Number Concepts to 1,000,000
Warm-up
What is 1,000 more than 347,852? (348,852.) What is 10,000 less? (337,852.) What digit changed in each case? This place value mental math activates prior knowledge and sets up the lesson.
Explore
Large number investigation: each group researches one large quantity (provincial population, distance to another planet, number of books in a large library) and represents it in expanded form, words, and on a number line. Share: what reference point did you use to make the number feel meaningful?
Formalize
Tsimshian counting systems: discuss that Tsimshian uses different word-forms for counting animals vs. people vs. objects. In English, we say two dogs, two people, two chairs, all with the same word two. This is one linguistic choice. Other cultures make different choices. What might be the cultural significance of counting living things differently from objects?
Number Concepts to 1,000,000
Estimation challenge: the BC provincial population is approximately 5,400,000. If each person needs 2 litres of water per day, how many litres per day total? About 10,800,000 litres. This connects large-number computation to real social needs.
Practice
Students represent 8 six-digit numbers in expanded form, order 6 numbers, and solve 3 estimation problems with large quantities. Exit ticket: what is the value of the 7 in 574,238?
Exit ticket
Students represent 8 six-digit numbers in expanded form, order 6 numbers, and solve 3 estimation problems with large quantities. Exit ticket: what is the value of the 7 in 574,238?
Step 1: Chunk at the comma: "three hundred forty-eight thousand" | "two hundred seven." The comma splits the number into two three-digit stories: the thousands story and the ones story.
Step 2: Expand it: 300,000 + 40,000 + 8,000 + 200 + 0 + 7. The zero holds the tens seat.
Step 3: Place it on a 300,000–400,000 number line: 348,207 sits just left of the halfway mark (350,000). Zoom the line: between 340,000 and 350,000, it's most of the way across.
Step 4: The relative-size question that reveals understanding: "How many times bigger is the 4 than the 8 in this number?" The 4 is 40,000; the 8 is 8,000 — five times bigger, even though 4 < 8 as digits. Place multiplies meaning.
Watch for: reading big numbers digit-by-digit ("three-four-eight…") under pressure. The comma-chunking read must survive a timed drill — it's how the number's SIZE gets felt.
Step 1: Build the ladder of tens with real anchors: 1,000 seconds ≈ 17 minutes (before lunch ends). 1,000,000 seconds ≈ 11½ DAYS. Same jump — thousand to million — turned minutes into weeks.
Step 2: Paper anchor: a ream is 500 sheets, about 5 cm thick. A million sheets ≈ 2,000 reams ≈ a 100-metre tower — taller than a 25-storey building.
Step 3: The counting anchor: counting one number per second, nonstop, reaching a million takes those 11½ days with no sleeping or eating. Reaching a thousand? Under 17 minutes tonight.
Step 4: Now use the feel: "our city has 80,000 people — how many school gyms (500 each) is that?" 160 gyms. "A million?" 2,000 gyms.
The purpose stated plainly: nobody SEES a million; we understand it by ratio to things we can see. Benchmarks are the eyes big numbers get borrowed.
Step 1: Locate the neighbourhood: ten-thousands around it are 480,000 and 490,000.
Step 2: Find the referee digit — the thousands place: 6. Six is 5-or-more → round UP: 490,000.
Step 3: Now the deliberately spicy one: round 485,000 to the nearest ten-thousand. It sits EXACTLY halfway between 480,000 and 490,000 — neither neighbour is nearer. Convention breaks the tie: round half UP → 490,000. Name it honestly as a convention (a rule adopted so everyone agrees), not a discovery.
Step 4: Context check: a headline says "about 490,000 attended." The true count was 486,500 — is the headline honest? Yes, to the nearest ten-thousand. Would "about 500,000" be honest? That's rounding to the nearest hundred-thousand — also defensible, noticeably more generous. Precision level is a CHOICE the writer makes, and readers should ask which one was chosen.
Exit: give a number that rounds to 260,000 at the nearest ten-thousand but NOT at the nearest thousand. (E.g., 264,300 → 260,000 ✓ / 264,000 ✗.)