Weekly Lesson Plan (ILAW) — Mathematics 10
Term 1 · Week 7 · Number and Algebra
| Learning Area | Mathematics |
| Grade Level | Grade 10 |
| Term / Week | Term 1, Week 7 |
| CG source | Quarter 1, competencies 9–10 (p. 65) |
| Format | ILAW — the template prescribed by DO No. 009, s. 2026 for SY 2026–2027 |
| Duration | 5 sessions × 45 minutes |
ILAW = Intentions · Learning Experiences · Assessment · Ways Forward. It replaces the DLL and the DLP from SY 2026–2027. For Day 1 at full teaching depth in the MATATAG Lesson Exemplar format, see
lesson-plan.md.
⚠️ The ILAW structure below is this repository's reading of the four named parts. The official template was not obtainable; see
source-catalogue.md. The content is verified against the CG. The layout is not.
I — INTENTIONS
Competencies, quoted verbatim from the CG
9. solve quadratic inequalities in two variables.
10. determine the region of solutions of a linear or quadratic inequality in two variables.
What has to change in the learner's head this week
Everything a Grade 10 learner has ever solved has had an answer you could write down. An equation gives a number. An inequality in one variable gives an interval — still writable, still markable on a line with a pen.
This week the answer is a region of the plane. It contains infinitely many points, no list of them is possible, and the only way to communicate it is to draw it. That is not a harder version of last week; it is a different kind of object.
And the method that gets you there is not algebra. It is two steps:
1. Draw the BOUNDARY. Replace the inequality sign with = and graph it.
2. TEST A POINT. Any point not on the boundary. Substitute.
True → shade that side.
False → shade the other side.
Step 2 is the whole week. Learners will want to decide the side by looking at the sign — "it says greater than, so shade above". That works often enough to feel like a rule and fails the moment the inequality is not written with y alone on the left.
Weekly objectives
By Friday, at least 80% of learners can:
- Graph the boundary of a linear or quadratic inequality in two variables, using a solid line for ≤ and ≥ and a broken line for < and >
- Choose a test point that is not on the boundary, substitute it, and shade accordingly
- Decide whether a given point is a solution, without graphing anything
- Recognise that two differently written inequalities can describe the same region, and check by testing rather than by comparing their signs
Objective 4 is the reason this week exists. A learner who can only shade correctly when the inequality arrives pre-arranged as y > … has learnt a layout, not a method.
21st-century skills and values
| Critical thinking | Refusing a shading decision until a point has actually been tested |
| Communication | A shaded graph is the answer — it must be readable by someone else |
| Rules and fairness (EsP) | Real rules define regions: setback distances, coverage areas, curfew zones. Whether you are inside one is not a matter of opinion |
II — LEARNING EXPERIENCES
Day 1 · The two that look different — 45 min
Full script in lesson-plan.md.
| Phase | Min | What happens |
|---|---|---|
| Prior knowledge | 5 | Solve x² − 4 > 0 on a number line. Answer: x < −2 or x > 2. Two rays, drawn |
| Purpose | 6 | Two inequalities on the board: y > x² − 4 and x² − y < 4. "Are these the same or different?" Take a vote. Do not settle it |
| Explicitation | 7 | The boundary y = x² − 4. Vertex (0, −4), zeros at −2 and 2. Broken curve, because both signs are strict |
| Worked example | 5 | Test (0, 0) in y > x² − 4: is 0 > −4? Yes. Shade the side containing the origin |
| Guided | 5 | Test (0, 0) in x² − y < 4: is 0 − 0 < 4? Yes. Same side. The two are one inequality |
| Independent | 5 | Test (0, −10) in both. False in both. Confirms the other side is excluded |
| Generalisation | 7 | Write the two-step routine. Say the sentence |
| Exit ticket | 5 | One inequality, one test point, one shaded sketch |
The class sentence, introduced on Day 1 and used all week:
"Don't decide which side. Test a point."
Day 2 · Linear inequalities and the broken line — 45 min
| Phase | Min | What happens |
|---|---|---|
| Recall | 5 | The two-step routine, from memory, before anything is written |
| Explicitation | 10 | y ≤ 2x + 1. Boundary y = 2x + 1, solid, because ≤ includes the line itself. Test (0, 0): is 0 ≤ 1? Yes — shade below |
| Contrast | 8 | y < 2x + 1. Identical shading, broken line. The only difference is whether the boundary points themselves are solutions |
| Guided | 10 | Three more: x + y ≥ 6, y > −x, 2x − 3y ≤ 12. Each with a named test point. y > −x cannot be tested at the origin — the origin is on it. Use (1, 1) |
| Independent | 7 | Two from the worksheet, Section A |
| Close | 5 | When can you NOT use the origin as your test point? When it is on the boundary |
The origin trap is worth its eight minutes. (0, 0) is the easiest test point and works most of the time, so learners stop checking whether it is available. y > −x passes through it. A learner who substitutes anyway gets 0 > 0, which is false, and confidently shades the wrong half — with no error visible in their working.
Day 3 · Quadratic boundaries — 45 min
| Phase | Min | What happens |
|---|---|---|
| Recall | 5 | The origin trap. One example where it is unusable |
| Explicitation | 12 | y ≥ x² − 2x − 3. Factor to find the zeros: (x − 3)(x + 1), so −1 and 3. Vertex at x = 1, y = −4. Solid curve |
| Test | 5 | (0, 0): is 0 ≥ −3? Yes. Shade inside the parabola |
| Contrast | 8 | y ≤ x² − 2x − 3, same curve, the other region. Both drawn on the board at once |
| Guided | 8 | y < −x² + 4 — a downward parabola. Test (0, 0): 0 < 4, true. Shade inside. Note that "inside" now means below |
| Independent | 7 | Worksheet Section B |
"Inside" is not a direction. For an upward parabola the region containing the vertex's open side is above; for a downward one it is below. Learners who have quietly translated "test the origin, it worked" into "shade inside" meet the counter-example on Day 3, not in the examination.
Day 4 · Is this point a solution? — 45 min
| Phase | Min | What happens |
|---|---|---|
| Recall | 5 | Two-step routine; solid versus broken |
| Explicitation | 8 | You do not need a graph to answer is (4, 5) a solution of y > x² − 12? Substitute: 5 > 16 − 12 = 4. True |
| The boundary case | 10 | Is (4, 4) a solution of y > x² − 12? 4 > 4 is false — it is on the boundary, and > excludes it. Is it a solution of y ≥ x² − 12? Yes |
| Guided | 10 | A table of five points against one inequality; each marked in, out, or on |
| Independent | 7 | Worksheet Section C |
| Close | 5 | Which points does a broken boundary leave out? Exactly the ones on it |
Day 5 · One region, many ways to write it — 45 min
| Phase | Min | What happens |
|---|---|---|
| Opening | 8 | Three inequalities on the board that describe one region. Teams test points to prove it |
| Group | 20 | Three Ways, One Region (offline-activities.md G-2) — sixteen cards, four regions × four representations |
| Weekly check | 12 | 10 items, assessment.md §6 |
| Close | 5 | Plant Week 8: "Next week the boundary is a V, not a line or a parabola. Same two steps." |
Resources
Required — no cost. Chalk and board; squared paper (Days 2–4); pencil and ruler. Squared paper is genuinely needed this week — freehand parabolas cannot be shaded honestly.
Explicitly NOT used: graphing calculators or graphing software. A tool that shades the region for you removes the only decision the week is about.
Optional. slides.html · game.html ·
worksheet.html · wall-chart.html ·
class-record.html
Contingency — no electricity, no devices, no squared paper
Days 1, 4 and 5 need no paper at all: the board carries the graph and learners answer orally, substituting aloud. Only Days 2 and 3 truly want squares, and a ruled exercise book turned sideways gives a usable grid. Individual Activity I-1 replaces the digital game exactly — it is the same judgement with no computing.
III — ASSESSMENT
| When | What | Component | Where |
|---|---|---|---|
| Day 1 | Exit ticket — one inequality graphed with its test point marked | Written Works | lesson-plan.md §IV |
| Days 2–4 | Worksheet Sections A–D | Written Works | worksheet.html |
| Day 3 | Observation during guided practice — is a point being tested, or a side being guessed? | Formative, not recorded | — |
| Day 5 | Group activity G-2, 12-point rubric | Performance Tasks | offline-activities.md |
| Day 5 | Weekly check, 10 items | Written Works | assessment.md §6 |
The single most informative thing to look at all week is whether a test point appears anywhere in the learner's working. A correct shading with no test point marked is not evidence of anything — half of all one-inequality questions can be shaded correctly by guessing.
Require the test point to be written down and circled on every graphed answer. Mark it. A learner who shades correctly without one has not yet shown the competency.
IV — WAYS FORWARD
| What you see | What it means | What to do |
|---|---|---|
| Correct shading, no test point written | Cannot be distinguished from a lucky guess | Re-ask with the inequality written as x² − y < 4 rather than y > x² − 4. If the shading survives, the method is real |
| Shades by the sign — "> means above" | The commonest outcome, and it passes most textbook questions | Day 2's rearranged forms, then I-2. Never mark it wrong when the answer is right; mark the missing test point |
| Solid and broken lines interchanged | Knows the region, not the boundary convention | Two minutes: which points does < leave out? Fix immediately — it costs a mark on every graph |
| Tests the origin when the origin is on the boundary | Has automated the easy case | I-3, where three of the six boundaries pass through the origin |
| Cannot graph the parabola at all | Week 7 is not the problem — Grade 9 Quarter 3 is | Small group on vertex and zeros only. Shade nothing until the curve is right |
| Secure by Wednesday | G-2 Round 4: write an inequality whose region is a given shaded picture. That is the inverse task and it is genuinely hard |
What this week feeds
Week 8 — absolute value inequalities. The boundary becomes a V and the two-step routine is unchanged; say so explicitly on Friday and Week 8 opens with a method already in hand.
Week 21 — problems involving geometric figures on the Cartesian plane. Deciding whether a point lies inside a circle is this week's test point wearing a different hat.
Grade 11 and beyond — every linear programming problem in Senior High School is this routine run several times over. Learners who leave Grade 10 shading by the sign will meet four constraints at once and have no way to check themselves.
Teacher's reflection
| Learners meeting the objectives | ______ of ______ |
| How many wrote a test point without being told to? | ______ of ______ |
| Did anyone use the origin when it was on the boundary? | |
| Did the vote on Day 1 change after the two were tested? | |
| Which day ran over? |
Part of the E-turo MATATAG artifact set. Companion files:
syllabus.md · lesson-plan.md ·
assessment.md · offline-activities.md ·
worksheet.html · class-record.html