Offline Classroom Activities — Mathematics 4

Term 1 · Week 7 · Number and Algebra strand · Place Value and the Value of a Digit

CG competencies 8 and 9. Five sessions; the competency is met at six digits, reached on Day 3.

Five activities: three individual options and two group/team options.

None of them needs electricity, a device, a printer, or a budget. Every material named is either already in the room or is something learners can bring from home for free. Each activity works in a class of 45 or more with fixed desks.

Preparing the digit tiles (once, reused all year)

Almost every activity below uses these. Make them once and they last the whole term.

• Cut squares roughly 5 cm × 5 cm from grocery-box cardboard.
• Write one digit, 0–9, large and dark, on each. One set of ten per learner or per pair.
• Learners can make their own sets during the first five minutes of Day 1 — it costs nothing and they take better care of tiles they cut themselves.

If cardboard is short: learners write digits on torn notebook paper. It works.

INDIVIDUAL ACTIVITIES

I-1 · Number Detective

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

Materials

• One set of digit tiles per learner (or a pencil and notebook)
• Board and chalk

Preparation

None beyond the tiles. Have ten five-digit numbers ready in your head or on a slip of paper. Include at least three that contain a zero.

Instructions

Part A — Build it (8 minutes).

1. Say: "I will call out a number. Build it with your tiles, left to right. Do not lift your hands until I say show."
2. Call a number aloud, twice, slowly: "Forty-seven thousand, two hundred five."
3. Say "Show." Every learner raises their built number.
4. Scan the room. You will see every error at once — this is the fastest formative read available to you and it costs nothing.
5. Ask one learner who built it correctly to explain the position of the zero.
6. Repeat with five more numbers.

Part B — Detective log (12 minutes).

Learners rule four columns in their notebooks and complete this for the numbers you write on the board:

Answer key

The last row is the one to check first when marking. 99 999 proves whether a learner understands that position — not the digit — decides worth.

Differentiation

• Down — four-digit numbers, tiles stay on the desk for every question.
• Up — after finishing, the learner writes three riddles of their own ("I am a five-digit number. My thousands digit is 7 and my value is…") and swaps with a neighbour.

Assessment

Collect the detective log. Mark out of 5. 4 or 5 correct = ready to move on. 3 or fewer = joins the small-group re-teach tomorrow.

I-2 · Newspaper Number Hunt

Time 25 minutes · Grouping Individual · Use Day 2, reading and writing in words

Materials

• Old newspapers, flyers, or receipts — ask learners to bring one sheet from home the day before
• Scissors or careful tearing; paste or tape
• Notebook

Preparation

Collect a stack of old newspapers over the week beforehand. Sari-sari stores and barangay halls will usually give them away. One sheet serves two learners.

Instructions

1. "Somewhere on your sheet there are numbers. Find five with four or more digits."
2. Cut or tear each one out and paste it in your notebook, one per line.
3. Beside each, write:
   • the number in words
   • the place value and value of its largest-place digit
   • what the number was counting (pesos, people, kilometres, votes)
4. Circle the number on your page that is the largest, and write one sentence saying how you know.

The writing rules to enforce

Put these on the board and leave them there:

• Hyphen between twenty-one and ninety-nine → forty-seven, not forty seven
• Comma after the thousands period → forty-seven thousand,* two hundred five*
• No "and" inside a whole number → not two hundred and five
• Group digits in threes from the right → 47 205, not 47205

Differentiation

• Down — three numbers instead of five; teacher supplies a word bank of number words.
• Up — find a number over 100 000, write it in words, and explain what the extra place is called.
• No newspaper available — use the prices from the nearest sari-sari store, written from memory, or the page numbers and figures inside the learner's own textbook.

Assessment — 10 points

I-3 · The Million Challenge

Time 25 minutes · Grouping Individual · Use Day 3, extension

This is the above-level task named in the lesson plan. It is open-ended on purpose: there is more than one right answer, and the reasoning is the point.

Materials

Notebook and pencil. Digit tiles help but are not required.

Instructions

Work through as many as you can. Show your reasoning for every answer.

1. Build the largest five-digit number you can using each of the digits 3, 0, 7, 1, 9 exactly once. Then build the smallest. Careful — think about where the 0 may and may not go.
2. I am a five-digit number. My ten thousands digit is 6. My ones digit is twice my ten thousands digit. All my other digits are 0. What number am I?
3. Using the digits 8, 5, 0, 2, 6 exactly once each, build a five-digit number in which the 5 has a value of 5 000. How many different numbers can you make?
4. A barangay has 48 267 residents. A neighbouring barangay has 1 more in the thousands place and 2 fewer in the hundreds place. How many residents does the neighbouring barangay have?
5. Write a six-digit number. Now say the place value and the value of every digit in it. What is the new place called?

Answer key

1. Largest 97 310; smallest 10 379. The 0 cannot lead — 07 139 is a four-digit number wearing a disguise. Accept any learner who explains this, however they word it.
2. There is no such number, and that is deliberate. Twice the ten thousands digit is 2 × 6 = 12, and 12 cannot sit in a single place. A learner who writes "impossible, because 12 is not one digit" has given the best possible answer — award full marks. If nobody spots it, discuss it as a class: noticing that a problem is broken is a real mathematical skill, and it is worth more than another correct sum.
3. 18 numbers. The 5 is pinned to the thousands place. The remaining digits 8, 0, 2, 6 fill the other four places in 4 × 3 × 2 × 1 = 24 ways, but the 6 arrangements that put 0 in the ten thousands place are not five-digit numbers at all. 24 − 6 = 18. At Grade 4, accept a learner who lists them systematically without using factorials.
4. 49 067. (48 267 → thousands 8 becomes 9 → 49 267; hundreds 2 becomes 0 → 49 067.)
5. Hundred thousands.

Assessment

Not scored out of a total. Record which items the learner attempted and whether the reasoning was sound. Item 2 is the one worth reading closely.

GROUP / TEAM ACTIVITIES

Both are designed so that every member has a named job. No spectators. Assign roles yourself — do not let groups volunteer, or the same learners will take the same jobs all year.

G-1 · Barangay Number Line

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

Materials

• 10 cardboard strips per group (recycled boxes), roughly 8 cm × 20 cm
• Marker or thick pencil
• A length of string, or a chalk line on the floor, or the edge of the blackboard
• Clothes pegs or tape, if available

Preparation

Draw a long horizontal line on the board or stretch string across the front of the room. Mark only the two ends: 0 and 100 000. Nothing in between — the learners supply that.

Roles — assign one to each member

In a group of 4, the Timekeeper also checks. In a group of 6, add a second Checker. Never remove the Explainer.

Instructions

1. (5 min) Each group receives five real quantities. Use figures from your own barangay where you can; otherwise these work:

   Quantity	Number
   Residents of Barangay San Isidro	47 205
   Learners enrolled in the district	8 940
   Pesos in the barangay youth budget	62 500
   Kilograms of rice harvested this season	15 038
   Metres from the school to the municipal hall	3 072

2. (8 min) The Recorder writes each number on a strip — in numerals on the front, in words on the back.

3. (10 min) The group decides where each strip belongs on the 0 → 100 000 line. The Checker must approve each placement by naming the ten thousands digit aloud before the Placer fixes it.

4. (7 min) Each group's Explainer presents one placement and the reasoning: "We put 15 038 here because its ten thousands digit is 1, so it is just past one tenth of the way."

5. (5 min) Whole class: which two numbers were hardest to separate? Why?

Managing 45+ learners at fixed desks

Groups of 5 give nine groups. Run the line at the board in three shifts of three groups while the other six groups complete their strips at their desks. Nobody moves furniture.

Differentiation

• Down — give the group a line already marked at every 10 000.
• Up — add a sixth strip with a six-digit number and ask where it would go. (It goes off the end — that realisation is the point.)

Assessment — group rubric, 12 points

G-2 · Place Value Market

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

A market role-play. Teams "buy" goods by building the exact price with digit tiles. It is noisy, competitive, and it makes the week's competency automatic.

Materials

• Two sets of digit tiles per team
• 12 "goods cards" — cardboard strips, each with an item and a price
• A bell, or anything that makes a noise

Preparation — about 15 minutes the night before

Write 12 goods cards. Prices between 10 000 and 99 999 pesos. Make at least four contain a zero. For example:

Roles

Instructions

1. (5 min) Set up. Each team takes a table or pushes two desks together. Tiles laid out.
2. (25 min) Rounds. For each round:
   • The Runner collects a goods card, face down.
   • The Buyer turns it over and reads the price aloud in words only — "forty-seven thousand, two hundred five pesos." The Builder must not see the card.
   • The Builder lays out the price in tiles.
   • The Auditor checks. When satisfied, the team rings the bell.
   • The teacher points at any one tile. The Cashier must give its place value and its value. If the Cashier is wrong, the sale does not go through — the team tries again next round.
   • Roles rotate every round. Everyone is the Cashier at least twice.
3. (10 min) Tally and discuss. Which prices were hardest? Nearly always the ones with a zero — draw that out explicitly.

Scoring

• 2 points — price built correctly
• 2 points — Cashier gives both place value and value correctly
• 1 bonus point — first team to a correct build in that round
• −1 point — bell rung before the Auditor has checked (this rule is what makes the Auditor's job real)

Managing 45+ learners at fixed desks

Teams of 6 give eight teams. Run two markets in parallel on opposite sides of the room, four teams each. Use two different bells so you can tell them apart. If the room cannot take it, run four teams while the other four complete I-1 Part B at their desks, then swap at the 20-minute mark.

Differentiation

• Down — the Buyer may show the card to the Builder after reading it aloud once.
• Up — prices go to six digits; the Cashier must also state which digit has the greatest value and why.

Assessment — team rubric, 12 points

After any of these activities

Three questions worth asking the whole class before the bell:

1. "Which digit was the hardest to be sure about?" — the answer is almost always 0.
2. "Did anyone change their mind partway through? What changed it?"
3. "Say the sentence." — "Place value is where. Value is how much."

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