Offline Classroom Activities — Mathematics 9

Term 1 · Week 7 · Slope as a Rate of Change · CG Quarter 1, competency 8

Five activities: three individual, two group. No electricity, no devices, no printing budget — and no calculators, deliberately.

Why no calculators

Every number in Week 7 is chosen so that the arithmetic is reasoning rather than keying. A slope of −25 litres per minute from a 200-litre drum gives a zero of 8 minutes, and a learner who divides 200 by 25 in their head has understood the question. Keyed in, it is two seconds and no thought.

Bring them back in Week 29, for the trigonometric ratios, where they are genuinely needed.

Squared paper

Days 2 and 5 need it. If you have none, rule one master grid in dark pen and trace through, or rule directly on the board and have learners copy only the axes they need. Ten minutes of ruling by five learners in a break makes a class set.

INDIVIDUAL ACTIVITIES

I-1 · Per What?

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

No graphs and no grids. Six contexts, and for each one the learner must produce a unit and a judgement.

Instructions

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 here.

(Teacher's copy. Learners get column 2 only.)

7. At the bottom, in one sentence: "Two of these zeros mean nothing. What do those two contexts have in common?" (Both have a positive slope and a positive starting amount, so y is never zero for any x that makes sense.)

The question to ask while circulating

"Per what?"

Ask it of every learner, every time, whether or not they have written a unit.

Differentiation

Assessment — 10 points

Written Works.

I-2 · Rise and Run

Time 20 minutes · Grouping Individual · Use Day 2

Slopes counted off a grid, before any formula. The sign is the point.

Materials

Squared paper, or grids copied from the board.

Instructions

Plot each pair of points, draw the line through them, and find the slope by counting.

(Teacher's copy. Learners get column 2 only.)

The two to discuss at the end

• Rows 1 and 5 have the same slope and look different on the page because they start in different places. Slope does not depend on where a line is, only on how it leans.
• Row 8 is undefined, not zero. Row 4 is zero. Learners swap these constantly. Zero means flat; undefined means you were asked to divide by nothing.

Assessment — 8 points

Written Works.

I-3 · The Missing Representation

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

The competency names three representations. This asks the learner to move between them in every direction.

Instructions

Each row gives you one representation. Produce the other two, then the slope and the zero.

(Teacher's copy. Learners get column 2 only. The table column is at x = 0, 1, 2, 3 for every row — including row 2, whose given table steps by 3.)

Why row 2 is the hard one

Its given table steps in threes, and the answer table steps in ones. A learner who reads the y-differences (−6) as the slope has forgotten to divide by Δx. The slope is −2, not −6, and this is where the week's marks are lost.

Why row 4 has no meaningful zero

−3 km. Say so, and say that saying so is the answer.

Assessment

Open task, three bands:

GROUP / TEAM ACTIVITIES

G-1 · The Rate Wall

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

Six real rates, six groups, one wall display of what a slope actually is.

Preparation

Write the assignments on the board.

Roles

The Writer working from the table rather than the context is deliberate — it forces the group to have produced a table that actually determines the equation.

Answer key

Group 5 has to compute its own rate first — ₱620 ÷ 8 hours = ₱77.50 per hour. That extra step is why it is worth assigning to a strong group.

Group 4's zero is not a whole number, and groups expect whole numbers. 133⅓ minutes is correct, and "about 2 hours 13 minutes" is a good answer.

Managing 45+ learners at fixed desks

Groups are whoever is within reach. With more than six, add jeepney: ₱13 for the first 4 km, then ₱1.80 per extra kilometre — a genuinely piecewise rate, and worth a discussion about why it is not one straight line.

Assessment — group rubric, 12 points

Performance Tasks.

G-2 · Three Ways, One Function

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

A matching relay. Every function appears four times — as a context, a table, an equation and a graph — and the teams must reunite them.

Preparation — 15 minutes the night before

Write or cut sixteen cards: four functions × four representations. Scrap paper is fine.

Instructions

Round 1 — 12 min. Match. Cards are shuffled and dealt. Teams sort all sixteen into four sets of four. Every match must be justified out loud to the Checker before the set is closed.

Round 2 — 10 min. Name. For each of the four functions, state the slope with its unit and the zero with its meaning.

Round 3 — 10 min. Make a fifth. Each team invents a fifth function and writes all four of its cards. The context must be real and local.

Round 4 — 8 min. Swap and solve. Teams exchange their fifth set, shuffled, and match it. A set that cannot be matched — because the four cards disagree — scores the maker zero.

Answer key — Round 2

B and D have the same zero and completely different meanings, and neither has anything to do with the other. That coincidence is worth pointing out: the number 8 is not the answer; the sentence is.

Why Round 4 is worth the eight minutes

Building four consistent representations of one function is much harder than reading them. A team whose cards disagree has learned exactly where their own understanding is thin, and the scoring makes that consequence explicit without a teacher having to mark anything.

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