Introduction
Place-Value Relationships is an important Grade 4 math skill because students are moving from simple answers toward explaining how the math works.
In this lesson, students use models, real questions, worked examples, practice problems, and two online quizzes to build confidence with place-value relationships.
What Is Place-Value Relationships?
Place-Value Relationships means choosing a model, naming what each number means, and explaining the strategy.
The goal is not only to get the answer. Students should be able to show the idea, explain the strategy, and check whether the answer makes sense.
Understanding Place-Value Relationships
Before solving, students should slow down and decide what each number, shape, unit, or label represents.
- Read the question carefully and identify what is being asked.
- Choose a model, equation, table, or diagram that matches the situation.
- Solve one step at a time and keep units or labels attached.
- Use the answer explanation to check that the result makes sense.
Visual Models
Visual Model 1
Question: Look at the place-value chart below. What is the value of the digit in the tens place?
| Thousands | Hundreds | Tens | Ones |
|---|---|---|---|
| \(2\) | \(3\) | \(7\) | \(4\) |
- A. \(7\)
- B. \(7{,}000\)
- C. \(700\)
- D. \(70\)
Why it works: Looking at the chart, the digit in the tens place is \(7\). Its value is \(7 \times 10 = \mathbf{70}\). \(\checkmark\)
Answer: \(70\)
Visual Model 2
Question: Maya built a model of the number \(2{,}345\) using base-ten blocks. How many thousands blocks did she use?
- A. \(5\)
- B. \(3\)
- C. \(4\)
- D. \(2\)
Why it works: In \(2{,}345\), the thousands digit is \(2\). Each thousands block represents \(1{,}000\), so Maya used \(\mathbf{2}\) thousands blocks. \(\checkmark\)
Answer: \(2\)
Worked Examples
Example 1
Question: Which digit is in the hundreds place of the number shown in the chart?
| Thousands | Hundreds | Tens | Ones |
|---|---|---|---|
| \(1\) | \(8\) | \(6\) | \(2\) |
- A. \(1\)
- B. \(2\)
- C. \(6\)
- D. \(8\)
- From the chart, the hundreds place (second column from the left) contains the digit \(\mathbf{8}\). \(\checkmark\)
Answer: \(8\)
Example 2
Question: Look at the place-value chart. Which statement is true?
| Thousands | Hundreds | Tens | Ones |
|---|---|---|---|
| \(4\) | \(2\) | \(6\) | \(8\) |
- A. The tens digit equals \(8\).
- B. The thousands digit is in the tens place.
- C. The hundreds place has value \(20\).
- D. The hundreds place has value \(200\).
- From the chart, the hundreds digit is \(2\).
- Its value is \(2 \times 100 = 200\).
- Statement B is \(\mathbf{\text{true}}\). \(\checkmark\)
Answer: The hundreds place has value \(200\)
Example 3
Question: Use the chart to find the number.
| Thousands | Hundreds | Tens | Ones |
|---|---|---|---|
| \(9\) | \(0\) | \(5\) | \(3\) |
- A. \(953\)
- B. \(9{,}503\)
- C. \(9{,}530\)
- D. \(9{,}053\)
- Reading the chart left to right: thousands \(9\), hundreds \(0\), tens \(5\), ones \(3\).
- This gives \(\mathbf{9{,}053}\). \(\checkmark\)
Answer: \(9{,}053\)
Real-World Word Problems
Problem 1
Question: A bookstore has \(3{,}041\) books on the shelves. How many complete hundreds of books are on the shelves?
- A. \(3\)
- B. \(300\)
- C. \(4\)
- D. \(30\)
Why it works: "How many complete hundreds" is just asking how many full groups of \(100\) fit in \(3{,}041\). Skip-count by \(100\)s: \(100, 200, \ldots, 3{,}000\)---that's \(30\) groups. The extra \(41\) books left over isn't enough for another group of \(100\). So the bookstore has \(\mathbf{30}\) complete hundreds. \checkmark
Answer: \(30\)
Problem 2
Question: In the number \(6{,}663\), the value of the digit \(6\) in the hundreds place is how many times the value of the digit \(6\) in the tens place?
- A. \(1\)
- B. \(1{,}000\)
- C. \(100\)
- D. \(10\)
Why it works: The \(6\) in the hundreds place is worth \(600\), and the \(6\) in the tens place is worth \(60\). Since \(600 \div 60 = 10\), the hundreds place is \(10\) times greater. \(\checkmark\)
Answer: \(10\)
Common Mistakes
- Rushing before identifying what the numbers represent.
- Choosing an operation that does not match the situation.
- Dropping labels, units, or context from the answer.
- Skipping the estimate or reasonableness check.
Strategy Tips
- Underline the question being asked.
- Use a model before jumping to computation.
- Write an equation that matches the story or picture.
- Explain the final answer in a sentence.
Practice Questions
Question 1
What is the value of the digit \(5\) in the number \(5{,}204\)?
- A. \(5\)
- B. \(50\)
- C. \(500\)
- D. \(5{,}000\)
Question 2
In the number \(4{,}449\), which digit appears in both the thousands and hundreds places?
- A. \(1\)
- B. \(9\)
- C. \(2\)
- D. \(4\)
Question 3
In the number \(7{,}777\), the digit \(7\) in the thousands place is how many times the value of the digit \(7\) in the ones place?
- A. \(10\)
- B. \(100\)
- C. \(1{,}000\)
- D. \(10{,}000\)
Question 4
What is the value of the digit \(8\) in the number \(1{,}289\)?
- A. \(8\)
- B. \(8{,}000\)
- C. \(800\)
- D. \(80\)
Question 5
In the number \(3{,}334\), the digit \(3\) appears in three places. What is the sum of the values of all three \(3\)'s?
- A. \(333\)
- B. \(3{,}300\)
- C. \(3{,}330\)
- D. \(3{,}333\)
Question 6
In the number \(5{,}059\), how many times greater is the value of the digit \(5\) in the thousands place than the digit \(5\) in the ones place?
- A. \(10\) times
- B. \(100\) times
- C. \(1{,}000\) times
- D. \(5\) times
Full Answer Explanations Click to show all answers and explanations
Question 1
Answer: \(5{,}000\)
The digit \(5\) is in the thousands place. Its value is \(5 \times 1{,}000 = \mathbf{5{,}000}\). \(\checkmark\)
Question 2
Answer: \(4\)
Look at each place in \(4{,}449\) from left to right: thousands \(= 4\), hundreds \(= 4\), tens \(= 4\), ones \(= 9\). The digit \(\mathbf{4}\) appears in the thousands place (worth \(4{,}000\)) and the hundreds place (worth \(400\)). Notice: same digit, but its value depends on its place---\(4{,}000\) is \(10 \times 400\). \checkmark
Question 3
Answer: \(1{,}000\)
The \(7\) in the thousands place is worth \(7{,}000\). The \(7\) in the ones place is worth \(7\). Since \(7{,}000 \div 7 = 1{,}000\), the answer is \(\mathbf{1{,}000}\) times. \(\checkmark\)
Question 4
Answer: \(80\)
In \(1{,}289\), the digit \(8\) is in the tens place. Its value is \(8 \times 10 = \mathbf{80}\). \(\checkmark\)
Question 5
Answer: \(3{,}330\)
Step 1: Find each \(3\)'s place---thousands, hundreds, and tens. Step 2: Calculate values: \(3{,}000 + 300 + 30 = \mathbf{3{,}330}\). \(\checkmark\)
Question 6
Answer: \(1{,}000\) times
The \(5\) in the thousands place is worth \(5{,}000\). The \(5\) in the ones place is worth \(5\). So \(5{,}000 \div 5 = \mathbf{1{,}000}\) times. \(\checkmark\)
Connection to Standards
This lesson supports Grade 4 math expectations for reasoning, modeling, problem solving, and explaining answers clearly. It connects classroom skills to the kind of questions students see on state math assessments.
Summary
Place-Value Relationships becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
GOLDEN RULE
Understand the model before choosing the operation.
