When comparing numbers, you first need to convert all forms to the same representation to see their true values clearly.

Let's convert each number to standard form. Card 1 says "twenty-eight thousand, four hundred six," which equals $$28,406$$. Card 2 shows $$20,000 + 8,000 + 400 + 60 = 28,460$$. The board shows $$28,460$$.

Now you can see the three numbers are: $$28,406$$, $$28,460$$, and $$28,460$$. Since two numbers are identical ($$28,460$$), and one is smaller ($$28,406$$), the arrangement from greatest to least is $$28,460 > 28,460 > 28,406$$. This matches answer choice C, which correctly identifies that Card 2 and the board number are equal.

Looking at the wrong answers: Choice A incorrectly states the numbers as $$28,460 > 28,406 > 28,046$$, but none of our numbers equals $$28,046$$ - this misreads Card 1. Choice B claims Card 1 and Card 2 are the same value, but Card 1 is $$28,406$$ while Card 2 is $$28,460$$ - they're different. Choice D suggests Card 1 has the largest value, but $$28,406$$ is actually the smallest of the three numbers.

Study tip: When comparing numbers in different forms (words, expanded notation, numerals), always convert everything to the same format first. This prevents confusion and helps you spot which numbers are actually equal. Pay close attention to place values when converting from words to numbers.

Code A: $$60,000 + 8,000 + 0 + 90 + 4 = 68,094$$. Code B: 'sixty-eight thousand, ninety-five' = $$68,095$$. Comparing: $$68,094$$ vs $$68,095$$. All digits are the same except the ones place: $$4 < 5$$, so $$68,094 < 68,095$$, meaning Code B > Code A. Choice A has correct numbers but wrong inequality. Choice C incorrectly calculates Code A as $$68,904$$. Choice D incorrectly calculates both codes.

All three students wrote the same number. Student A's expanded form: $$50,000 + 2,000 + 80 + 7 = 52,087$$. Student B's word form 'fifty-two thousand, eighty-seven' also equals $$52,087$$. So Student C wrote $$52,087$$. Comparing to $$52,870$$: both have same ten-thousands, thousands, and hundreds digits, but in the tens place, $$0 < 7$$, so $$52,087 < 52,870$$. Choice B has correct numeral but wrong inequality direction. Choices C and D incorrectly identify Student C's number as $$52,807$$.

When comparing large numbers, you need to convert them to the same form and then compare place values systematically from left to right, just like reading.

First, let's convert the expanded form to standard form: $$80,000 + 7,000 + 0 + 50 + 3 = 87,053$$. The word form "eighty-seven thousand, fifty-four" equals $$87,054$$. Now you're comparing $$87,053$$ and $$87,054$$.

To compare numbers with the same number of digits, start from the leftmost place value and work right until you find a difference. Both numbers have $$8$$ in the ten-thousands place and $$7$$ in the thousands place. Both have $$0$$ in the hundreds place and $$5$$ in the tens place. The first difference appears in the ones place: $$3 < 4$$. Since $$3 < 4$$, we know $$87,053 < 87,054$$.

Choice A is wrong because having the same digits in some places doesn't make numbers equal—you must check all place values. Choice B incorrectly suggests that having a zero in the hundreds place makes a number larger, when actually both numbers have zero in the hundreds place, and zeros don't increase a number's value. Choice D is wrong because it claims the word form has "larger tens and hundreds digits," but both numbers have identical tens digits (5) and hundreds digits (0).

Remember: when comparing numbers, convert to the same form first, then compare place values from left to right until you find the first difference. That difference determines which number is larger.

When you see a question about writing numbers in expanded form, you need to break down each digit according to its place value position. Think of expanded form as showing exactly what each digit contributes to the total number.

Let's work through "eighty-six thousand, four hundred nine" step by step. First, write it in standard form: 86,409. Now examine each digit's place value:

• 8 is in the ten-thousands place: $$8 \times 10,000 = 80,000$$
• 6 is in the thousands place: $$6 \times 1,000 = 6,000$$
• 4 is in the hundreds place: $$4 \times 100 = 400$$
• 0 is in the tens place: $$0 \times 10 = 0$$
• 9 is in the ones place: $$9 \times 1 = 9$$

So the complete expanded form is $$80,000 + 6,000 + 400 + 0 + 9$$, which matches answer choice D.

Looking at the wrong answers: Choice A incorrectly shows 90 instead of 9, suggesting confusion about the tens place. Choice B writes $$60,000$$ instead of $$6,000$$, misplacing the 6 in the ten-thousands rather than thousands place. Choice C combines the first two terms into $$86,000$$, which isn't true expanded form since it doesn't break down every single digit.

Remember this strategy: When writing expanded form, account for every digit in every place value position, even if it's zero. Write out each place value separately rather than combining terms, and double-check that each digit matches its correct place value.

When comparing large numbers, you need to work systematically from left to right, starting with the highest place value. First, let's convert Maria's expanded form into standard form: $$40,000 + 7,000 + 200 + 60 + 5 = 47,265$$. Now you're comparing $$47,265$$ and $$49,312$$.

To compare these five-digit numbers, start with the ten-thousands place (the leftmost digit). In $$47,265$$, the ten-thousands digit is $$4$$. In $$49,312$$, the ten-thousands digit is $$9$$. Since $$4 < 9$$, you know immediately that $$47,265 < 49,312$$. When digits in the highest place value are different, you don't need to check any other digits.

Choice A is wrong because having "more digits in the thousands place" doesn't make sense - each number has exactly one thousands digit. The comparison is also backwards. Choice B makes an error by focusing on the thousands digits ($$7$$ and $$3$$) instead of starting with the highest place value. While $$7 > 3$$ is true, the ten-thousands place determines the relationship. Choice C incorrectly assumes equal numbers of digits means equal value - both numbers have five digits, but that doesn't make them equal.

Choice D correctly identifies that $$47,265 < 49,312$$ because $$4 < 9$$ in the ten-thousands place.

Strategy tip: Always compare numbers by starting with the leftmost (highest place value) digit and working right. As soon as you find digits that are different, you can determine which number is larger without checking the remaining digits.

This question tests 4th grade ability to read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form, and to compare numbers using place value understanding (CCSS.4.NBT.2). Multi-digit numbers can be represented in three main forms: standard form (digits with commas like 45,678), word form (words like 'forty-five thousand, six hundred seventy-eight'), and expanded form (place values added like 40,000 + 5,000 + 600 + 70 + 8). When comparing numbers, we examine digits from left to right, starting with the highest place value—whichever number has the larger digit in the leftmost differing position is the greater number. The numbers 256,431 and 265,134 need to be compared, requiring students to compare place values from left to right and recognize the tens of thousands place as the first difference. Choice C is correct because it uses '<' to show 256,431 < 265,134, as the 5 in tens of thousands is less than 6. Choice B fails by using '>', which would be wrong as it reverses the comparison, often when students compare rightmost digits first. To help students: Line up numbers by place value and compare left to right—first difference determines which is greater. Emphasize that zero holds a place but represents 'none,' and watch for comparing from the right instead of left.

This question tests 4th grade ability to read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form, and to compare numbers using place value understanding (CCSS.4.NBT.2). Multi-digit numbers can be represented in three main forms: standard form (digits with commas like 45,678), word form (words like 'forty-five thousand, six hundred seventy-eight'), and expanded form (place values added like 40,000 + 5,000 + 600 + 70 + 8). When comparing numbers, we examine digits from left to right, starting with the highest place value—whichever number has the larger digit in the leftmost position is the greater number. The numbers 271,608 and 271,680 need to be compared, requiring students to compare place values from left to right and recognize zero as a placeholder. Choice B is correct because it correctly compares the tens place, showing 271,680 is greater than 271,608. Choice A represents comparing rightmost digits instead of leftmost, which happens when students compare rightmost digits first instead of leftmost. To help students: For comparing, line up numbers by place value and compare left to right—first difference determines which is greater. Use place value charts to show each digit's position and value. Emphasize that zero holds a place but represents 'none' of that place value (271,608 = two hundred seventy-one thousand, six hundred [zero tens,] eight).

This question tests 4th grade ability to read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form, and to compare numbers using place value understanding (CCSS.4.NBT.2). Multi-digit numbers can be represented in three main forms: standard form (digits with commas like $45,678$), word form (words like 'forty-five thousand, six hundred seventy-eight'), and expanded form (place values added like $40,000 + 5,000 + 600 + 70 + 8$). When comparing numbers, we examine digits from left to right, starting with the highest place value—whichever number has the larger digit in the leftmost position is the greater number. The numbers $64,918$ and $64,891$ need to be compared, requiring students to compare place values from left to right, focusing on the hundreds place where they first differ. Choice B is correct because it uses '>' to show $64,918 > 64,891$, as the hundreds digit $9 > 8$, demonstrating proper comparison. Choice A represents the wrong symbol by reversing the inequality, which happens when students compare rightmost digits instead of leftmost. To help students: Line up numbers by place value and compare left to right; practice with charts. Emphasize the first difference determines which is greater, and watch for comparing backwards.

This question tests 4th grade ability to read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form, and to compare numbers using place value understanding (CCSS.4.NBT.2). Multi-digit numbers can be represented in three main forms: standard form (digits with commas like 45,678), word form (words like 'forty-five thousand, six hundred seventy-eight'), and expanded form (place values added like 40,000 + 5,000 + 600 + 70 + 8). When comparing numbers, we examine digits from left to right, starting with the highest place value—whichever number has the larger digit in the leftmost position is the greater number. The word form 'ninety-two thousand, six hundred fifteen' needs to be converted to standard form, requiring students to recognize place values like ninety-two thousand as 92,000 and six hundred fifteen as 615. Choice B is correct because it properly represents the value as 92,615, with correct comma placement and digit positioning, demonstrating understanding of place value and number representation. Choice A represents misplacing the digits by swapping 1 and 5, which happens when students don't understand the grouping in word form like 'six hundred fifteen' meaning 615. To help students: For word form, practice reading aloud and mapping to digits; use place value charts to align words to positions. Watch for common errors like omitting commas or adding unnecessary zeros, and emphasize comparing by lining up place values.