Number Concepts to 10,000
Warm-up
Show 3,847 with base-ten blocks. What is the value of the 3? (3000.) The 8? (800.) The 4? (40.) The 7? (7.) Now: what number is 1,000 more than 3,847? (4,847.) What is 100 less? (3,747.) Quick mental math using place value.
Explore
Multiples investigation: each group explores multiples of a different single-digit number (3, 4, 6, 7, 8, 9) using a hundred chart. Colour all multiples. Describe the pattern. What do you notice about numbers that appear in two groups? (Common multiples.)
Formalize
Four-digit decomposition challenge: show 6,203 on a place value mat. What is the value of each digit? Record as expanded form: 6000 + 200 + 0 + 3. Note: zero as placeholder in the tens position keeps the 2 in the hundreds and 3 in the ones.
Number Concepts to 10,000
Estimation context: a hockey arena holds about 20,000 people. If half the seats are filled, about how many people are there? (10,000.) This is benchmark reasoning with four-digit numbers in a real-world context.
Practice
Students represent 6 four-digit numbers in expanded form and with base-ten blocks, list multiples of 4 to 40, and place 8 numbers on a 0-10,000 number line. Exit ticket: what is 1,000 more than 7,843?
Exit ticket
Students represent 6 four-digit numbers in expanded form and with base-ten blocks, list multiples of 4 to 40, and place 8 numbers on a 0-10,000 number line. Exit ticket: what is 1,000 more than 7,843?
Step 1: Read it in chunks at the comma: "six thousand" [comma] "two hundred eight." The comma is a spoken pause, not decoration.
Step 2: Expand by place: 6,208 = 6,000 + 200 + 0 + 8. The tens place holds a zero — it must appear in the expansion's THINKING even though 0 adds nothing, because it's what keeps the 2 in the hundreds seat.
Step 3: Build it fast with place-value cards: a 6000 card, a 200 card, an 8 card sliding together. Where's the zero? Hiding under the stack — placeholders always are.
Step 4: The dictation gauntlet: write two thousand forty (2,040), two thousand four hundred (2,400), two thousand four (2,004). Same words nearly — wildly different numbers. Read each back aloud to self-check.
Watch for: "six thousand two hundred and eight" written as 6,200 + 8 = 62,008 style concatenations. The cards cure it: numbers COMPRESS, they don't concatenate.
Step 1: Compare by highest place first. All are 4-digit numbers (thousands). Thousands digits: 4, 5, 4. So 5,013 is the largest immediately — one digit decided it, despite 4,987 LOOKING big and 5,013 looking full of small digits.
Step 2: Break the 4-thousands tie at the hundreds: 4,987 has 9 hundreds; 4,899 has 8. So 4,899 < 4,987.
Step 3: Final order: 4,899 < 4,987 < 5,013.
Step 4: Place them on a 4,800–5,100 number line: 4,899 just before the 4,900 mark; 4,987 close to 5,000; 5,013 just past it. Notice how CLOSE the three numbers really are — the line shows nearness that digit-comparison hides.
The misconception to smoke out: "4,987 > 5,013 because 9 and 8 beat 0 and 1." Left-most place wins; later digits only referee ties. One flat sentence to install: a thousand beats any pile of hundreds.
Step 1: Nearest thousand: the candidates are 7,000 and 8,000. The referee is the hundreds digit: 4 — less than 5, so round DOWN: 7,000.
Step 2: Nearest hundred: candidates 7,400 and 7,500; referee is the tens digit: 6 — five-or-more, round UP: 7,500.
Step 3: Nearest ten: candidates 7,460 and 7,470; referee is the ones digit: 9 — round up: 7,470.
Step 4: Sit with the odd result: the SAME number rounded three ways gave 7,000, then 7,500, then 7,470 — and rounding to the thousand went DOWN while the others went up. Each rounding answers a different question ("which thousand-neighbourhood?" vs "which ten?"). There is no single "rounded value" of a number — only a rounded value AT a chosen precision.
Step 5: Anchor in purpose: reporting a school's 7,469 books to a newspaper ("about 7,500") vs. to a shelf-buying committee (7,470 matters). Precision follows purpose.