Understand Place Value Relationships
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4th Grade Math › Understand Place Value Relationships
Chen compares $700$ and $70$. Which statement correctly describes the relationship between them?
$700$ is 100 times $70$.
$70$ is 10 times $700$.
$700$ is 10 times $70$.
$700$ is $70$ more than $70$.
Explanation
This question tests 4th grade understanding that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (CCSS.4.NBT.1). Our place value system is based on groups of 10. Each place value position is 10 times the position to its right—ones become tens (×10), tens become hundreds (×10), hundreds become thousands (×10). This means that the same digit in adjacent places has values that differ by a factor of 10. Chen compares 700 and 70, where the 7 is in the hundreds place (700) and tens place (70), requiring students to recognize that 700 is 10 times 70. Choice B is correct because calculating 700 ÷ 70 = 10 shows that 700 is 10 times 70. This demonstrates understanding that adjacent place values have a 10-to-1 relationship. Choice A represents using 100 instead of 10 (confused with non-adjacent places), which happens when students don't understand multiplicative relationships between places. To help students: Use place value charts or base-ten blocks to show that 1 hundred = 10 tens, 1 thousand = 10 hundreds. Emphasize the pattern: moving one place to the left multiplies by 10, moving one place to the right divides by 10. Practice with division: 700 ÷ 70 = 10, 5,000 ÷ 500 = 10, 30 ÷ 3 = 10 (always 10 for adjacent places).
In the number 2,222, the digit 2 in the tens place represents what value compared to the digit 2 in the ones place?
It is 2 times as much.
It is 100 times as much.
It is 10 times as much.
It is the same value.
Explanation
This question tests 4th grade understanding that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (CCSS.4.NBT.1). Our place value system is based on groups of 10. Each place value position is 10 times the position to its right—ones become tens (×10), tens become hundreds (×10), hundreds become thousands (×10). This means that the same digit in adjacent places has values that differ by a factor of 10. For example, 7 in the hundreds place (700) is 10 times the 7 in the tens place (70). In the number 2,222, the digit 2 appears in the tens place (value 20) and the ones place (value 2), requiring students to recognize that 20 is 10 times 2. Choice A is correct because calculating that 20 is 10 times 2 demonstrates understanding that adjacent place values have a 10-to-1 relationship. Choice B represents using 100 instead of 10 (confused with non-adjacent places), which happens when students don't understand multiplicative relationships between places. To help students: Use place value charts or base-ten blocks to show that 1 hundred = 10 tens, 1 thousand = 10 hundreds. Emphasize the pattern: moving one place to the left multiplies by 10, moving one place to the right divides by 10. Practice with division: 700 ÷ 70 = 10, 5,000 ÷ 500 = 10, 30 ÷ 3 = 10 (always 10 for adjacent places). Use numbers with repeating digits (4,440, 7,777) to make the relationship clear. Point out that the DIGIT stays the same, but the VALUE changes by 10 times. Watch for: students who subtract instead of divide, students who use 100 for the relationship (that's for places two positions apart), and students who give the digit value instead of the multiplicative relationship.
Look at the number 3,333. The digit 3 in the tens place represents how many times what it represents in the ones place?
2
10
30
100
Explanation
This question tests 4th grade understanding that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (CCSS.4.NBT.1). Our place value system is based on groups of 10. Each place value position is 10 times the position to its right—ones become tens (×10), tens become hundreds (×10), hundreds become thousands (×10). This means that the same digit in adjacent places has values that differ by a factor of 10. For example, 7 in the hundreds place (700) is 10 times the 7 in the tens place (70). In the number 3,333, the digit 3 appears in the tens place (value 30) and the ones place (value 3), requiring students to recognize that 30 is 10 times 3. Choice C is correct because dividing the larger value by the smaller value: 30 ÷ 3 = 10, demonstrating understanding that adjacent place values have a 10-to-1 relationship. Choice D represents using 100 instead of 10 (confused with non-adjacent places), which happens when students think about distance between places rather than value relationship. To help students: Use place value charts or base-ten blocks to show that 1 hundred = 10 tens, 1 thousand = 10 hundreds. Emphasize the pattern: moving one place to the left multiplies by 10, moving one place to the right divides by 10. Practice with division: 700 ÷ 70 = 10, 5,000 ÷ 500 = 10, 30 ÷ 3 = 10 (always 10 for adjacent places). Use numbers with repeating digits (4,440, 7,777) to make the relationship clear. Point out that the DIGIT stays the same, but the VALUE changes by 10 times. Watch for: students who subtract instead of divide, students who use 100 for the relationship (that's for places two positions apart), and students who give the digit value instead of the multiplicative relationship.
In the number 6,600, the digit 6 in the thousands place represents how many times what the digit 6 in the hundreds place represents?
6
10
60
100
Explanation
This question tests 4th grade understanding that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (CCSS.4.NBT.1). Our place value system is based on groups of 10. Each place value position is 10 times the position to its right—ones become tens (×10), tens become hundreds (×10), hundreds become thousands (×10). This means that the same digit in adjacent places has values that differ by a factor of 10. For example, 7 in the hundreds place (700) is 10 times the 7 in the tens place (70). In the number 6,600, the digit 6 appears in the thousands place (value 6,000) and the hundreds place (value 600), requiring students to recognize that 6,000 is 10 times 600. Choice B is correct because dividing the larger value by the smaller value: 6,000 ÷ 600 = 10, demonstrating understanding that adjacent place values have a 10-to-1 relationship. Choice D represents using 100 instead of 10 (confused with non-adjacent places), which happens when students confuse operations. To help students: Use place value charts or base-ten blocks to show that 1 hundred = 10 tens, 1 thousand = 10 hundreds. Emphasize the pattern: moving one place to the left multiplies by 10, moving one place to the right divides by 10. Practice with division: 700 ÷ 70 = 10, 5,000 ÷ 500 = 10, 30 ÷ 3 = 10 (always 10 for adjacent places). Use numbers with repeating digits (4,440, 7,777) to make the relationship clear. Point out that the DIGIT stays the same, but the VALUE changes by 10 times. Watch for: students who subtract instead of divide, students who use 100 for the relationship (that's for places two positions apart), and students who give the digit value instead of the multiplicative relationship.
Yuki compares $40$ and $4$. How many times greater is $40$ than $4$?
0.1
10
36
100
Explanation
This question tests 4th grade understanding that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (CCSS.4.NBT.1). Our place value system is based on groups of 10. Each place value position is 10 times the position to its right—ones become tens (×10), tens become hundreds (×10), hundreds become thousands (×10). This means that the same digit in adjacent places has values that differ by a factor of 10. Yuki compares 40 and 4, where the 4 is in the tens place (40) and ones place (4), requiring students to calculate 40 ÷ 4. Choice A is correct because dividing the larger value by the smaller value: 40 ÷ 4 = 10. This demonstrates understanding that adjacent place values have a 10-to-1 relationship. Choice B represents using 100 instead of 10 (confused with non-adjacent places), which happens when students think the relationship is always 100. To help students: Use place value charts or base-ten blocks to show that 1 hundred = 10 tens, 1 thousand = 10 hundreds. Emphasize the pattern: moving one place to the left multiplies by 10, moving one place to the right divides by 10. Practice with division: 700 ÷ 70 = 10, 5,000 ÷ 500 = 10, 30 ÷ 3 = 10 (always 10 for adjacent places).
Based on the ten-times place value relationship, what is $70 \div 7$?
0.1
10
63
100
Explanation
This question tests 4th grade understanding that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (CCSS.4.NBT.1). Our place value system is based on groups of 10. Each place value position is 10 times the position to its right—ones become tens (×10), tens become hundreds (×10), hundreds become thousands (×10). This means that the same digit in adjacent places has values that differ by a factor of 10. For example, 7 in the hundreds place (700) is 10 times the 7 in the tens place (70). In this problem, students use place value to find 70 ÷ 7, where 70 (7 tens) and 7 (7 ones) require identifying the multiplicative relationship. Choice C is correct because dividing the larger value by the smaller value: 70 ÷ 7 = 10, recognizing that each place is 10 times the place to its right. Choice D represents using 100 instead of 10 (confused with non-adjacent places), which happens when students think about distance between places rather than value relationship. To help students: Use place value charts or base-ten blocks to show that 1 hundred = 10 tens, 1 thousand = 10 hundreds. Emphasize the pattern: moving one place to the left multiplies by 10, moving one place to the right divides by 10. Practice with division: 700 ÷ 70 = 10, 5,000 ÷ 500 = 10, 30 ÷ 3 = 10 (always 10 for adjacent places). Use numbers with repeating digits (4,440, 7,777) to make the relationship clear. Point out that the DIGIT stays the same, but the VALUE changes by 10 times. Watch for: students who subtract instead of divide, students who use 100 for the relationship (that's for places two positions apart), and students who give the digit value instead of the multiplicative relationship.
In the number 8,880, the digit 8 in the hundreds place represents how many times what the digit 8 in the tens place represents?
8
10
100
800
Explanation
This question tests 4th grade understanding that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (CCSS.4.NBT.1). Our place value system is based on groups of 10. Each place value position is 10 times the position to its right—ones become tens (×10), tens become hundreds (×10), hundreds become thousands (×10). This means that the same digit in adjacent places has values that differ by a factor of 10. For example, 7 in the hundreds place (700) is 10 times the 7 in the tens place (70). In the number 8,880, the digit 8 appears in the hundreds place (value 800) and the tens place (value 80), requiring students to calculate 800 ÷ 80 to identify the multiplicative relationship. Choice A is correct because dividing the larger value by the smaller value: 800 ÷ 80 = 10, recognizing that each place is 10 times the place to its right. Choice C represents using 100 instead of 10 (confused with non-adjacent places), which happens when students don't understand multiplicative relationships between places. To help students: Use place value charts or base-ten blocks to show that 1 hundred = 10 tens, 1 thousand = 10 hundreds. Emphasize the pattern: moving one place to the left multiplies by 10, moving one place to the right divides by 10. Practice with division: 700 ÷ 70 = 10, 5,000 ÷ 500 = 10, 30 ÷ 3 = 10 (always 10 for adjacent places). Use numbers with repeating digits (4,440, 7,777) to make the relationship clear. Point out that the DIGIT stays the same, but the VALUE changes by 10 times. Watch for: students who subtract instead of divide, students who use 100 for the relationship (that's for places two positions apart), and students who give the digit value instead of the multiplicative relationship.
Based on place value, what is $600 \div 60$?
0.1
10
100
540
Explanation
This question tests 4th grade understanding that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (CCSS.4.NBT.1). Our place value system is based on groups of 10. Each place value position is 10 times the position to its right—ones become tens (×10), tens become hundreds (×10), hundreds become thousands (×10). This means that the same digit in adjacent places has values that differ by a factor of 10. For example, 7 in the hundreds place (700) is 10 times the 7 in the tens place (70). In this problem, students compare 600 (6 hundreds) and 60 (6 tens), requiring them to calculate 600 ÷ 60 to identify the multiplicative relationship. Choice C is correct because dividing the larger value by the smaller value: 600 ÷ 60 = 10, recognizing that each place is 10 times the place to its right. Choice D represents using 100 instead of 10 (confused with non-adjacent places), which happens when students confuse operations. To help students: Use place value charts or base-ten blocks to show that 1 hundred = 10 tens, 1 thousand = 10 hundreds. Emphasize the pattern: moving one place to the left multiplies by 10, moving one place to the right divides by 10. Practice with division: 700 ÷ 70 = 10, 5,000 ÷ 500 = 10, 30 ÷ 3 = 10 (always 10 for adjacent places). Use numbers with repeating digits (4,440, 7,777) to make the relationship clear. Point out that the DIGIT stays the same, but the VALUE changes by 10 times. Watch for: students who subtract instead of divide, students who use 100 for the relationship (that's for places two positions apart), and students who give the digit value instead of the multiplicative relationship.
Keisha says, “$9,000$ is 10 times $900$ because the 9 moved one place left.” Is Keisha correct?
No, because $9,000$ is 100 times $900$.
No, because $9,000$ and $900$ are equal.
Yes, because $9 + 0 + 0 + 0 = 9$.
Yes, because $9,000 \div 900 = 10$.
Explanation
This question tests 4th grade understanding that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (CCSS.4.NBT.1). Our place value system is based on groups of 10. Each place value position is 10 times the position to its right—ones become tens (×10), tens become hundreds (×10), hundreds become thousands (×10). This means that the same digit in adjacent places has values that differ by a factor of 10. For example, 7 in the hundreds place (700) is 10 times the 7 in the tens place (70). In this problem, students evaluate if 9,000 (9 thousands) is 10 times 900 (9 hundreds), requiring them to calculate 9,000 ÷ 900 to verify the relationship. Choice A is correct because dividing the larger value by the smaller value: 9,000 ÷ 900 = 10, recognizing that each place is 10 times the place to its right. Choice C represents using 100 instead of 10 (confused with non-adjacent places), which happens when students don't understand multiplicative relationships between places. To help students: Use place value charts or base-ten blocks to show that 1 hundred = 10 tens, 1 thousand = 10 hundreds. Emphasize the pattern: moving one place to the left multiplies by 10, moving one place to the right divides by 10. Practice with division: 700 ÷ 70 = 10, 5,000 ÷ 500 = 10, 30 ÷ 3 = 10 (always 10 for adjacent places). Use numbers with repeating digits (4,440, 7,777) to make the relationship clear. Point out that the DIGIT stays the same, but the VALUE changes by 10 times. Watch for: students who subtract instead of divide, students who use 100 for the relationship (that's for places two positions apart), and students who give the digit value instead of the multiplicative relationship.
In the number $4,440$, how many times greater is the value of the digit 4 in the thousands place than the digit 4 in the hundreds place?
1
4
10
100
Explanation
This question tests 4th grade understanding that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (CCSS.4.NBT.1). Our place value system is based on groups of 10. Each place value position is 10 times the position to its right—ones become tens (×10), tens become hundreds (×10), hundreds become thousands (×10). This means that the same digit in adjacent places has values that differ by a factor of 10. In the number 4,440, the digit 4 appears in the thousands place (value 4,000) and the hundreds place (value 400), requiring students to calculate 4,000 ÷ 400. Choice C is correct because dividing the larger value by the smaller value: 4,000 ÷ 400 = 10. This demonstrates understanding that adjacent place values have a 10-to-1 relationship. Choice D represents using 100 instead of 10 (confused with non-adjacent places), which happens when students think about the relationship between thousands and tens instead of adjacent places. To help students: Use place value charts or base-ten blocks to show that 1 hundred = 10 tens, 1 thousand = 10 hundreds. Emphasize the pattern: moving one place to the left multiplies by 10, moving one place to the right divides by 10. Use numbers with repeating digits (4,440, 7,777) to make the relationship clear.