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.
- 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.
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
Moving a digit one place left makes its value ten times as great. Ten ones equal one ten; ten tens equal one hundred; ten hundreds equal one thousand.
Zero as a placeholder
In 3,008 the zeros show there are no hundreds or tens. Removing them would make 38—a different number.
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.
- 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.
- 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.
- 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.
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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
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.
- 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.
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.
- 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.
- 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.