Number Concepts to 1000
Warm-up
Show 342 with base-ten blocks. What number is this? What does the 3 mean? (300, three hundreds.) What does the 4 mean? (40, four tens.) Now show 408. What is missing? (No tens rod.) What does the zero mean in 408? It holds the tens place so the 4 stays a four hundred.
Explore
Skip-count challenge: start at 347, count by 10s forward to 437. What changed? (Only the tens digit.) Start at 695, count forward by 5s to 720. What happened at 700? Bridge-crossing moments reveal the carry mechanism of place value.
Formalize
Introduce the 1000-cube (a cube made of 10 hundreds flats). 1000 = 10 hundreds = 100 tens = 1000 ones. Ask: if a school has 847 students, how would you show this with base-ten blocks? How many hundreds? Tens? Ones? Write the value of each digit.
Number Concepts to 1000
Estimation challenge: show a jar of approximately 250 objects. Is it closer to 100, 200, or 300? How do you know? Use benchmark groupings: I can see about 5 groups of 50, so roughly 250. This connects three-digit estimation to the benchmark thinking from Grade 2.
Practice
Students represent 8 three-digit numbers with blocks and record the value of each digit. Skip-count by 4s, 6s, and 9s from given starting points. Exit ticket: what is the value of each digit in 628?
Exit ticket
Students represent 8 three-digit numbers with blocks and record the value of each digit. Skip-count by 4s, 6s, and 9s from given starting points. Exit ticket: what is the value of each digit in 628?
Step 1: Build 347 with base-ten materials: 3 flats (hundreds), 4 rods (tens), 7 units. Count it up in stages: 100, 200, 300 → 310, 320, 330, 340 → 341 … 347.
Step 2: Record the standard decomposition: 347 = 300 + 40 + 7.
Step 3: Now the non-standard decompositions that show real understanding: 347 = 200 + 140 + 7 (trade a flat for ten rods) and 347 = 300 + 30 + 17 (trade a rod for ten units). Build each with the materials to prove they're all the same number.
Why the weird ones matter: subtraction with regrouping IS a non-standard decomposition ("rewrite 347 as 300 + 30 + 17 so I can take 9 units away"). Students who practice flexible splitting never see regrouping as magic.
Step 1: Line the numbers up by place value: 507 → 5 hundreds, 0 tens, 7 ones. 570 → 5 hundreds, 7 tens, 0 ones.
Step 2: Compare from the LEFT (the biggest place first): hundreds tie (5 = 5). Move right: tens — 0 vs 7. Decision made: 570 is greater. The ones never even get a vote.
Step 3: Say why left-to-right works: one ten outweighs any number of loose ones (a 7 in the ones column is worth 7; a 7 in the tens column is worth 70). Bigger places always dominate.
Step 4: Record with the symbol: 507 < 570, read aloud both directions.
Watch for: the student who says "507 is bigger because 7 beats 0 at the end." Send them to the materials: 5 flats + 7 units versus 5 flats + 7 rods, side by side. The pile answers.
The error: asked to write four hundred seven, a student writes 47 — "four… and seven." The zero got skipped because nothing was SAID for the tens.
Step 1: Build both numbers: 47 is 4 rods and 7 units; 407 is 4 FLATS, an empty tens pile, and 7 units. Put them side by side — they're not remotely the same amount.
Step 2: Explain the zero's job: the 0 in 407 is a placeholder — it reports "the tens column is empty" so that the 4 stays pushed out in the hundreds place. Without it, the 4 slides into the tens and the number collapses to 47.
Step 3: Practice the danger cases in dictation: four hundred seventy (470), four hundred seven (407), forty-seven (47). Same digits available; the zeros' positions carry all the meaning.
Step 4: The habit: after writing any dictated number, read it BACK aloud. "407 — four hundred seven ✓." The read-back catches placeholder slips instantly.