Lesson Exemplar — Mathematics 9

Term 1 · Week 7 · Day 1 · Number and Algebra

This is one day. For the whole of Week 7 in the format DepEd prescribes for filing, see lesson-plan-ilaw.md. This document is the teaching script for Monday.

I. CURRICULUM CONTENT, STANDARDS, AND LESSON COMPETENCIES

A. Content Standards

Quoted from the MATATAG Mathematics Curriculum Guide (DepEd, August 2023, p. 60), Grade 9 Quarter 1, content standard 4:

The learners demonstrate knowledge and understanding of graphs of linear functions, and the identification of domain and range, slope, intercepts, and zeros.

B. Performance Standards

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. (NA)

C. Learning Competencies and Objectives

Competency — CG Quarter 1, number 8, 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.

Objectives for this session. By the end of 45 minutes, at least 80% of learners can:

1. Build a table of values from a stated rate, and write the matching equation
2. Identify the slope in the equation and state its unit
3. Find the zero of the function and say what it means in the context
4. Recognise a case where the zero is a valid number with no meaning, and say so

Objective 4 is the lesson. Objectives 1–3 are the machinery. A learner trained to "interpret the zero" without judgement will explain what minus two and a half kilometres means, and that habit is worse than not interpreting at all.

D. Content

A slope is a rate. It always has a unit, and the unit tells you what it means.

The class sentence, introduced at §D: "Twelve pesos per what? Say the unit, or you have not said the slope."

E. Integration

II. LEARNING RESOURCES

Required — no cost. Chalk and the board; paper and pencil. Squared paper helps but is not needed today — Day 1 works in tables and words, not graphs.

Explicitly NOT used today: calculators. Every number is chosen to be reasoned.

Optional. slides.html slides 1–9 · game.html Round 1 · worksheet.html · wall-chart.html

III. TEACHING AND LEARNING PROCEDURE

A. Activating Prior Knowledge — 5 minutes (0:00 → 0:05)

Three Grade 7 rates, oral, round the room. Every answer must carry its unit.

If a learner answers "80", ask "eighty what?" and wait. Do this every time today.

B. Establishing Lesson Purpose — 6 minutes (0:05 → 0:11)

Write on the board:

A tricycle charges ₱30 to start,
then ₱12 for every kilometre.

Build the table with the class, aloud:

Then ask:

"Which number in that table is the slope?"

It is not in the table. It is the difference between consecutive fares — and it is in the sentence at the top. Let the class hunt for a moment before saying so.

C. Developing and Deepening Understanding — 22 minutes (0:11 → 0:33)

C.1 Explicitation — the equation and its two numbers (7 min) (0:11 → 0:18)

Write:

y = 12x + 30

Then interrogate both numbers, one at a time:

"What is the 12?" — the slope. "What is its unit?"

Wait for it. Pesos per kilometre. Write the unit next to the 12 on the board.

"What is the 30?" — the y-intercept. "What is its unit?"

Pesos. Just pesos — not pesos per anything, because it is not a rate. Write it.

"So the two numbers in this equation are not the same kind of thing at all. One is a rate. One is an amount."

C.2 Worked example — the zero (5 min) (0:18 → 0:23)

"The zero of a function is where y = 0. Here that means: when is the fare nothing?"

12x + 30 = 0
      12x = −30
        x = −2.5

Let the class sit with it. Then:

"Minus two and a half kilometres. What does that mean?"

Take answers. Some learners will try to explain it — going backwards, a refund, a discount. Let them try, then say it plainly:

"It means nothing. The number is correct and the situation is impossible. The zero of this function is −2.5, and it has no meaning here. That is a complete answer, and you are allowed to give it."

This is the moment of the lesson. Nine years of schooling have taught these learners that every answer has a meaning and that saying "this means nothing" is giving up. Today it is the right answer, and it needs to be praised out loud when someone offers it.

C.3 Guided practice — we do (5 min) (0:23 → 0:28)

Second context, worked together:

"A drum holds 200 litres. It drains at 25 litres per minute."

Put the two contexts side by side on the board:

"Same mathematics. Same steps. One answer means something and one does not — and only you can tell which, because only you know what x stands for."

C.4 Independent practice — you do (5 min) (0:28 → 0:33)

For each: write the equation, give the slope with its unit, find the zero, and say what the zero means — or that it means nothing.

(Teacher's copy. Learners get column 1 only.)

Circulate with one question:

"Per what?"

D. Making Generalizations — 7 minutes (0:33 → 0:40)

Build the two statements together and write them where they will stay all week:

   A SLOPE IS A RATE.  It has a unit:  y-units per x-unit.

   A ZERO IS AN x-VALUE.  It may or may not mean something.
   Saying "it means nothing here" is a correct answer.

Then a quick oral check of the wage row: its zero is 0, and that does mean something — no hours, no pay. So a zero of zero is not automatically meaningless either. Every case is judged on its own.

Say the class sentence together, twice.

Then plant Day 2, and do not answer it:

"Every context today told you the rate in words. Tomorrow I give you a line on squared paper and no words at all. How will you find the rate then?"

E. Contingency — no electricity, no devices

This lesson has no digital dependency and needs no squared paper. It is tables, an equation and two questions. If there is no paper at all, build both tables on the board and have learners answer orally in full sentences — which is arguably better, since the whole objective is a spoken unit.

IV. EVALUATING LEARNING: FORMATIVE ASSESSMENT AND TEACHER'S REFLECTION

A. Evaluating Learning — 5 minutes (0:40 → 0:45)

Exit ticket. On a quarter-sheet:

A candle is 24 cm tall. It burns 3 cm every hour.

1. Write the equation.                y = ______________

2. What is the slope?    ______   Its unit?  ______________

3. Find the zero.                     x = ______

4. What does the zero mean here?
   ____________________________________________________

Marking key.

Scoring, and what to do about it.

Read item 2's unit before anything else. A blank there is the whole lesson missing, however good items 1, 3 and 4 look.

B. Teacher's Remarks

C. Teacher's Reflection

• Did someone say "it means nothing" unprompted? If you had to supply it, the class has not yet been given permission to refuse a question — and that permission is worth more than the content.
• Was the difference between the 12 and the 30 clear? One is a rate, one is an amount. Learners who cannot separate them will read every y-intercept as a slope in Week 8.
• How many said "eighty" instead of "eighty kilometres per hour" at §A? That number at the start of the lesson and the number at the exit ticket are the same measurement, forty minutes apart.

Anticipated Misconceptions

Differentiation

The Rest of the Week

Day 2 opens with today's closing question — how will you find the rate with no words? Ask it before drawing anything.

Part of the E-turo MATATAG artifact set. Companion files: lesson-plan-ilaw.md · syllabus.md · assessment.md · worksheet.html · slides.html · game.html · offline-activities.md · class-record.html