Number Forms
What is the value of the 7 in 374,218?
70,000
In 44,218, what is the value of each 4?
4,000
Compare 45,218 ___ 45,281
Write both numbers and use <, >, =
45,218 < 45,281
Round 6,482 to nearest thousand.
6,000
True or False?
In 225,418, both 2s have the same value.
False.
200,000 ≠ 20,000.
Write 506,032 in expanded form.
500,000 + 6,000 + 30 +2
Complete:
6,000 × 10 = ______
60,000
Compare 307,419 ___ 307,391
Write both numbers and use <, >, =
307,419 > 307,391
Round 38,719 to nearest thousand.
39,000
Agree or disagree?
“In 660,315, the first 6 is worth 10 times as much as the second 6.”
Students must provide the evidence for the points.
Agree.
600,000 = 60,000 × 10.
⭐ DOUBLE POINTS
Write this number in standard form (with proper commas):
eight hundred four thousand, two hundred seventeen
804,217
In 330,418, how many times greater is the value of the first 3 than the second 3?
10 times greater
Compare 582,614 ___ 582,641
Write both numbers and use <, >, =
582,614 < 582,641
Round 682,419 to nearest ten thousand.
680,000
A student says: “405,218 is greater than 405,281 because 8 is greater than 2.”
Is the student's argument reasonable? Explain.
No.
Compare from the greatest place. The first difference is in the tens place: 1 ten < 8 tens
Therefore:
405,218 < 405,281
Write 620,405 in word form.
six hundred twenty thousand, four hundred five
Ms. Ka says:
“In 770,215, the first 7 is worth 100 times as much as the second 7.”
Is Ms. Ka correct? Prove it.
SPECIAL CARD: Students only get the points if they catch the teacher's mistake AND prove it.
No.
First 7 = 700,000
Second 7 = 70,000
70,000 × 10 = 700,000
Therefore, the first 7 is 10 times the value of the second 7
Which digit/place proves that 674,281 > 674,218?
The 8 in the tens place
Round 347,821 to nearest hundred thousand.
300,000
A student says: “347,821 rounds to 350,000 when rounded to the nearest ten thousand.”
Prove or disprove the statement.
True.
The ten-thousands digit is 4.
The digit directly to its right is 7.
Since 7 ≥ 5, the 4 rounds up to 5.
347,821 → 350,000
A student writes:
403,072 = 400,000 + 3,000 + 700 + 2
Find the mistake and write the correct expanded form.
The student used 700 instead of 70.
403,072 = 400,000 + 3,000 + 70 + 2
Complete the relationship:
8,000 → 80,000 → 800,000
Explain what happens to the value of the 8 each time it moves one place to the left.
Its value becomes 10 times greater each time.
A student says 529,481 > 529,841 because 4 > 8. Find the mistake and explain.
8 > 4.
The open symbol eats the larger number
A student says 452,681 rounds to 452,000 when rounded to the nearest thousand. Agree or disagree? Prove it.
No, because the 6 in the hundreds place value makes the 2 round up.
453,000
Conjecture:
“If the same digit appears twice next to each other in a number, the digit on the left is always worth 10 times as much as the digit on the right.”
Prove or disprove it.
SPECIAL CARD — STEAL: The selecting team gets the first opportunity to Decide → Prove → Explain. If their argument is incomplete, another team can steal the $500 by giving a complete mathematical argument.
The statement is true for adjacent places in our base-ten place-value system.
Example:
55,000
First 5 = 50,000
Second 5 = 5,000
5,000 × 10 = 50,000