Mathematics • Year 7 • Unit 1 • Lesson 1
Place Value and Whole Numbers
Build the basics: read large numbers by their periods, write them in words, and compare two numbers by lining up the digits and looking at the first place where they differ.
1. I do — fully worked example
Read every line. Each step has a short reason on the right so you can see why, not just what.
Problem. Write 4,560,231 in words, then say what the digit 5 is worth.
Step 1 — Split into periods of three from the right.
4 | 560 | 231
Reason: commas in big numbers always separate periods of 3 digits. The period names from the right are: units, thousands, millions.
Step 2 — Name each period.
4 → millions 560 → thousands 231 → units
Reason: 4 sits in the millions period, 560 sits in the thousands period, 231 sits in the units period.
Step 3 — Read each period as a small number, then add the period name.
"four million" + "five hundred and sixty thousand" + "two hundred and thirty-one"
Reason: the word "and" only goes before the very last tens/units chunk.
Step 4 — Find the value of the digit 5.
5 sits in the hundred-thousands place → worth 500,000.
Reason: place value = the digit × the column heading. Here 5 × 100,000 = 500,000.
Answer: "Four million, five hundred and sixty thousand, two hundred and thirty-one." The 5 is worth 500,000.
2. We do — fill in the missing steps
Same structure as Section 1, but with the working faded. Fill in each blank line. 4 marks
Problem. Write 7,030,052 in words and state the value of the digit 3.
Step 1 — Split into periods of three from the right:
7 | _____ | _____
Step 2 — Name each period:
7 → ____________ 030 → ____________ 052 → ____________
Step 3 — Read each period (watch out: 030 is just "thirty", not "thirty zero"):
"_______ million, _______ thousand and _______"
Step 4 — Value of the digit 3:
3 sits in the ____________ place, so it is worth _________.
3. You do — independent practice
Show your working in the space under each problem. The first four are foundation, the middle two are standard, and the last two are extension.
Foundation — single step
3.1 Write 5,062 in words. 1 mark
3.2 In the number 38,471, what is the value of the digit 8? 1 mark
3.3 Write the number "six hundred and fourteen thousand, two hundred" in digits. 1 mark
3.4 Place > or < between the two numbers: 4,712 ____ 4,721. 1 mark
Standard — combine two ideas
3.5 Write 12,045,600 in words. 2 marks
3.6 Compare 5,678,901 and 5,687,109. Which is larger, and which place value column decides? 2 marks
Extension — push your thinking
3.7 Arrange these four numbers from smallest to largest: 405,910 450,019 405,091 450,109. Show how you decided each comparison. 3 marks
3.8 Without changing any digits, rearrange the digits 2, 7, 0, 5, 9 to make (a) the largest possible 5-digit number, and (b) the smallest possible 5-digit number. Explain why the 0 cannot go first in part (b). 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do (7,030,052)
Step 1: 7 | 030 | 052.
Step 2: 7 → millions, 030 → thousands, 052 → units.
Step 3: "Seven million, thirty thousand and fifty-two".
Step 4: The digit 3 is in the ten-thousands place, so it is worth 30,000.
3.1 — Write 5,062 in words
"Five thousand and sixty-two." The 0 in the hundreds column is a placeholder — we don't say "five thousand zero hundred and sixty-two".
3.2 — Value of digit 8 in 38,471
The 8 sits in the thousands column, so its value is 8,000.
3.3 — "Six hundred and fourteen thousand, two hundred" in digits
614,200. The thousands period is 614 and the units period is 200.
3.4 — Compare 4,712 and 4,721
Thousands match (4 = 4). Hundreds match (7 = 7). Tens differ: 1 < 2. So 4,712 < 4,721.
3.5 — Write 12,045,600 in words
Split: 12 | 045 | 600. Read each period: "twelve million", "forty-five thousand", "six hundred".
Answer: "Twelve million, forty-five thousand and six hundred."
3.6 — Compare 5,678,901 and 5,687,109
Millions match (5 = 5). Hundred-thousands match (6 = 6). Ten-thousands differ: 7 < 8. So 5,687,109 is larger. The ten-thousands column decides.
3.7 — Order four 6-digit numbers
Line up: all start with 4. Hundred-thousands split them into two groups: 0xx and 5xx.
Group "40xxxx": 405,091 vs 405,910 — tens of thousands tie at 5, thousands tie at 0, but hundreds differ: 0 < 9, so 405,091 < 405,910.
Group "45xxxx": 450,019 vs 450,109 — first differ at the hundreds column: 0 < 1, so 450,019 < 450,109.
Final order: 405,091 < 405,910 < 450,019 < 450,109.
3.8 — Largest and smallest 5-digit numbers from {2, 7, 0, 5, 9}
(a) Largest: put the biggest digits in the highest place values. 97,520.
(b) Smallest: put the smallest digits in the highest place values — but 0 cannot lead, otherwise it becomes a 4-digit number. So the smallest non-zero digit (2) goes first, then 0, then the rest in ascending order: 20,579.
Why 0 can't lead: 02,579 is just the 4-digit number 2,579 — the 0 has no place to anchor.