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Offline Activities — Mathematics 3

Term 1 · Week 7 · Rounding · CG Quarter 1, competency 12

This is the English copy of a Filipino document. Grade 3 is taught in the mother tongue under MTB-MLE — this is the last year of it — so offline-activities.md is the version a Grade 3 teacher actually uses and the one to treat as authoritative. Activity names stay in Filipino, because that is what the children are told to do. This copy exists for school heads, supervisors and anyone planning provision who does not read Filipino.

Five activities that need no electricity, no electronic device and no internet. Three are individual and two are group.

Grade Level Grade 3
Competency Round numbers to the nearest ten, hundred, or thousand
Class size 45–55 learners in fixed seating

The floor number line

One material is at the centre of the whole week, and it is free.

What is needed. One long line — rope, chalk on concrete, sheets of paper taped together, or a groove scratched in the dirt — marked 100, 110, 120, … 200, one pace apart.

Why on the floor and not on paper. The child measures the distance with their feet, not their eyes. A child who stands on 149 and walks to both ends counts 49 paces and 51 paces, and will not forget it. On paper they only look at the digit.

If there is no space. Draw it across the full width of the board and let the child trace it with a finger while counting aloud. Still better than paper.

INDIVIDUAL ACTIVITIES

I-1 · Alin ang Mas Malapit? (Which Is Nearer?)

Duration 20 minutes · Individual · Use on Day 1, as a substitute for the game

No rounding is asked for. Only two distances, and which is smaller. This is the whole competency without the word "round" in it, and a child who cannot do this is only guessing on the worksheet.

Instructions

Write the two candidates on the board and leave them there:

100                              200

Read the numbers out one at a time. The child writes three things: distance from 100, distance from 200, and which is nearer.

# Number Distance from 100 Distance from 200 Nearer
1 149 49 51 100
2 151 51 49 200
3 108 8 92 100
4 196 96 4 200
5 133 33 67 100
6 175 75 25 200
7 162 62 38 200
8 147 47 53 100
9 150 50 50 equal → 200
10 199 99 1 200

What to ask while walking around

"What are your two distances?"

Not "what is the answer?". The answer can be guessed; the two distances cannot.

Why items 1, 2 and 8 sit together

149 and 151 are two apart and have different answers. 147 looks far from 151 but both are close to the middle. A child who looks at the digit sees only 4, 5 and 4 — and misses the point.

Item 9

The exact half. Nothing is nearer. The agreement is up. Say that it is an agreement, not a truth — no mathematics decides it.

Assessment — 30 points

Three per item: two distances and the choice. Count the distance columns separately. A child with the right answer and blank distances has not yet shown the competency.

I-2 · Isang Bilang, Tatlong Sagot (One Number, Three Answers)

Duration 20 minutes · Individual · Use on Day 2 or Day 4

One number, three levels of rounding, and the discovery that the three answers differ.

# Number To the ten To the hundred To the thousand
1 149 150 100 0
2 1 449 1 450 1 400 1 000
3 2 648 2 650 2 600 3 000
4 5 049 5 050 5 000 5 000
5 8 762 8 760 8 800 9 000
6 4 500 4 500 4 500 5 000

The three worth discussing

Item 1 shows that the answer can be 0. To the nearest thousand, 149 is nearer to 0 than to 1 000 — 149 against 851. It is surprising, and it is correct.

Item 4 has two identical answers, to the hundred and to the thousand. That is not an error. 5 049 is near 5 000 in two ways.

Item 6 does not change to the ten or to the hundred — it is already a multiple of both. It changes only to the thousand, and there it is the exact half.

Assessment — 18 points

Three per number. If the tens column is high and the hundreds column is low, that is the digit rule working at one level only.

I-3 · Isang Beses Lamang (Once Only)

Duration 25 minutes · Individual · Use on Day 3

The whole activity is about chain rounding — doing it twice.

Instructions

For each number, fill in three boxes:

  1. The wrong method: round to the ten first, then round that answer to the hundred
  2. The right method: round from the original number, straight to the hundred
  3. Do they differ?
Number Wrong method Right method Differ?
149 150 → 200 100 Yes
249 250 → 300 200 Yes
1 449 1 450 → 1 500 1 400 Yes
3 449 3 450 → 3 500 3 400 Yes
5 049 5 050 → 5 100 5 000 Yes

The closing question

"The first step is not wrong. The second is not wrong either. Why is the answer wrong?"

Because after the first step, you are no longer looking at the original number. 149 is near 100. 150 is near 200. They are different numbers.

Write on the board and leave it there:

Isang beses lamang. Mula sa orihinal. — Once only. From the original.

Assessment — 15 points

Three per number. The third column matters most — a child who writes "No" even once has not yet seen the difference.

GROUP ACTIVITIES

G-1 · Ang Linya sa Sahig (The Floor Line)

Duration 35 minutes · Whole class, in four groups · Use on Day 5

The number line on the floor, and the children themselves are the numbers.

Preparation

One line from 100 to 200, marked every ten. Two children stand at the two ends as the candidates. One child stands at the number that is read out. The rest count.

The cycle

  1. Read the number. The number-child stands at the right place on the line.
  2. They walk to the left candidate, the class counting aloud.
  3. They come back and walk to the right candidate, counting again.
  4. The class says which is smaller.
  5. Swap roles.

The twelve numbers

# Number Distance left Distance right Answer
1 149 49 51 100
2 151 51 49 200
3 105 5 95 100
4 195 95 5 200
5 120 20 80 100
6 180 80 20 200
7 148 48 52 100
8 152 52 48 200
9 137 37 63 100
10 164 64 36 200
11 150 50 50 equal → 200
12 199 99 1 200

Items 1 and 2, and 7 and 8, are pairs. Two or four apart, and different answers. Once a child has walked both, it cannot be taken away from them.

Item 11 is equal. The child stops in the middle. Tell the class: up is an agreement.

Managing 45+ learners

One line, four groups waiting their turn, and everyone counts aloud even when they are not the one walking. The counting is the activity, not the walking. If there is no space inside, do it outdoors or in the corridor.

Assessment — group rubric, 12 points

Criterion 3 2 1 0
Position on the line Accurate on every number One wrong Two or three wrong More
The two distances Counted aloud and both correct One only Counted but wrong Not counted
The choice Correct, and said why Correct Guessed None
The exact half Recognised and called an agreement Recognised Not noticed —

G-2 · Ang Pagtatalo (The Dispute)

Duration 40 minutes · Groups of 4–5 · Use on Day 5, or in place of G-1

Each group is given another child's answer, and has to say whether it is right or wrong — and if wrong, where it went wrong.

The eight answers

# The question The child's answer Right? Where it went wrong
1 149 to the nearest hundred 200 Wrong Chain rounding, or a digit rule. Distances: 49 against 51
2 149 to the nearest ten 150 Right —
3 4 500 to the nearest thousand 5 000 Right The exact half, and up is the agreement
4 2 648 to the nearest hundred 2 700 Wrong Rounded to the ten first (2 650). Distances: 48 against 52
5 196 to the nearest hundred 100 Wrong Always rounding down. Distances: 96 against 4
6 8 762 to the nearest hundred 8 800 Right Distances: 62 against 38
7 149 to the nearest thousand 1 000 Wrong Distances: 149 against 851. The answer is 0
8 5 049 to the nearest thousand 5 000 Right Distances: 49 against 951

Instructions

Round one — 15 min. Examine all eight. For each, write right or wrong, and for each wrong one, write the two distances that prove it.

Round two — 15 min. Choose one wrong answer and write the explanation you would give that child. Not "you are wrong" but where the path changed.

Round three — 10 min. Make up a wrong answer of your own — one that looks right — and give it to another group to examine.

Why four of them are right

If all of them were wrong, the group would simply look for an error in each without measuring anything. The four correct ones force them to measure all eight.

Item 7 is the hardest of the eight. 149 to the nearest thousand is 0, not 1 000. It is surprising, and only measuring can settle it.

Assessment — group rubric, 12 points

Criterion 3 2 1 0
The eight verdicts All eight correct Six or seven Four or five Fewer than four
The distances Written for all four wrong ones For three For one or two None
The explanation Said where the path changed Said it was wrong and why Only said it was wrong None
The invented error Looked right and caught the other group The error was obvious at once Unclear Not attempted

Which activity to choose

If the class is… Use
Without materials, and it is still Day 1 I-1 — a complete substitute for the game
Guessing instead of measuring I-1, and mark the distance columns
Thinking there is one rounded form I-2 — three answers to one number
Rounding twice I-3 — the whole activity is about that
In need of feeling the distance G-1 — with the feet, not the eyes
Secure and in need of more G-2 — catching an error is harder than rounding

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