Offline Classroom Activities — Mathematics 7

Term 1 · Week 7 · Percentage Increase and Decrease · CG Quarter 1, competency 7

Five activities: three individual, two group. Every one runs with no electricity, no devices and no printing budget. None of them uses a calculator — see the note below.

Why no calculators this week

Every problem here is "250 × 1.12" to a calculator, and that keystroke hides the one thing Week 7 exists to teach: what the percentage was taken of. A learner who can key it in and cannot say the base will produce plausible wrong answers all through Weeks 8 and 9, where the base is buried in words like commission and sales tax.

Where the arithmetic is genuinely too heavy for a learner, reduce the numbers, not the thinking — round pesos and friendly percentages. Every activity below says how.

Bring calculators back in Week 8.

Collecting the raw material (do this the week before)

Ask every learner to bring one of the following. It costs nothing and it is the whole of Day 5:

• A store receipt with a discount on it
• A photograph or copy of a price tag showing "was / now"
• A flyer, tarpaulin photo, or newspaper page advertising a sale
• A load or remittance receipt showing a service charge

Thirty learners bring thirty real bases. If nothing arrives, G-2 supplies its own.

INDIVIDUAL ACTIVITIES

I-1 · The Two-Column Ledger

Time 20 minutes · Grouping Individual · Use Day 1, replaces the digital game

The point is not the answers. It is that every learner writes two different peso amounts for the same percentage, in their own hand, five times.

Materials

• Paper and pencil. A ruler helps but is not needed.

Preparation

Write the ledger frame on the board once; learners copy it.

        UP                          DOWN
   ___% of ₱_____ = ₱_____     ___% of ₱_____ = ₱_____
   ₱_____ + ₱_____ = ₱_____    ₱_____ − ₱_____ = ₱_____

Instructions

Complete the ledger for each row. Every blank must be filled — the second of ₱_____ is the one that matters.

(Teacher's copy. Learners get columns 1–4 only.)

6. At the bottom, answer in one sentence: "In every row the two amounts were different. Why?"

Row 4 goes down first, and the second amount is smaller than the first — ₱102 against ₱120. Every other row has the second amount larger. Learners who have generalised "the second one is always bigger" get caught here, correctly: what is always true is that the base changed, not the direction it changed in.

The question to ask while circulating

"That second percentage — of what?"

Differentiation

Assessment — 10 points

Written Works.

I-2 · Ten and One

Time 15 minutes · Grouping Individual · Use Day 2, and again on Day 4

Every percentage a Grade 7 learner needs can be built from 10% and 1% by adding, doubling and halving. A learner who owns those two never needs a formula and never needs a calculator.

Materials

• Paper and pencil.

Instructions

Part A — the two building blocks. Two minutes.

Part B — build the rest. Five minutes. Show how you built each one.

Part C — the trap. One minute, and it is the point of the activity:

₱200 goes up 10%. Then it goes up 10% again. Is that the same as going up 20%? ______

No. 200 → 220 → 242, but 200 up 20% is 240. ₱2 more. The second 10% was of ₱220.

(Teacher's copy throughout.)

How to run it

Time Parts A and B strictly, swap papers, mark from the board, and record only the class total. Run it again on Day 4 and compare. That comparison is the evidence, not the individual scores.

Differentiation

Assessment

Not scored individually. Record the class total on Day 2 and Day 4.

I-3 · The Undo Hunt

Time 25 minutes · Grouping Individual · Use Day 4, extension

Day 1 established that up 20% then down 20% does not return. This asks the obvious next question — then what would? — and it is much harder than it looks.

Materials

• Paper and pencil.

Instructions

A price goes up by a certain percentage. You want it back exactly where it started. By what percentage must it come down?

Work with ₱100 every time — it makes the arithmetic easy and the answer is the same whatever you start with.

Then the reverse direction:

Answer key

The insight worth surfacing at the end

Ask what learners notice. Two things are there, and both are worth naming:

1. The two percentages are never the same — except in the impossible case of 0%.
2. They come in pairs, both ways round. Up 25% is undone by down 20%; down 20% is undone by up 25%. Up 100% by down 50%; down 50% by up 100%. The pairs are the same pairs read backwards.

A learner who finds the rule — the down percentage is the rise divided by the new price — has said the whole of Week 7 in one sentence, and should be asked to say it to the class.

Assessment

Open task, three bands:

GROUP / TEAM ACTIVITIES

Both assume a crowded room with fixed desks. Neither requires moving furniture.

G-1 · The Price Tag Wall

Time 35 minutes · Groups of 5 · Use Day 3, consolidation

The class builds one discount reference chart that stays on the wall for the rest of the term — and that every learner can check their Day 5 flyer against.

Materials

• One large sheet per group — cartolina, newspaper, taped bond paper
• Pencil and a straight edge
• Tape

Preparation

Write the assignments on the board. Each group takes one price and finds it after each of four discounts.

Roles — assign one to each member, do not let them volunteer

Instructions

1. 5 min — roles assigned, sheet ruled into five columns.
2. 20 min — build the row.
3. 5 min — Checker verifies by multiplier (×0.90, ×0.80, ×0.75, ×0.50). Disagreements are resolved by both members working again, not by taking one answer.
4. 5 min — sheets taped up in price order, Reporters read their row.

Answer key

What to point out once the wall is up

• Every column is a fixed multiplier. The 25% column is three quarters of the price column, all the way down. Colour or box one column to show it.
• ₱350 and ₱750 give centavos at 25% off. Real shops round these, and which way they round is worth thirty seconds of discussion.

Managing 45+ learners at fixed desks

Add ₱99 and ₱1 999 as groups 7 and 8 — the prices real shops actually use. Their answers are uglier on purpose (₱99 less 25% is ₱74.25), and that is the point: the tag is designed to look cheap, not to divide neatly.

Differentiation

Assessment — group rubric, 12 points

Performance Tasks.

G-2 · Checking the Flyer

Time 40 minutes · Teams of 5–6 · Use Day 5, application

The week's skill pointed at something that is actually trying to mislead the learner.

Materials

• The flyers, receipts and price tags collected the week before
• Paper and pencil

Preparation — 5 minutes

If nothing was collected, write these four real-shaped claims on the board. They are constructed, not copied from any named business.

  A.  "50% OFF!  Plus an EXTRA 20% off at the counter!"      original ₱1 000
  B.  "Was ₱1 250 — NOW ₱1 000!  SAVE 25%!"
  C.  "Buy 3, get 1 free."                                   each item ₱120
  D.  "Price increased by only 8% this year, after last
       year's 8% rise."                                      two years ago: ₱500

Roles

Instructions

Part 1 — 18 min. For each claim: find the true final price, then judge the claim as TRUE, FALSE, or TRUE BUT MISLEADING, with a reason.

Part 2 — 12 min. Write one sentence of advice for a shopper, for each claim.

Part 3 — 10 min. Reporters present. Take all four claims, one team each.

Answer key

Claim B is the only outright false one, and it is the most common real error — dividing the saving by the new price instead of the old. Teams will often mark it TRUE because ₱250 off ₱1 000 feels like 25%. Make them name the base out loud.

Claim C is not a percentage claim at all, and half the teams will treat it as one. Getting 1 free in 4 is a saving of ¼ = 25%, not ⅓. The confusion — three paid, one free, so "a third off" — is worth the full three minutes.

Managing 45+ learners at fixed desks

Teams are rows; only the Reader and Reporter stand. With more than eight teams, assign two teams per claim and let them compare verdicts in Part 3 — disagreement between two teams on the same claim is the best possible discussion.

Differentiation

Assessment — group rubric, 12 points

Performance Tasks.

Which activity to reach for

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