A focused Grade 4 learning session for Place-Value Relationships using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can explain the relationship between neighboring place values.
Place-Value Relationships means choosing a model, naming what each number means, and explaining the strategy.
Question: Look at the place-value chart below. What is the value of the digit in the tens place?
| Thousands | Hundreds | Tens | Ones |
|---|---|---|---|
| \(2\) | \(3\) | \(7\) | \(4\) |
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: \(70\)
Question: Which digit is in the hundreds place of the number shown in the chart?
| Thousands | Hundreds | Tens | Ones |
|---|---|---|---|
| \(1\) | \(8\) | \(6\) | \(2\) |
Answer: \(8\)
Question: Look at the place-value chart. Which statement is true?
| Thousands | Hundreds | Tens | Ones |
|---|---|---|---|
| \(4\) | \(2\) | \(6\) | \(8\) |
Answer: The hundreds place has value \(200\)
Question: A bookstore has \(3{,}041\) books on the shelves. How many complete hundreds of books are on the shelves?
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: \(30\)
Place-Value Relationships becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
Understand the model before choosing the operation.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
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?
Answer D: \(10\)
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. \(\checkmark\)
What is the value of the digit \(5\) in the number \(5{,}204\)?
Answer D: \(5{,}000\)
The digit \(5\) is in the thousands place. Its value is \(5 \times 1{,}000 = \mathbf{5{,}000}\). \(\checkmark\)
Look at the place-value chart below. What is the value of the digit in the tens place?
Answer D: \(70\)
Looking at the chart, the digit in the tens place is \(7\). Its value is \(7 \times 10 = \mathbf{70}\). \(\checkmark\)
In the number \(4{,}449\), which digit appears in both the thousands and hundreds places?
Answer D: \(4\)
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
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?
Answer C: \(1{,}000\)
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. \(\checkmark\)
Maya built a model of the number \(2{,}345\) using base-ten blocks. How many thousands blocks did she use?
Answer D: \(2\)
In \(2{,}345\), the thousands digit is \(2\). Each thousands block represents \(1{,}000\), so Maya used \(\mathbf{2}\) thousands blocks. \(\checkmark\)
What is the value of the digit \(8\) in the number \(1{,}289\)?
Answer D: \(80\)
In \(1{,}289\), the digit \(8\) is in the tens place. Its value is \(8 \times 10 = \mathbf{80}\). \(\checkmark\)
In the number \(3{,}334\), the digit \(3\) appears in three places. What is the sum of the values of all three \(3\)'s?
Answer C: \(3{,}330\)
Step 1: Find each \(3\)'s place---thousands, hundreds, and tens. Step 2: Calculate values: \(3{,}000 + 300 + 30 = \mathbf{3{,}330}\). \(\checkmark\)
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?
Answer C: \(1{,}000\) 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. \(\checkmark\)
Which digit is in the hundreds place of the number shown in the chart?
Answer D: \(8\)
From the chart, the hundreds place (second column from the left) contains the digit \(\mathbf{8}\). \(\checkmark\)
A digit has a value of \(600\). In which place is this digit located?
Answer C: Hundreds
Read the value backwards: \(600 = 6 \times 100\). A digit's value equals \(\text{digit} \times \text{place value}\). Since the place value here is \(100\), the digit must be in the \(\mathbf{\text{hundreds}}\) place. Quick check: the places are ones (\(\times 1\)), tens (\(\times 10\)), hundreds (\(\times 100\)), thousands (\(\times 1{,}000\)). \checkmark
