evaluating | 5 | Exit ticket: for y = −2x + 8, give the slope, the y-intercept and the zero. |
Worked set (teacher's copy):
| Equation | Slope | y-intercept | Zero |
|---|---|---|---|
| y = 3x − 5 | 3 | −5 | 5/3 |
| y = −2x + 8 | −2 | 8 | 4 |
| y = ½x + 3 | ½ | 3 | −6 |
| y = 7 − 4x | −4 | 7 | 7/4 |
| 2y = 6x + 10 | 3 | 5 | −5/3 |
Day 4 · Slope from a table of values
| Phase | Min | What happens |
|---|---|---|
| Recall | 5 | Three slopes from equations, timed. |
| Purpose | 5 | A table with x = 0, 1, 2, 3 and y = 5, 8, 11, 14. "Is this linear? How can you tell?" |
| Developing | 23 | Constant difference. y goes up 3 each time x goes up 1, so the slope is 3. Then a table stepping by 2: x = 0, 2, 4, 6 and y = 20, 14, 8, 2 — y falls 6 for every 2 of x, so the slope is −3, not −6. This is where the week's errors concentrate. Then a constant table (slope 0), and one stepping by 5. Then build the equation from the table and find the zero. |
| Generalising | 7 | Slope from a table is change in y ÷ change in x — the same rise over run, without a picture. If the ratio is not constant, the relationship is not linear. |
| Evaluating | 5 | Exit ticket: from a table stepping by 5, give the slope and the zero. |
Worked set (teacher's copy):
| Table | Δy | Δx | Slope | Equation | Zero |
|---|---|---|---|---|---|
| x 0,1,2,3 → y 5,8,11,14 | 3 | 1 | 3 | y = 3x + 5 | −5/3 |
| x 0,2,4,6 → y 20,14,8,2 | −6 | 2 | −3 | y = −3x + 20 | 20/3 |
| x 1,3,5,7 → y 4,4,4,4 | 0 | 2 | 0 | y = 4 | none |
| x 0,5,10,15 → y 100,75,50,25 | −25 | 5 | −5 | y = −5x + 100 | 20 |
Day 5 · One function, three ways, and the weekly check
| Phase | Min | What happens |
|---|---|---|
| Recall | 5 | The class sentence, then one slope from each representation. |
| Purpose | 4 | Board: a graph, an equation and a table — all of the same function, unlabelled. "Prove they are the same." |
| Developing | 16 | Learners match and justify. Then the reverse: given one representation, produce the other two. Four rounds, each with the slope stated with its unit and the zero stated with its meaning. |
| Weekly check | 15 | Ten items — assessment.md §6. Written Works. |
| Closing | 5 | Day 1 exit tickets returned. One line: "On Monday I thought ______. Now I know ______." |
A — ASSESSMENT
A. Formative — not graded, used to steer
| Day | Evidence gathered | What it tells you |
|---|---|---|
| 1 | Whether the slope was given with a unit, unprompted | The single best predictor of the week |
| 1 | Exit ticket — the candle's zero and its meaning | Whether "interpret the zero" has become a reflex or a judgement |
| 2 | Exit ticket — slope and zero from a graph | Whether the sign is read or guessed |
| 3 | Exit ticket — y = −2x + 8, all three quantities | Whether y-intercept and zero are being confused |
| 4 | Exit ticket — a table stepping by 5 | Whether Δx is being divided by, or ignored |
| 5 | The matching task | Whether the three representations are one idea or three topics |
The single most useful check all week is asking "per what?" of any slope. It takes five seconds and it separates a learner who computed from one who understands.
Also available all week: the Teacher Panel in game.html.
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 | Examinations (30%) | assessment.md §4 |
| Term 1 Examination — 40 items | Examinations (40%) | assessment.md §5 |
| Group Activity 1 and 2 | Performance Tasks | rubrics in assessment.md §7 |
| What Does the Number Mean? (term task) | Performance Tasks | rubric in assessment.md §7 |
Recording and transmutation: class-record.html.
C. Success criteria for the week
- Find the slope of a linear function from a graph, an equation and a table
- State that slope with its unit when there is a context
- Find the zero, and say what it means — or that it means nothing
- Not confuse the zero with the y-intercept
Criterion 4 is the one that predicts Week 8 and Quarter 3. A learner who swaps them will graph every line through the wrong point and will misread every parabola's intercepts in Term 2.
W — WAYS FORWARD
A. Remediation — for learners giving slopes without units after Day 2
Do not re-teach rise over run. Re-teach per, concretely:
- Only contexts, no bare graphs, for one session: fares, wages, fuel. Every answer must be a sentence — "eighty pesos for every one hour" — before it is a number.
- Tables with Δx = 1 only, so the division is invisible and the meaning is not.
- Ten minutes during Day 3 and Day 4 independent work, small group.
B. Enrichment — for learners secure by Day 2
- "Two lines have slopes 3 and −⅓. Draw them. What do you notice?" (Perpendicular — Quarter 2 competency 1 arriving early, and by discovery.)
- "A function has slope 0. What is its zero?" (Either none, or every x — depending on whether it is y = 4 or y = 0. A genuinely interesting edge case.)
- "Find a real relationship whose slope changes." (It is not linear — the opening of Quarter 3.)
- Game Round 3 from Day 2.
C. Differentiation held all week
| Group | Adjustment | Same competency? |
|---|---|---|
| Below level | Whole-number grid steps only; Δx = 1 tables; contexts limited to money and time | Yes — arithmetic reduced, interpretation identical |
| On level | As written | Yes |
| Above level | The perpendicular-slopes discovery, the slope-0 edge case, Round 3 from Day 2 | Yes — extended by depth |
| Language support | Per is taught as the word that names the second unit, before any computation | Yes |
| Additional needs | Pre-ruled axes; enlarged grids; verbal exit ticket; peer scribe | Yes |
D. Teacher's reflection
| Learners meeting the week's intentions | ______ of ______ |
| How many gave a slope without a unit on Day 1? | ______ of ______ |
| Named for remediation | |
| Did anyone invent a meaning for the −2.5 km zero? | That is the trained reflex, and it is worth naming to the class |
| Which day ran over, and what was cut | |
| Who is still confusing the zero with the y-intercept by Friday? | Names. Quarter 3 will punish it |
E. Next week
Week 8 carries three competencies — graphing a linear function with domain, range, intercepts and slope; representing real-life relationships in different forms; and solving problems. It is the heaviest week in Term 1 and it assumes all four of §C. If criterion 4 is not met for most of the class, spend Day 1 of Week 8 separating the zero from the y-intercept and compress the problem-solving; the syllabus flags Week 27, not Week 8, as the place with slack.
Part of the E-turo MATATAG artifact set. Companion files:
lesson-plan.md · syllabus.md ·
assessment.md · worksheet.html ·
slides.html · game.html ·
offline-activities.md · class-record.html