3A · Chapter 1 · Lesson 02
Place Value — Part 1
Identify the thousands, hundreds, tens, and ones places., Distinguish a digit from its value., Explain exchanges between adjacent places.
Your starting challenge
In 5,555, are the four 5s worth the same amount? Why can the same digit stand for different quantities?
By the end, you can…
- Identify the thousands, hundreds, tens, and ones places.
- Distinguish a digit from its value.
- Explain exchanges between adjacent places.
Before starting, you should know…
- Read and write numbers through 10,000.
Entry · 2 questions
Quick prerequisite check
Try these two before the lesson. If either is confusing, review the listed prerequisites first.
- E1 Write 4,060 in words.
Show answer and reasoning
Answer: four thousand sixty
Read the thousands group, then the remaining hundreds/tens/ones: four thousand sixty.
If your answer differs — Grouping mistake: Sketch thousands, hundreds, tens, and ones. If a zero is needed to keep a place, write it. Check by adding the place values. Review this concept. - E2 Write “seven thousand three hundred twelve” using digits.
Show answer and reasoning
Answer: 7,312
The words describe 7,000 + 300 + 10 + 2, which is 7,312.
If your answer differs — Grouping mistake: Sketch thousands, hundreds, tens, and ones. If a zero is needed to keep a place, write it. Check by adding the place values. Review this concept.
Vocabulary to know
| place | A position in a numeral, such as hundreds. |
|---|---|
| place value | The value a digit represents because of its position. |
| exchange | Regroup ten units into one unit of the next larger place. |
Learn the concept
A digit is not a value
In 5,555, the thousands digit is 5 but its value is 5,000. The hundreds digit is also 5 but its value is 500. A correct explanation distinguishes these.
The ten-to-one structure
Each place to the left represents units ten times as valuable, for the same digit. Five ones equal 5; five tens equal 50; five hundreds equal 500; five thousands equal 5,000. Ten bundles of 100 are exchanged for a single bundle of 1,000 without gaining or losing anything.
Zero as a placeholder
In 3,008 the zeros show there are no hundreds or tens. Removing them would make 38—a different number.
Each column to the left is worth ten times the one beside it: 5,000 is ten times 500; 500 is ten times 50; and 50 is ten times 5.
Follow the mathematics: Build → Sketch → Explain → Verify
- Build: Put five counters into each place on a place-value mat. The five counters in the thousands column must stand for 5,000 ones, not five ones.
- Sketch: Draw four columns: thousands, hundreds, tens, and ones. Draw five marks in each; label each column 5,000, 500, 50, and 5.
- Name: The digit is 5 in every place, but the values differ. Explain why moving one place left multiplies its value by ten.
- Verify: Compare 5,555 and 5,055. One has 5 hundreds and the other 0 hundreds. Explain the value difference without guessing.
No physical blocks? Use identical paper squares or draw labeled bundles. Try the steps before opening the worked examples.
Work through examples
Study the explanation; then try each check before opening its answer.
Worked example 1
Find the value, not the digit
What is the value of the 7 in 7,482?
- The 7 is in the thousands position.
- Each thousand is worth 1,000.
- 7 × 1,000 = 7,000.
Result: 7,000
Now you try · Understanding check 1
In 5,731, what is the value of the digit in the hundreds place?Reveal answer and explanation
700 — The hundreds digit is 7; each unit has value 100, so its value is 7 × 100 = 700.
Worked example 2
Compare neighboring places
How many tens equal 3 hundreds?
- One hundred is 10 tens.
- Three hundreds are 3 × 10 tens.
Result: 30 tens
Now you try · Understanding check 2
How many hundreds equal 4 thousands?Reveal answer and explanation
40 — Each thousand is ten hundreds, so four thousands are forty hundreds.
Worked example 3
Identify a placeholder
What is the tens digit of 9,406 and what does it contribute?
- Separate 9 thousands, 4 hundreds, 0 tens, 6 ones.
- A zero digit contributes zero tens while keeping ones in the correct position.
Result: 0; it contributes 0
Now you try · Understanding check 3
In 9,046, what is the value of the digit in the tens place?Reveal answer and explanation
40 — The tens digit is 4; each unit has value 10, so its value is 4 × 10 = 40.
Guided · 4 questions
Guided practice
Try each problem; return to a visual model if you need one.
- G1 In 6,392, what is the value of the digit in the hundreds place?
Show answer and reasoning
Answer: 300
The hundreds digit is 3; each unit has value 100, so its value is 3 × 100 = 300.
If your answer differs — Digit versus value: Circle the requested digit, name its column, then multiply the digit by 1,000, 100, 10, or 1. Review this concept. - G2 In 8,036, what is the value of the digit in the tens place?
Show answer and reasoning
Answer: 30
The tens digit is 3; each unit has value 10, so its value is 3 × 10 = 30.
If your answer differs — Digit versus value: Circle the requested digit, name its column, then multiply the digit by 1,000, 100, 10, or 1. Review this concept. - G3 In 7,821, what is the value of the digit in the thousands place?
Show answer and reasoning
Answer: 7,000
The thousands digit is 7; each unit has value 1,000, so its value is 7 × 1,000 = 7,000.
If your answer differs — Digit versus value: Circle the requested digit, name its column, then multiply the digit by 1,000, 100, 10, or 1. Review this concept. - G4 In 7,095, what is the value of the digit in the ones place?
Show answer and reasoning
Answer: 5
The ones digit is 5; each unit has value 1, so its value is 5 × 1 = 5.
If your answer differs — Digit versus value: Circle the requested digit, name its column, then multiply the digit by 1,000, 100, 10, or 1. Review this concept.
Independent · 8 questions
Independent practice
Work without looking at examples first. Show your thinking on paper.
- I1 In 4,263, what is the value of the digit in the tens place?
Show answer and reasoning
Answer: 60
The tens digit is 6; each unit has value 10, so its value is 6 × 10 = 60.
If your answer differs — Digit versus value: Circle the requested digit, name its column, then multiply the digit by 1,000, 100, 10, or 1. Review this concept. - I2 In 6,934, what is the value of the digit in the hundreds place?
Show answer and reasoning
Answer: 900
The hundreds digit is 9; each unit has value 100, so its value is 9 × 100 = 900.
If your answer differs — Digit versus value: Circle the requested digit, name its column, then multiply the digit by 1,000, 100, 10, or 1. Review this concept. - I3 In 5,801, what is the value of the digit in the ones place?
Show answer and reasoning
Answer: 1
The ones digit is 1; each unit has value 1, so its value is 1 × 1 = 1.
If your answer differs — Digit versus value: Circle the requested digit, name its column, then multiply the digit by 1,000, 100, 10, or 1. Review this concept. - I4 In 9,070, what is the value of the digit in the thousands place?
Show answer and reasoning
Answer: 9,000
The thousands digit is 9; each unit has value 1,000, so its value is 9 × 1,000 = 9,000.
If your answer differs — Digit versus value: Circle the requested digit, name its column, then multiply the digit by 1,000, 100, 10, or 1. Review this concept. - I5 In 4,308, what is the value of the digit in the tens place?
Show answer and reasoning
Answer: 0
The tens digit is 0; each unit has value 10, so its value is 0 × 10 = 0.
If your answer differs — Digit versus value: Circle the requested digit, name its column, then multiply the digit by 1,000, 100, 10, or 1. Review this concept. - I6 In 8,652, what is the value of the digit in the hundreds place?
Show answer and reasoning
Answer: 600
The hundreds digit is 6; each unit has value 100, so its value is 6 × 100 = 600.
If your answer differs — Digit versus value: Circle the requested digit, name its column, then multiply the digit by 1,000, 100, 10, or 1. Review this concept. - I7 In 7,006, what is the value of the digit in the ones place?
Show answer and reasoning
Answer: 6
The ones digit is 6; each unit has value 1, so its value is 6 × 1 = 6.
If your answer differs — Digit versus value: Circle the requested digit, name its column, then multiply the digit by 1,000, 100, 10, or 1. Review this concept. - I8 In 1,249, what is the value of the digit in the thousands place?
Show answer and reasoning
Answer: 1,000
The thousands digit is 1; each unit has value 1,000, so its value is 1 × 1,000 = 1,000.
If your answer differs — Digit versus value: Circle the requested digit, name its column, then multiply the digit by 1,000, 100, 10, or 1. Review this concept.
Challenge · 2 questions
Challenge and transfer
These nonroutine problems require you to explain or adapt what you learned.
- C1 In 3,330, by what factor is the value of the thousands digit greater than the value of the tens digit?
Show answer and reasoning
Answer: 100
3,000 ÷ 30 = 100.
If your answer differs — Digit versus value: Circle the requested digit, name its column, then multiply the digit by 1,000, 100, 10, or 1. Review this concept. - C2 A digit 6 has value 600 in a number. How much would its value be if it moved two places to the left?
Show answer and reasoning
Answer: 60,000
Every move left multiplies its value by ten: 600 × 100 = 60,000. This extends beyond the current number range.
If your answer differs — Digit versus value: Circle the requested digit, name its column, then multiply the digit by 1,000, 100, 10, or 1. Review this concept.
Exit · 3 questions
Exit check
Use these fresh problems to decide whether to proceed. Answers should be independent.
- E1 In 8,069, what is the value of the digit in the hundreds place?
Show answer and reasoning
Answer: 0
The hundreds digit is 0; each unit has value 100, so its value is 0 × 100 = 0.
If your answer differs — Digit versus value: Circle the requested digit, name its column, then multiply the digit by 1,000, 100, 10, or 1. Review this concept. - E2 In 2,841, what is the value of the digit in the tens place?
Show answer and reasoning
Answer: 40
The tens digit is 4; each unit has value 10, so its value is 4 × 10 = 40.
If your answer differs — Digit versus value: Circle the requested digit, name its column, then multiply the digit by 1,000, 100, 10, or 1. Review this concept. - E3 What is ten times the value of a 4 in the tens place?
Show answer and reasoning
Answer: 400
4 tens are 40; ten times 40 is 400.
If your answer differs — Digit versus value: Circle the requested digit, name its column, then multiply the digit by 1,000, 100, 10, or 1. Review this concept.