Mathematics • Year 7 • Unit 1 • Lesson 1
Place Value in the Real World
Use place value to read crowd sizes, compare game scores, work out bank balances, and check that you've written cheques correctly. Numbers in the real world all rely on the same place value system.
1. Word problems
Each problem uses the place value ideas from Lesson 1: splitting into periods, writing in words, comparing two large numbers, or identifying the value of a digit. Show your working — a single answer with no working only earns half marks.
1.1 — Concert crowd. A music news website reports that 87,560 fans attended a concert at Allianz Stadium.
(a) Write this number in words.
(b) What is the value of the digit 8 in this number? 2 marks
1.2 — Game high scores. Three friends compare their best Minecraft survival scores: Liam = 1,204,560, Aisha = 1,240,065, Noah = 1,204,650.
(a) Who has the highest score?
(b) Who has the lowest? Show the place value column that decided each comparison. 3 marks
1.3 — Bank balance check. A bank statement shows Jordan's account balance as $52,408. Jordan thinks they should have $52,480.
(a) Are the two amounts equal?
(b) If not, which is larger, and by how many dollars are they different? 2 marks
1.4 — Country populations. A geography text gives the populations of three towns as:
Town A: 6,070 Town B: 6,700 Town C: 6,007.
(a) Write each population in words.
(b) Order them from smallest to largest. 3 marks
1.5 — Cheque writing. Maya is writing a cheque for "two hundred and four thousand and fifty dollars". She writes the digits as $204,500. The bank rejects the cheque because the amount in words and digits don't match.
(a) Write out the correct digit form of the amount in words.
(b) Explain (one sentence) what mistake Maya made with place value. 3 marks
2. Explain your thinking
This question is about communication, not just answers. Use full sentences. 4 marks
2.1 A classmate says "100 has more digits than 99, so 100 must be larger because more digits always means a bigger number." In your own words, explain (i) whether the conclusion is correct, (ii) why the reasoning is wrong, and (iii) what the correct rule for comparing whole numbers is. Use a specific example to back up your explanation.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Concert crowd 87,560
(a) "Eighty-seven thousand, five hundred and sixty".
(b) The 8 is in the ten-thousands place, so it is worth 80,000.
1.2 — Game high scores
Line them up by units:
Liam: 1,204,560 Aisha: 1,240,065 Noah: 1,204,650.
Millions tie (all 1). Hundred-thousands tie (all 2). Ten-thousands: Liam & Noah = 0, Aisha = 4 — so Aisha is highest.
Between Liam and Noah (both 1,204,___): thousands tie (4 = 4), hundreds tie (5 = 6? no — Liam: 5, Noah: 6), so Liam < Noah. Liam is lowest.
Order: Liam (1,204,560) < Noah (1,204,650) < Aisha (1,240,065).
1.3 — Bank balance
(a) No, they are not equal.
(b) Compare: $52,408 and $52,480. The tens column differs: 0 < 8, so $52,480 is larger. Difference: 480 − 408 = $72.
1.4 — Town populations
(a) 6,070 → "six thousand and seventy"; 6,700 → "six thousand, seven hundred"; 6,007 → "six thousand and seven".
(b) Smallest to largest: 6,007 < 6,070 < 6,700. (Thousands all tie at 6 — the hundreds column splits 6,700 off as largest; then the tens column splits 6,070 above 6,007.)
1.5 — Cheque writing
(a) "Two hundred and four thousand and fifty" = $204,050. Periods: 204 (thousands) | 050 (units) = "fifty".
(b) Maya wrote 204,500 instead of 204,050. She put the 5 in the hundreds column when it should have gone in the tens column. "Fifty" means 5 tens, not 5 hundreds.
2.1 — Explain your thinking (sample response)
The conclusion is correct in this case — 100 IS larger than 99 — but the reasoning is wrong. The "more digits = bigger" idea only works when comparing numbers with a different number of digits. Once two numbers have the same number of digits, you have to look place by place from the left and find the first column where they differ. For example, 199 has the same three digits as 200, but 200 > 199 because the hundreds column differs (2 > 1). And 999 has the same three digits as 100, but 999 > 100. So the correct rule is: more digits beats fewer digits, but when the digit counts match, compare from the left until a column differs.
Marking: 1 for saying conclusion is correct but reasoning is incomplete; 1 for naming "same number of digits" condition; 1 for "compare from the left"; 1 for a concrete supporting example.