Mathematics • Year 7 • Unit 1 • Lesson 1
Place Value — Mixed Challenge
Pull everything from Lesson 1 together: read and write numbers in periods, identify the value of a digit, compare and order large numbers, and spot a classic place value mistake. Finish with an open-ended digit puzzle.
1. Mixed problems — choose the right idea
Each question uses a different part of Lesson 1. Decide which idea applies before you start writing. Show your working. 2 marks each
1.1 Write 3,008,420 in words.
1.2 Write the number "nine hundred and forty thousand and seven" in digits.
1.3 In the number 6,729,054, what is the value of the digit 7? What is the value of the digit 9?
1.4 Place the correct symbol (>, < or =) between each pair:
(a) 39,408 ____ 39,480 (b) 1,000,000 ____ 999,999 (c) 504,200 ____ 504,200
1.5 Arrange these from smallest to largest: 78,090 78,900 7,890 78,009.
1.6 The population of Newcastle is reported as 322,278 people. The population of Wollongong is reported as 305,880 people. Which city has more people, and by how many?
2. Find the mistake
Another Year 7 student has tried to write "two million, fifty thousand and four" in digits. Their working is shown below. Exactly one line contains a mistake. Spot it, explain why it's wrong, then re-do the working correctly. 3 marks
Student's working — convert "two million, fifty thousand and four" to digits:
Line 1: Three periods needed: millions, thousands, units.
Line 2: Millions period = "two" → 2
Line 3: Thousands period = "fifty" → 500
Line 4: Units period = "four" → 004
Line 5: Answer: 2,500,004
(a) Which line contains the mistake?
(b) Explain in one or two sentences why that line is wrong.
(c) Write out the corrected working in full, including the corrected final answer.
Stuck? "Fifty" means 5 tens — not 5 hundreds. Inside the thousands period, the 50 still has to go in the tens column.3. Open-ended challenge — digits in different places
This question has more than one correct answer. Show one that works and explain. 4 marks
3.1 Using each of the digits 1, 4, 6 and 9 exactly once, create a 4-digit number that:
(i) is greater than 6,000
(ii) has the digit 4 in the tens column
(iii) is an even number.
Write down your number, then explain in one or two sentences how you used place value to satisfy all three rules.
Bonus: How many different 4-digit numbers can you make that satisfy all three rules? List them all.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Write 3,008,420 in words
Split: 3 | 008 | 420. Read: "three million", "eight thousand", "four hundred and twenty". (008 → "eight" — drop the leading zeros.)
Answer: "Three million, eight thousand, four hundred and twenty".
1.2 — "Nine hundred and forty thousand and seven" in digits
Thousands period: "nine hundred and forty" = 940. Units period: "seven" = 007.
Answer: 940,007.
1.3 — Values of digits 7 and 9 in 6,729,054
The 7 sits in the hundred-thousands column, so it is worth 700,000.
The 9 sits in the thousands column, so it is worth 9,000.
1.4 — Compare
(a) 39,408 < 39,480 (tens differ: 0 < 8).
(b) 1,000,000 > 999,999 (1,000,000 has more digits).
(c) 504,200 = 504,200 (identical).
1.5 — Order from smallest to largest
7,890 has only 4 digits — it's smaller than the others (all 5 digits).
Among 78,090; 78,900; 78,009: thousands tie (8); hundreds split them: 78,009 and 78,090 vs 78,900. So 78,900 is largest. Between 78,009 and 78,090, the tens differ: 0 < 9, so 78,009 < 78,090.
Final order: 7,890 < 78,009 < 78,090 < 78,900.
1.6 — Newcastle vs Wollongong
Compare 322,278 and 305,880. Hundred-thousands tie (3 = 3). Ten-thousands differ: 2 > 0, so Newcastle has more people.
Difference: 322,278 − 305,880 = 16,398 people.
2 — Find the mistake
(a) The mistake is on Line 3.
(b) "Fifty" is 5 tens (50), not 5 hundreds (500). The student put the digit 5 in the wrong column of the thousands period.
(c) Corrected working:
Line 3 (fixed): thousands period = "fifty" → 050.
Putting the periods together: 2 | 050 | 004 → 2,050,004.
Quick sanity check: read 2,050,004 aloud — "two million, fifty thousand and four". That matches the original.
3 — Digit puzzle (sample solution)
The thousands digit must be 6 or 9 (rule i). The tens digit must be 4 (rule ii). The units digit must be even — among 1, 6, 9 only 6 is even (rule iii).
Case A: thousands = 9. Then units = 6, tens = 4, and the hundreds digit must be 1 (the only one left). Number: 9,146.
Case B: thousands = 6 — but then we can't put 6 in the units column too (each digit used exactly once). So no number with thousands = 6 works.
Only one number works: 9,146. Check: 9,146 > 6,000 ✓, tens digit is 4 ✓, units digit 6 is even ✓.
Marking: 2 marks for finding 9,146; 1 for explaining the place value choices; 1 for the bonus — recognising that only one number works.