Lesson Exemplar — Mathematics 7

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 — every question, every anticipated wrong answer, every timing.

I. CURRICULUM CONTENT, STANDARDS, AND LESSON COMPETENCIES

A. Content Standards

Quoted from the MATATAG Mathematics Curriculum Guide (DepEd, August 2023, p. 52), Grade 7 Quarter 1, content standard 3:

The learners should have knowledge and understanding of the application of percentages.

B. Performance Standards

By the end of the quarter, the learners are able to use percentages in different contexts. (NA)

C. Learning Competencies and Objectives

Competency — CG Quarter 1, number 7, quoted verbatim:

7. solve problems involving: a. percentage increase, and b. percentage decrease.

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

1. Predict, and commit publicly, what happens to ₱100 after +20% then −20%
2. Compute both steps longhand and obtain ₱96
3. Explain that the two 20% amounts differ because the base changed
4. Apply the same reasoning to four further amounts and percentages

Objective 3 is the lesson. A learner who leaves with "the answer is ₱96" and no account of why has memorised one arithmetic fact. Everything in Weeks 8 and 9 — discount, commission, sales tax, simple interest, rates — turns on identifying the base, and this is the day it is named.

D. Content

A percentage is always a percentage of something.

The class sentence, introduced at §D and repeated all week: "Percent of what? Change the what, and you change the amount."

The word "multiplier" is not used today. It arrives on Day 2. Introduced now, it lets learners compute 1.2 × 0.8 correctly without ever noticing that ₱20 and ₱24 are different amounts — which is the only thing this lesson is for.

E. Integration

II. LEARNING RESOURCES

Required — no cost.

Explicitly NOT used today: calculators. See the note at §III.C.4.

Optional — if available.

Prepared in advance: nothing.

III. TEACHING AND LEARNING PROCEDURE

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

Four quick ones, oral, round the room:

10% of 200  =        10% of 350  =        20% of 200  =        5% of 200  =

Then, to the class:

"How did you find 10%? Did you divide by ten, or did you move the digits?"

Both are fine. Note who divided and who moved — the digit-movers will be faster all week, and the dividers are the ones who will slow down when the numbers stop being round.

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

Write on the board, and read it aloud slowly:

A shirt costs ₱100.

  The price goes UP 20%.

  Then the price goes DOWN 20%.

  What does it cost now?

Say:

"Do not compute it. I want a prediction. Hands up for ₱100 — back where we started."

Count the hands. Write the number on the board. Most of the class will vote ₱100. Then:

"Hands up for more than ₱100." … "For less than ₱100."

Record all three counts and leave them:

back to ₱100:  27        more:  4        less:  5

Then:

"Twenty-seven of you say it comes back to a hundred. That is the obvious answer, and it is the answer almost every adult gives. In fifteen minutes you will know whether it is right."

Do not resolve it. Move to §C.

If your class votes "less" by a majority — occasionally a class has met this before — do not deflate. Say: "Good. Then tell me by how much, and why." The prediction is cheap; the explanation is the lesson, and almost nobody has that.

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

C.1 Explicitation — the two columns (6 min) (0:11 → 0:17)

Rule the board into two columns, headed UP and DOWN. Work them one at a time, and say every step out loud.

Column 1 — UP.

"The price is ₱100. It goes up 20%. Twenty per cent of what?"

Wait for it. Someone will say "of a hundred." Write of ₱100 in the column.

UP
  20% of ₱100 = ₱20
  ₱100 + ₱20  = ₱120

Column 2 — DOWN.

"Now it goes down 20%. Twenty per cent of what?"

This is the moment of the lesson. Many will say "of a hundred" out of momentum. Do not correct — ask again:

"What does the shirt cost right now, before it goes down?"

₱120. So:

DOWN
  20% of ₱120 = ₱24
  ₱120 − ₱24  = ₱96

Now put the two amounts side by side, large, and circle them:

        ₱20            ₱24

"Same percentage. Different amount. Why?"

Take answers until someone says the bases were different. Then write ₱96 under the question and let the class react.

C.2 Worked example — I do (5 min) (0:17 → 0:22)

Second example, narrated the same way, with a bigger number so the gap is unmistakable:

₱1 200 goes UP 25%,  then DOWN 25%.

  UP:    25% of ₱1 200 = ₱300   →  ₱1 500
  DOWN:  25% of ₱1 500 = ₱375   →  ₱1 125

"Three hundred, then three hundred and seventy-five. The second one is bigger every time. Why is it always bigger?"

Because after an increase, the base is always larger than it was. So the same percentage of it is a larger amount. So you always land below the start.

C.3 Guided practice — we do (5 min) (0:22 → 0:27)

Together, and ask rather than tell: ₱800, DOWN 15% first, then UP 15%.

Then the question that ties it together:

"We went down first this time, and we still ended below ₱800. Does the order matter?"

Check it: ₱800 up 15% is ₱920; ₱920 down 15% is ₱782. The same. Let the class sit with that for a moment — it is genuinely surprising and it is the seed of Day 2's multiplier.

C.4 Independent practice — you do (6 min) (0:27 → 0:33)

On the board:

Two steps each. Show the two amounts separately.

(Teacher's copy. Learners get the first three columns only.)

Circulate with one question:

"That percentage — of what?"

No calculators, and it costs something to hold the line. A calculator turns every row into two keystrokes and hides the two separate amounts, which are the entire point. Learners who find the arithmetic hard should be given rows 1, 2 and 5 only — 20%, 10% and 50% of round numbers — not a calculator.

Row 5 is the one to display at the end. Two 50% moves take ₱240 to ₱180 — a quarter of the value gone. The effect is not a rounding curiosity; it grows with the percentage.

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

Return to the three vote counts from §B, still on the board. Ask which was right — and then call on a learner who voted ₱100 to come and cross it out and write the answer.

Now build the statement together. Accept any wording, then sharpen to:

A percentage is always a percentage OF something.
After the price goes up, the "something" is bigger.
So the same percentage is a bigger amount — and you land below where you started.

Say the class sentence together, twice: "Percent of what? Change the what, and you change the amount."

Then plant Day 2, and do not answer it:

"Tomorrow, one question. Every one of you did two calculations for each row today. There is a way to do each row in one. Think about it tonight."

E. Contingency — no electricity, no devices

This lesson has no digital dependency at all. It needs a board and the ability to say "of" with emphasis. If there is no board, it runs orally with learners working on paper; the two amounts must still be written down side by side by every learner, because seeing ₱20 next to ₱24 is the mechanism.

If the class has no paper, work rows 1 and 5 only, entirely on the ground with a stick, and use the whole 22 minutes on those two.

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

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

Exit ticket. On a quarter-sheet, individually:

A bag costs ₱500. The price goes UP 10%. Then it goes DOWN 10%.

1. Predict first — will it be more than ₱500,
   less than ₱500, or exactly ₱500?   ______

2. Now work it out, in two steps.
   UP:    10% of ______ = ______  →  ______
   DOWN:  10% of ______ = ______  →  ______

3. In one sentence: why is your answer not ₱500?
   ____________________________________________

Marking key.

Scoring, and what to do about it.

The blanks in item 2 are doing real work. Writing "10% of ______" forces the learner to state the base twice, and the second blank is where the whole lesson either landed or did not. A learner who writes ₱500 in both is telling you exactly what to reteach.

B. Teacher's Remarks

C. Teacher's Reflection

• Did the "20% of what?" question at §C.1 land, or did you end up answering it yourself? If you answered it, the class did not have the idea — they had your idea.
• How many learners wrote ₱500 in the second blank of the exit ticket? That number is the most honest measure of the lesson.
• Did the order-does-not-matter discovery at §C.3 get noticed, or rushed past? It is Day 2's hook and it is worth thirty seconds even if it costs a practice row.
• Was there a learner who argued for ₱100 after the working was on the board? That is worth pursuing rather than closing down — the argument is usually "but it's the same percentage", which is exactly right and exactly the point.

Anticipated Misconceptions

Differentiation

The Rest of the Week

Day 2 opens with today's closing question — is there a way to do each row in one calculation? If §D ran short and you did not ask it, ask it at the start of Day 2 before showing anything.

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