Lesson 1 — Hundreds, Tens & Ones

Summary

Learners bundle objects into groups of ten, then bundle ten tens into a hundred, and discover that a three-digit number is hundreds, tens, and ones — for example, four hundreds, three tens, and two ones is four hundred thirty-two. They read and record numbers as hundreds, tens, and ones, treating place value as something you can hold and count, not just a symbol.

Objectives

• Use place value to 1,000 to read, write, round, and compare whole numbers. (D05.S1.03.01)

Connection

Last year you bundled tens and ones to count to one hundred. This year the same idea grows one step bigger. A market seller counts seeds into piles of ten, then stacks ten piles into a basket of one hundred; a festival organizer counts people in rows of ten and blocks of one hundred; a village counts its mangoes in sacks of one hundred. Most peoples group by ten because ten fingers make ten easy to see. Some peoples have kept count other ways — by fives, by twenties, with knots on a cord, or with tally marks — and every counting way is a real way to keep track. Today you add the next bundle: ten tens is one hundred.

Materials

• About 300 small objects (pebbles, seeds, beans, buttons)
• Ten small cups, bags, or cloth squares for groups of ten
• Paper or slate and a drawing tool

Preparation

• Give each learner or pair about 300 objects and ten holders.
• Clear space to move, bundle, and count aloud.
• Prepare (or plan to draw) a quick example of “four hundreds, three tens, and two ones.”

Facilitator note

This lesson is written to the learner (“you”). It builds directly on Grade 2, where learners bundled tens and ones to read two-digit numbers; today the bundle grows to the hundred — the key idea is that ten tens make one hundred, the same unitizing move as before, one step bigger (Clements & Sarama, 2014). Teach the one new skill as a worked example (philosophy §13): bundle ten, bundle ten tens into a hundred, then read hundreds, tens, and ones aloud before learners try it themselves. Keep it concrete: objects first, symbols last. No one’s speed at bundling measures their smartness, and a number is a fact about a collection, never a worth about a person. The digits 0–9 we use today are one number system among many — they reached the wider world through Arabic-speaking scholars from India, while other peoples used tally marks, knots, and many other ways (Ifrah, 2000; Zaslavsky, 1999). Count in the home language; number words differ across languages and all are correct. For learners who are Deaf or hard of hearing, count in sign or by tapping each bundle; for learners who are blind or low-vision, move objects into cups so the number grows by feel and sound. Learners with limited hand or body movement direct a partner to move each object. Mastery arrives at its own pace for each child.

Procedure

1. Gather — remember the ten (5 min). Last year you bundled objects into groups of ten. Make one group of ten right now. Hold up your ten fingers — that is one ten.
2. Worked example — ten tens make a hundred (8 min). Watch and help: make one group of ten, then another, all the way to ten groups of ten. Count the tens: ten, twenty, thirty … ninety, one hundred. Ten tens make one hundred. Now make four hundreds, three tens, and two loose ones. Count: four hundred … four hundred ten, twenty, thirty … four hundred thirty … thirty-one, thirty-two. Four hundreds, three tens, and two ones is four hundred thirty-two. Say it together.
3. Guided practice — build and read (15 min). From your own collection, make as many hundreds as you can (ten tens each), then tens, then loose ones. Count your hundreds by hundreds, your tens by tens, then count on the ones. Say your number. Now write it: how many hundreds? How many tens? How many ones?
4. Trade and check (10 min). Trade bundles with a friend. Read their hundreds, tens, and ones, and let them read yours. Do you both agree on the number? If not, count again together, kindly. A second count that matches is a sign you read it well.
5. Record it (5 min). Draw your number on paper — four big squares for four hundreds, three lines for three tens, and two dots for two ones — and write the digits beside your drawing.
6. Close (2 min). Remember: every three-digit number is hundreds, tens, and ones. Ten ones is a ten; ten tens is a hundred. You can now hold a big number in your hands.

Differentiation

• Support: Build only up to two hundreds today; add more hundreds another day, echoing each hundred number.
• Support (motor): Bundle larger, easy-to-grip objects, or have a partner move objects while the learner counts and directs.
• Extension: Build a number, then build the number that is one hundred more (or ten more) and say how you know.

Assessment

• Formative (observation): Does the learner group ten ones into a ten and ten tens into a hundred, count the hundreds by hundreds, and count on the tens and ones to say and write the number?
• Formative (oral): Can the learner tell how many hundreds, tens, and ones are in a number they built?

Home connection

At home, gather a pile of beans, stones, or buttons, make groups of ten and groups of a hundred, and tell a grown-up how many hundreds, tens, and ones there are — and what number that makes.

Resources

• Clements, D. H., & Sarama, J. (2014). Learning and Teaching Early Math: The Learning Trajectories Approach (2nd ed.). Routledge. (Unitizing — seeing ten ones as one ten and ten tens as one hundred — as the foundation of place value.)
• Ifrah, G. (2000). The Universal History of Numbers. John Wiley & Sons. (The decimal positional system with zero originated in India and spread via Arabic-speaking scholars; it is one system among many.)
• Zaslavsky, C. (1999). Africa Counts: Number and Pattern in African Cultures (3rd ed.). Lawrence Hill Books. (Counting and tally systems across many traditions.)