Offline Classroom Activities — Mathematics 5

Term 1 · Week 7 · Multiplying a Fraction by a Fraction · CG Quarter 1, competency 8

Five activities: three individual, two group. Every one of them runs with no electricity, no devices and no printing budget. Where a printed sheet would help, an equivalent board-and-paper route is given beside it.

	Activity	Time	Grouping	Best used
I-1	The Fold Book	20 min	Individual	Day 1 — replaces the digital game
I-2	Grid Cards	25 min	Individual	Day 2–3 — the model and the rule
I-3	The Product Hunt	25 min	Individual	Day 4 — extension
G-1	The Product Wall	35 min	Groups of 5	Day 4 — consolidation
G-2	Cooking for the Fiesta	40 min	Teams of 5–6	Day 5 — application

Preparing the paper (once, reused all week)

The only consumable this week is rectangular scrap. Any of these work:

Used bond paper cut in four
Old newspaper torn into roughly A6 pieces
The blank reverse of last term's handouts
Cartolina offcuts from a previous display

About 8 pieces per learner covers the whole week. They do not need to be the same size as each other, and saying so out loud is worth thirty seconds: "Your whole and my whole are different sizes, and half of each is still a half." That single remark heads off the most common Grade 5 fraction error — comparing fractions of different wholes.

Pre-creasing thirds and fifths the night before saves five minutes a day and is worth doing for any class where fine-motor difficulty is present.

INDIVIDUAL ACTIVITIES

I-1 · The Fold Book

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

A learner leaves this activity holding physical proof that ½ × ½ = ¼. That object is the point; the recording sheet is secondary.

Materials

5 rectangular scraps per learner
Pencil (two different hatching directions are enough — coloured crayon is optional)
One quarter-sheet for recording

Preparation

None. Tear the paper in front of the class.

Instructions

Fold, shade, count each of the five pairs below, one per scrap.
On each scrap, write the two fractions in the top corner before folding.
After opening, write the count in the bottom corner: pieces altogether and pieces with both marks.
Stack the five scraps in order and staple or tie them — that is the fold book.
On the recording quarter-sheet, copy the five results into the table.

	Fold this	Then this	Pieces altogether	Both marks	Product	Simplest form
1	½	½	4	1	1/4	¼
2	½	⅓	6	1	1/6	⅙
3	⅔	½	6	2	2/6	⅓
4	¾	½	8	3	3/8	⅜
5	⅔	¾	12	6	6/12	½

(Teacher's copy. Learners receive columns 1–3 only.)

At the bottom of the recording sheet, answer in one sentence: "Was every product smaller than both the fractions you started with?"

The question to ask while circulating

Only one, and ask it of every learner:

"Is your answer smaller than both the fractions you started with?"

A learner who has counted correctly but cannot answer this has produced numbers without meaning. Note the name — that is the Day 2 small group.

Differentiation

Group	Adjustment
Below level	Rows 1–3 only, done carefully, with pre-creased scraps
On level	All five
Above level	All five, then: "Make a sixth page where the product is exactly ⅒." (⅕ × ½, or ½ × ⅕)
Additional needs	Pre-folded scraps; the recording sheet may be dictated to a peer scribe

Assessment — 10 points

Criterion	Points
Five folds completed and stacked	2
Counts correct on all five (1 point each, ½ point if only one column is right)	5
Products written in simplest form	2
Closing sentence answered, with any reasoning	1

Written Works.

I-2 · Grid Cards

Time 25 minutes · Grouping Individual · Use Day 2–3, the model and the rule

Folding cannot reach ⅗ × ¾. This activity is where the learner discovers that for themselves and reaches for a grid instead.

Materials

Squared paper if you have it; plain paper and a ruler if you do not
Pencil

Preparation

If drawing grids by hand will eat the lesson, draw one grid on the board of each size needed (3 × 4, 4 × 5, 5 × 6, 6 × 8) and have learners copy the one they need. Copying a grid is not the competency.

Instructions

For each product: decide the grid size, draw it, shade across, shade down, count.

The rule for deciding — which learners should state before drawing:

Columns = the denominator of the first fraction. Rows = the denominator of the second.

	Product	Grid needed	Shaded cells	Total cells	Answer	Simplest form
1	⅔ × ¾	3 × 4	6	12	6/12	½
2	⅗ × ¾	5 × 4	9	20	9/20	9/20
3	⅖ × ⅚	5 × 6	10	30	10/30	⅓
4	⅜ × ⅔	8 × 3	6	24	6/24	¼
5	⅞ × ½	8 × 2	7	16	7/16	7/16
6	¾ × ⅘	4 × 5	12	20	12/20	⅗
7	⅚ × ⅗	6 × 5	15	30	15/30	½
8	⅗ × ½	5 × 2	3	10	3/10	3/10

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

The moment this activity is designed to produce

After item 3 or 4, a learner will notice they can get the shaded count without drawing — 2 × 5 = 10, 5 × 6 = 30. When that happens, do not confirm it. Say:

"Try it on the next one and check it against the drawing. If it works three times in a row, come and tell the class."

That learner then delivers Day 3's rule, which is worth far more than hearing it from you.

Differentiation

Group	Adjustment
Below level	Items 1, 5 and 8 only — the smallest grids. Grids pre-drawn
On level	Items 1–6
Above level	All eight, then: "Item 7 gives ½. So does item 1. Find a third pair that gives ½ and prove it without drawing."
Additional needs	Enlarged pre-drawn grids; shading may be marked with an X in each cell rather than filled

Assessment — 10 points

Criterion	Points
Grid size chosen correctly (½ point each, 8 items)	4
Counts and products correct (½ point each)	4
Simplest form given where reduction is possible (items 1, 3, 4, 6, 7)	2

Written Works.

I-3 · The Product Hunt

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

Every other activity this week runs forwards: two fractions in, one product out. This one runs backwards, which is harder, open-ended, and the fastest way to tell a secure learner from a fluent one.

Materials

Paper and pencil. Nothing else.

Instructions

The answer is given. Find the question — as many times as you can.

For each target below, find pairs of fractions whose product is exactly that target. Both fractions must be proper (smaller than 1), and no denominator may be larger than 10. Write each pair and show the multiplication that proves it.

Target	Find at least
¼	3 pairs
⅓	3 pairs
½	2 pairs
⅙	3 pairs

Answer key

Not exhaustive — accept any pair that multiplies correctly and obeys the two rules.

Target	Valid pairs (denominators ≤ 10, both proper)	Check
¼	½ × ½	1/4
	¾ × ⅓	3/12 = ¼
	⅔ × ⅜	6/24 = ¼
	⅖ × ⅝	10/40 = ¼
	⅚ × 3/10	15/60 = ¼
	⅞ × 2/7	14/56 = ¼
⅓	½ × ⅔	2/6 = ⅓
	¾ × 4/9	12/36 = ⅓
	⅗ × 5/9	15/45 = ⅓
	⅖ × ⅚	10/30 = ⅓
½	⅔ × ¾	6/12 = ½
	⅗ × ⅚	15/30 = ½
	⅘ × ⅝	20/40 = ½
	⅞ × 4/7	28/56 = ½
⅙	½ × ⅓	1/6
	⅔ × ¼	2/12 = ⅙
	⅚ × ⅕	5/30 = ⅙
	¾ × 2/9	6/36 = ⅙
	⅜ × 4/9	12/72 = ⅙

The strategy worth surfacing at the end

Ask the class how they found their pairs. Two methods will emerge, and both are worth naming:

Guess and check — multiply pairs until one lands. Slow, but it works.
Build from the target — ¼ is 1/4, and 1/4 = (1 × 1)/(2 × 2), or (1 × 3)/(3 × 4), or (2 × 3)/(3 × 8). Take any fraction equivalent to the target and split its numerator and denominator between two fractions.

Method 2 is genuinely a Grade 8 factoring idea arriving early. A learner who finds it should be asked to explain it, slowly, to the class.

Assessment

Not scored out of a fixed total — the task is open. Record against three bands:

Band	Evidence
Extending	Met every target, found a systematic method, can explain it
Secure	Met every target by guess and check, all products verified correctly
Developing	Met some targets; products correct where found

Performance Tasks, if you use it as a graded piece. Most teachers will not — its value is diagnostic.

GROUP / TEAM ACTIVITIES

Both activities assume a crowded room with fixed desks. Neither requires learners to move furniture, and each names what to do when the class is 45 or more.

G-1 · The Product Wall

Time 35 minutes · Groups of 5 · Use Day 4, consolidation

The class builds one large reference chart, in pieces, that stays on the wall for the rest of the term.

Materials

One sheet of paper per group, as large as you can find (cartolina, newspaper, taped-together bond paper)
Pencil, and a ruler or any straight edge
Tape, paste, or a nail

Preparation

Write the group assignments on the board before the class comes in. Each group gets one first fraction and produces its whole row.

Group	First fraction	Products to build
1	½	½×½, ½×⅓, ½×¼, ½×⅕
2	⅓	⅓×½, ⅓×⅓, ⅓×¼, ⅓×⅕
3	¼	¼×½, ¼×⅓, ¼×¼, ¼×⅕
4	⅔	⅔×½, ⅔×⅓, ⅔×¼, ⅔×⅕
5	¾	¾×½, ¾×⅓, ¾×¼, ¾×⅕
6	⅗	⅗×½, ⅗×⅓, ⅗×¼, ⅗×⅕

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

Role	Responsibility
Grid-drawer	Draws the four grids, correctly sized. Draws nothing else
Shader	Shades across and down. May not write numbers
Counter	Counts cells and states the fraction aloud. May not shade
Recorder	Writes the product and the simplest form under each grid
Checker	Verifies every product by the rule — numerator × numerator — independently, and signs the sheet

The split between Shader and Counter is deliberate: it forces the count to be spoken, which is where errors surface.

Instructions

5 min — roles assigned, sheet ruled into four boxes.
20 min — build the four models and record the products.
5 min — Checker verifies all four by the rule and signs. Any disagreement is resolved by recounting the grid, not by arguing.
5 min — sheets taped to the wall in order, Reporters read their row aloud.

Answer key

	× ½	× ⅓	× ¼	× ⅕
½	¼	⅙	⅛	⅒
⅓	⅙	⅑	1/12	1/15
¼	⅛	1/12	1/16	1/20
⅔	⅓	2/9	⅙	2/15
¾	⅜	¼	3/16	3/20
⅗	3/10	⅕	3/20	3/25

What to point out once the wall is up

Two things, and they are worth five minutes:

Every product is smaller than both factors. Thirty-six examples, on the wall, all week.
The table is symmetric across the diagonal where both fractions appear — ½ × ⅓ and ⅓ × ½ both give ⅙. Order does not matter. Ask why, and let someone answer with the grid rotated.

Managing 45+ learners at fixed desks

Run seven or eight groups rather than six by adding ⅖ and ⅘ rows. Nobody moves: the group is whoever is within arm's reach. Pass the large sheet along the row rather than gathering around it.

Differentiation

Group	Adjustment
Below level	Assign row ½ or ¼ — unit fractions, smallest grids
Above level	Assign row ⅗, and ask the group to predict the ⅘ row without drawing it
Additional needs	The Counter role is fully verbal; the Checker role can be done with a calculator

Assessment — group rubric, 12 points

Criterion	3	2	1
Accuracy	All four products correct and in simplest form	3 correct	2 or fewer
Model quality	Grids correctly sized, shading legible from the back of the room	Correct but untidy	Grid size wrong
Roles	Every member did their own role only	Roles blurred once or twice	One or two members did everything
Verification	Checker verified independently and caught or confirmed each	Checker signed without visible working	No verification

Performance Tasks.

G-2 · Cooking for the Fiesta

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

The week's arithmetic, inside a problem the learners recognise. This is the activity that teaches "of" means multiply better than any exercise set, because the word appears naturally.

Materials

Paper and pencil per team
The recipe below, copied onto the board (do not print it — copying it is the first task and it slows them down usefully)

Preparation — 5 minutes

Write the recipe on the board:

BIKO — serves 12

  3/4  kilo glutinous rice
  1/2  kilo brown sugar
  2/3  litre coconut milk
  1/4  kilo grated coconut
  1/2  teaspoon salt

Roles

Role	Responsibility
Reader	Reads each line aloud and states what operation is needed. May not compute
Computer A	Works the first three ingredients
Computer B	Works the last two ingredients
Checker	Recomputes every answer independently. Signs each line
Reporter	Presents to the class and answers one question from another team
Timekeeper (6th member)	Calls the halfway point and the two-minute warning

Instructions

Part 1 — 12 min. Half the recipe. The fiesta committee needs enough for 6 people. Every quantity must be halved. Write each as a multiplication.

Part 2 — 12 min. Two-thirds of the recipe. A different committee needs enough for 8 people — that is ⅔ of 12. Every quantity multiplied by ⅔.

Part 3 — 8 min. The question that matters. Answer in writing, as a team:

"For Part 1 you multiplied by ½. Every answer got smaller. Is there any quantity you could multiply this recipe by that would make the answers bigger? Give one, and explain."

Part 4 — 8 min. Reporters present Part 3. Take three teams, not all of them.

Answer key

Part 1 — × ½ (serves 6)

Ingredient	Working	Answer
Glutinous rice	½ × ¾	⅜ kilo
Brown sugar	½ × ½	¼ kilo
Coconut milk	½ × ⅔	⅓ litre
Grated coconut	½ × ¼	⅛ kilo
Salt	½ × ½	¼ teaspoon

Part 2 — × ⅔ (serves 8)

Ingredient	Working	Answer
Glutinous rice	⅔ × ¾	½ kilo
Brown sugar	⅔ × ½	⅓ kilo
Coconut milk	⅔ × ⅔	4/9 litre
Grated coconut	⅔ × ¼	⅙ kilo
Salt	⅔ × ½	⅓ teaspoon

Part 3. Any multiplier greater than 1. Expected answers: "double it — multiply by 2, for 24 people"; "one and a half times, for 18". Accept 3/2, 2, 2½, or "×2". The reasoning required is that the multiplier is more than one whole, not the specific number.

The trap in Part 2, and it catches most teams. ⅔ × ¾ = 6/12 = ½ kilo, which is more than the ⅜ kilo of Part 1. Teams that have absorbed "multiplying makes it smaller" too literally will assume they have erred. They have not — ⅔ is a bigger multiplier than ½, so a bigger answer follows. If no team raises it, raise it yourself in Part 4. It is the sharpest available demonstration that the week's sentence is about size relative to one, not about multiplication in general.

Managing 45+ learners at fixed desks

Teams are rows. The Reader stands; nobody else moves. If there are more than eight teams, run Part 4 with four reporters and have the rest submit Part 3 in writing.

Differentiation

Group	Adjustment
Below level	Part 1 only, with the multiplication written out for the first line as a model
On level	Parts 1–3
Above level	Add Part 2b — "scale it for 18 people" (× 3/2), which requires an improper multiplier
Language support	The Reader role may be performed in the mother tongue; the written record is in English
Additional needs	Computer roles may use fraction strips; the Reporter may present from written notes

Assessment — group rubric, 12 points

Criterion	3	2	1
Part 1 accuracy	All five correct and simplified	3–4 correct	2 or fewer
Part 2 accuracy	All five correct and simplified	3–4 correct	2 or fewer
Reasoning in Part 3	Correct, with a clear explanation of why a multiplier over 1 increases the amount	Correct multiplier, thin explanation	Incorrect or absent
Roles and verification	Every role performed; Checker signed each line	Roles blurred, or checking partial	One or two members did everything

Performance Tasks.

Which activity to reach for

If your class…	Run
Has no devices at all	I-1 on Day 1, I-2 on Day 2 — together they replace the game entirely
Is split on the Day 1 exit ticket	I-2 with pre-drawn grids for the lower half, I-3 for the upper
Finished early and is restless	I-3. It has no ceiling
Needs the term performance-task mark	G-1 or G-2 — both are rubric-scored and both are defensible as Performance Tasks
Has one 40-minute slot and nothing prepared	G-2. The only preparation is writing five lines on the board

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