Compare Two-Digit Numbers - 1st Grade Math

1. Is this statement true: $56 < 52$?
   Answer: False This question tests 1st grade ability to compare two two-digit numbers using place value understanding (CCSS.1.NBT.3). To compare two-digit numbers, always start by comparing the tens place digits. The number with more tens is greater, regardless of the ones; if the tens are equal, then compare the ones place digits—the number with more ones is greater. For example, 56 is not less than 52; actually 56 > 52 because same tens but 6 ones > 2 ones. The stimulus asks if the statement 56 < 52 is true. Choice B is correct because the statement is false since 56 > 52. Choice A is a common error where students reverse the comparison, perhaps confusing symbol direction, which happens because symbol direction is easily confused. To help students: Use base-10 blocks to show visual magnitude; emphasize 'compare tens first—that's most important'; practice with number lines showing position; teach symbol direction ('mouth opens to bigger number'); compare numbers with same tens to highlight ones importance; compare numbers with different tens to show tens dominate; provide many examples of 'tricky' cases like 39 vs 41; use place value charts to organize thinking; practice writing comparison statements; connect to real contexts (scores, ages, quantities).
2. Which symbol makes this true: 43 ____ 40?
   Answer: > Whenever you see two numbers with a blank between them, your job is to be a "number detective" and figure out which one is bigger, smaller, or if they're the same. The three symbols you can use are the "greater than" sign (>), the "less than" sign (<), and the "equals" sign (=). Here, you're comparing 43 and 40. Both numbers have 4 tens, so look at the ones place: 43 has 3 ones, but 40 has 0 ones. Since 3 is more than 0, the number 43 is bigger than 40. That means you need the "greater than" sign, which points its open, hungry mouth toward the bigger number: 43 > 40. Think of the symbol like an alligator that always wants to eat the larger snack! The "less than" sign (<) is wrong because it would say 43 is smaller than 40, but 43 is actually the bigger number. The "equals" sign (=) is wrong because these two numbers are not the same — 43 and 40 are three apart, so they can't be equal. (The empty fourth choice isn't a symbol at all, so it can't make the sentence true.) A great trick to remember: the alligator mouth always opens toward the bigger number and the pointy tip points to the smaller one. Line up your numbers by tens and ones, compare, and let the hungry alligator munch the largest number!
3. Lisa arranged three numbers in order: $29$, $32$, $26$. She says this is from least to greatest. What mistake did Lisa make?
   Answer: She put the numbers in greatest to least order instead Lisa arranged the numbers from greatest to least ($32 > 29 > 26$) instead of least to greatest. The correct order from least to greatest should be $26$, $29$, $32$. She compared the numbers correctly but arranged them in the wrong order.
4. Which symbol makes this true: 45 ____ 23?
   Answer: > Whenever you see two numbers with a blank between them, your job is to compare their sizes and choose the symbol that shows which is bigger, which is smaller, or if they're equal. A helpful trick: the "greater than" (>) and "less than" (<) symbols are like a hungry mouth that always wants to eat the bigger number—the open side faces the larger amount. To compare 45 and 23, look at the tens place first. 45 has 4 tens, while 23 has only 2 tens. Since 4 tens is more than 2 tens, 45 is the bigger number. That means 45 is greater than 23, so the correct symbol is >. The open, wide side points toward 45, the larger number. The "less than" symbol (<) is wrong because it would say 45 is smaller than 23, but 45 is actually bigger—the tens place proves it. The "equal" symbol (=) is wrong because 45 and 23 are not the same number; equal only works when both sides match exactly, like 23 = 23. The blank choice (no symbol) is wrong because a comparison always needs a symbol to be true—leaving it empty doesn't tell us anything. A quick tip: always compare the tens digit first. If the tens are the same, then look at the ones. And remember the mouth trick—the open mouth always "eats" the bigger number, so point the wide side toward whichever number is larger.
5. Maya has 6 tens and 7 ones; Amir has 6 tens and 7 ones. Which symbol makes this true: 67 ____ 67?
   Answer: = Whenever you compare two numbers, a great first step is to break each one into its tens and ones. This helps you see exactly how big each number is before you decide which comparison symbol fits. Look closely at what Maya and Amir have. Maya has 6 tens and 7 ones. Six tens is 6 × 10 = 60, and 7 ones is just 7, so Maya has 60 + 7 = 67. Amir also has 6 tens and 7 ones, which is also 67. Since both numbers are made from the same amount of tens and the same amount of ones, they are exactly equal. That means the "equal to" sign, =, makes the sentence true: 67 = 67. The "less than" symbol, <, would only be correct if the first number were smaller than the second, but 67 is not smaller than 67. The "greater than" symbol, >, would only work if the first number were bigger, and 67 is not bigger than 67 — they're the same. The blank fourth choice offers no symbol at all, so it can't make a true comparison sentence. A helpful trick: when both numbers have the same digits in the same spots, they must be equal, so reach for the = sign. Remember that the open mouth of < or > always "eats" the bigger number — but when the numbers match, there's nothing bigger to eat!
6. Which is less: 40 or 43?
   Answer: 40 40 is less than 43, since it comes first when counting up. 43 is the larger of the two numbers, not the smaller one. Saying they are equal ignores that 40 and 43 are different numbers. 34 mixes up the digits of 43 and isn't one of the numbers being compared. Only 40 is correctly identified as less than 43.
7. Look at the number line. Which comparison correctly shows the relationship between $48$ and $52$?
   Answer: $48 < 52$ because $48$ is to the left of $52$ $48 < 52$ because on a number line, numbers increase from left to right. Since $48$ would be to the left of $52$, this shows $48 < 52$. We can also verify this by comparing tens and ones: both have the same tens digit ($4$ vs $5$ tens), but $4$ tens is less than $5$ tens.
8. Put these numbers in order from least to greatest: 38, 45, 52.
   Answer: 38, 45, 52 This question tests 1st grade ability to compare two two-digit numbers using place value understanding (CCSS.1.NBT.3), extended to ordering three numbers. To compare two-digit numbers, always start by comparing the tens place digits. The number with more tens is greater, regardless of the ones; if the tens are equal, then compare the ones place digits—the number with more ones is greater. For example, comparing 38, 45, 52: 38 has 3 tens (smallest), then 45 with 4 tens, then 52 with 5 tens. The stimulus requires ordering 38, 45, 52 from least to greatest. Choice D is correct because 38, 45, 52 is the order from least to greatest, as 3 tens < 4 tens < 5 tens. Choice C is a common error where students reverse the order, putting greatest first, which happens because the concept of least to greatest is still developing and they might think of descending order. To help students: Use base-10 blocks to show visual magnitude; emphasize 'compare tens first—that's most important'; practice with number lines showing position; teach symbol direction ('mouth opens to bigger number'); compare numbers with same tens to highlight ones importance; compare numbers with different tens to show tens dominate; provide many examples of 'tricky' cases like 39 vs 41; use place value charts to organize thinking; practice writing comparison statements; connect to real contexts (scores, ages, quantities).
9. Sofia has 56 stickers and Chen has 52. Who has more?
   Answer: Sofia This question tests 1st grade ability to compare two two-digit numbers using place value understanding (CCSS.1.NBT.B.3). To compare two-digit numbers, always start by comparing the tens place digits. The number with more tens is greater, regardless of the ones; if the tens are equal, then compare the ones place digits—the number with more ones is greater. The stimulus involves comparing Sofia's 56 stickers to Chen's 52 to determine who has more. Choice A (Sofia) is correct because when tens are equal (both have 5 tens), 56 > 52 since 6 ones > 2 ones. Choice B (Chen) is a common error where students only compare ones digits and ignore tens, saying 52 > 56 because 2 < 6 but mistakenly focusing on the wrong place, which happens because place value understanding is still developing. To help students: Use base-10 blocks to show visual magnitude; emphasize 'compare tens first—that's most important'; practice with number lines showing position; teach symbol direction ('mouth opens to bigger number'); compare numbers with same tens to highlight ones importance; compare numbers with different tens to show tens dominate; provide many examples of 'tricky' cases like 39 vs 41; use place value charts to organize thinking; practice writing comparison statements; connect to real contexts (scores, ages, quantities).
10. Which symbol makes this true: 67 ____ 67?
    Answer: = When you compare two numbers, you're deciding whether one is bigger, smaller, or exactly the same as the other. Three special symbols help you show this: the "less than" sign, the "greater than" sign, and the "equals" sign. The trick is to look carefully at both numbers first. Here, both numbers are 67. They have the same digits in the same places—the same 6 in the tens spot and the same 7 in the ones spot. Since the numbers are identical, they are equal, so the "equals" sign (=) is what makes the sentence true: 67 = 67. The "less than" sign (<) would say the first 67 is smaller than the second 67, but a number can't be smaller than itself. The "greater than" sign (>) would say the first 67 is bigger than the second, but a number can't be bigger than itself either. Both of those signs are only correct when the two numbers are actually different. The blank last choice offers no symbol at all, so it can't make the sentence true—every comparison needs a symbol in the middle. A handy memory trick for the future: the "greater than" and "less than" signs look like a hungry alligator's mouth, and the mouth always opens toward the bigger number. But when both numbers match exactly, the alligator isn't hungry for either side—you use the equals sign, which is just two matching lines, perfect for two matching numbers.
11. Which is less: 40 or 43?
    Answer: 40 This question tests 1st grade ability to compare two two-digit numbers using place value understanding (CCSS.1.NBT.3). To compare two-digit numbers, always start by comparing the tens place digits. The number with more tens is greater, regardless of the ones; if the tens are equal, then compare the ones place digits—the number with more ones is greater. For example, 40 < 43 because both have 4 tens, but 0 ones < 3 ones. The stimulus asks which is less between 40 and 43. Choice B is correct because 40 is less than 43 since tens are equal but 0 ones < 3 ones. Choice A is a common error where students think the number with more in ones is smaller if they ignore tens, but here it's reversed, which happens because students often focus on individual digit values rather than place value. To help students: Use base-10 blocks to show visual magnitude; emphasize 'compare tens first—that's most important'; practice with number lines showing position; teach symbol direction ('mouth opens to bigger number'); compare numbers with same tens to highlight ones importance; compare numbers with different tens to show tens dominate; provide many examples of 'tricky' cases like 39 vs 41; use place value charts to organize thinking; practice writing comparison statements; connect to real contexts (scores, ages, quantities).
12. Sofia has 5 tens and 6 ones; Chen has 5 tens and 2 ones. Which symbol makes this true: 56 ____ 52?
    Answer: > When you compare two numbers, always start with the biggest place value—here that's the tens place. Think of tens as bundles of ten sticks and ones as single sticks. Whoever has more bundles wins, and you only check the single sticks if the bundles are equal. Both Sofia and Chen have 5 tens, so their bundles are tied at 50. Now look at the ones: Sofia has 6 ones (making 56) and Chen has 2 ones (making 52). Since 6 > 2, Sofia's number is bigger. That means 56 > 52, so the greater than symbol makes the sentence true. The open, wide part of the symbol always faces the bigger number, and 56 is on the left. The less than symbol (<) would say that 56 is smaller than 52, but that's backwards—56 comes after 52 when you count, so it can't be smaller. The equals symbol (=) would mean both numbers are exactly the same, but 56 and 52 are different because their ones don't match. The blank choice isn't a comparison symbol at all, so it can't complete the sentence. A handy memory trick: picture the greater-than and less-than symbols as an alligator's mouth—the alligator is hungry and always opens wide to eat the bigger number. Here the mouth opens toward 56, giving you 56 > 52. Whenever the tens are equal, let the ones decide!
13. Which symbol makes this true: 78 ____ 25?
    Answer: > Whenever you compare two numbers, you're asking "which one is bigger?" A great trick is to think of the comparison symbols as a hungry mouth that always opens toward the larger number. The pointy end points at the smaller number. Start by comparing the numbers digit by digit. Look at the tens place first: 78 has 7 tens, while 25 has only 2 tens. Since 7 tens is more than 2 tens, you know right away that 78 is greater than 25. So the symbol should open its "mouth" toward the 78, giving you 78 > 25, the greater than symbol. Now let's check the other choices. The less than symbol (<) would say 78 is smaller than 25 — but that's backwards, since 78 is clearly the bigger number. The equals symbol (=) would say both numbers are exactly the same, but 78 and 25 are different amounts, so that can't be right. The blank fourth choice offers no symbol at all, so it can't make the sentence true either. A helpful way to remember: the open, wide side of the symbol always faces the bigger number, and the small, pointy tip faces the smaller number. When comparing two-digit numbers, always start with the tens place — whichever number has more tens is the greater one. If the tens are equal, then move on and compare the ones place.
14. Which comparison symbol makes this statement true: 45 ____ 54?
    Answer: < When you compare two numbers, you're figuring out which one is bigger, which one is smaller, or if they're equal. A helpful trick is to think of the comparison symbol as a hungry mouth that always wants to "eat" the bigger number—the open side points toward the larger value. Look at the two numbers: 45 and 54. Since both have two digits, start by comparing the tens place. The number 45 has 4 tens, while 54 has 5 tens. Because 4 tens is less than 5 tens, you know 45 is smaller than 54. That means you need the "less than" symbol, which points its small, closed tip toward the smaller number: 45 < 54. The "equals" sign (=) is wrong because these two numbers are not the same value—45 and 54 are different, even though they use the same digits in a different order. The "greater than" symbol (>) is wrong because it would say 45 is bigger than 54, but 45 is actually the smaller number. The blank choice with no symbol is wrong because a comparison statement always needs a symbol to be complete and true. A great memory aid: the open end of the symbol always faces the bigger number, and the pointy end faces the smaller one. When both numbers have the same number of digits, compare the leftmost digits first—that's the tens place here, and it decides the answer.
15. Maya has 56 stickers. Chen has 52 stickers. Who has more?
    Answer: Maya This question tests 1st grade ability to compare two two-digit numbers using place value understanding (CCSS.1.NBT.3). To compare two-digit numbers, always start by comparing the tens place digits. The number with more tens is greater, regardless of the ones; if the tens are equal, then compare the ones place digits—the number with more ones is greater. For example, 56 > 52 because when tens are equal (both have 5 tens), 6 ones > 2 ones. The stimulus shows a comparison of quantities: Maya with 56 stickers and Chen with 52 stickers, asking who has more. Choice A is correct because Maya has more since when tens are equal (both 5 tens), 6 ones > 2 ones. Choice B is a common error where students only compare ones digits and ignore tens (saying Chen has more because 2 > nothing specific, but miscounting), which happens because place value understanding is still developing. To help students: Use base-10 blocks to show visual magnitude; emphasize 'compare tens first—that's most important'; practice with number lines showing position; teach symbol direction ('mouth opens to bigger number'); compare numbers with same tens to highlight ones importance; compare numbers with different tens to show tens dominate; provide many examples of 'tricky' cases like 39 vs 41; use place value charts to organize thinking; practice writing comparison statements; connect to real contexts (scores, ages, quantities).
16. Which number is less: 56 or 52?
    Answer: 52 This question tests 1st grade ability to compare two two-digit numbers using place value understanding (CCSS.1.NBT.3). To compare two-digit numbers, always start by comparing the tens place digits. The number with more tens is greater, regardless of the ones; if the tens are equal, then compare the ones place digits—the number with more ones is greater. For example, 52 < 56 because when tens are equal (both 5 tens), 2 ones < 6 ones. The stimulus shows two numbers, 56 and 52, asking which is less. Choice B is correct because 52 is less since when tens are equal, 2 ones < 6 ones. Choice A is a common error where students think the larger ones digit makes the number smaller (confusing 56 as less), which happens because students often focus on individual digit values rather than place value. To help students: Use base-10 blocks to show visual magnitude; emphasize 'compare tens first—that's most important'; practice with number lines showing position; teach symbol direction ('mouth opens to bigger number'); compare numbers with same tens to highlight ones importance; compare numbers with different tens to show tens dominate; provide many examples of 'tricky' cases like 39 vs 41; use place value charts to organize thinking; practice writing comparison statements; connect to real contexts (scores, ages, quantities).
17. Amir has 61 cards. Keisha has 16 cards. Who has more?
    Answer: Amir This question tests 1st grade ability to compare two two-digit numbers using place value understanding (CCSS.1.NBT.3). To compare two-digit numbers, always start by comparing the tens place digits. The number with more tens is greater, regardless of the ones; if the tens are equal, then compare the ones place digits—the number with more ones is greater. For example, 61 > 16 because 6 tens > 1 ten (we don't even need to look at the ones). The stimulus shows a comparison of quantities: Amir with 61 cards and Keisha with 16 cards, asking who has more. Choice A is correct because Amir has more since 6 tens > 1 ten. Choice B is a common error where students only compare ones digits and ignore tens (saying Keisha has more because 6 > 1), which happens because place value understanding is still developing. To help students: Use base-10 blocks to show visual magnitude; emphasize 'compare tens first—that's most important'; practice with number lines showing position; teach symbol direction ('mouth opens to bigger number'); compare numbers with same tens to highlight ones importance; compare numbers with different tens to show tens dominate; provide many examples of 'tricky' cases like 39 vs 41; use place value charts to organize thinking; practice writing comparison statements; connect to real contexts (scores, ages, quantities).
18. Yuki has 4 tens and 7 ones; Carlos has 4 tens and 9 ones. Which is greater: 47 or 49?
    Answer: 49 This question tests 1st grade ability to compare two two-digit numbers using place value understanding (CCSS.1.NBT.3). To compare two-digit numbers, always start by comparing the tens place digits. The number with more tens is greater, regardless of the ones; if the tens are equal, then compare the ones place digits—the number with more ones is greater. For example, 49 > 47 because both have 4 tens, but 9 ones > 7 ones. The stimulus describes Yuki with 4 tens and 7 ones (47) and Carlos with 4 tens and 9 ones (49), asking which is greater. Choice B is correct because 49 is greater than 47 since tens are equal but 9 ones > 7 ones. Choice A is a common error where students might think fewer ones mean greater, but that's not the case, which happens because place value understanding is still developing. To help students: Use base-10 blocks to show visual magnitude; emphasize 'compare tens first—that's most important'; practice with number lines showing position; teach symbol direction ('mouth opens to bigger number'); compare numbers with same tens to highlight ones importance; compare numbers with different tens to show tens dominate; provide many examples of 'tricky' cases like 39 vs 41; use place value charts to organize thinking; practice writing comparison statements; connect to real contexts (scores, ages, quantities).
19. Jamal has 3 tens and 8 ones; Emma has 4 tens and 5 ones. Which symbol makes this true: 38 ____ 45?
    Answer: < When you compare two numbers, the trick is to look at the tens place first, because tens are worth more than ones. Think of the symbols like a hungry mouth: the open side always "eats" the bigger number, so the small end points to the smaller number. Jamal has 3 tens and 8 ones, which is 30 + 8 = 38. Emma has 4 tens and 5 ones, which is 40 + 5 = 45. Now compare the tens: Jamal has 3 tens, but Emma has 4 tens. Since 3 tens is less than 4 tens, 38 is smaller than 45. That means you write 38 < 45, with the pointy end aimed at the smaller number, 38. The "equals" choice would only be right if both numbers were exactly the same, but 38 and 45 are different, so that doesn't work. The "greater than" symbol would mean 38 is bigger than 45 — but that's backwards, because Jamal has fewer tens than Emma. Don't get tricked into thinking 38 is bigger just because 8 ones is more than 5 ones; the ones only matter when the tens are equal, and here they aren't. A smart study habit: always check the tens place first when comparing two-digit numbers. Only if the tens are the same do you move on to compare the ones. And remember — the open mouth of < or > always faces the bigger number!
20. Amir has 38 marbles and Maya has 45. Who has fewer?
    Answer: Amir This question tests 1st grade ability to compare two two-digit numbers using place value understanding (CCSS.1.NBT.B.3). To compare two-digit numbers, always start by comparing the tens place digits. The number with more tens is greater, regardless of the ones; if the tens are equal, then compare the ones place digits—the number with more ones is greater. The stimulus involves comparing Amir's 38 marbles to Maya's 45 to determine who has fewer. Choice A (Amir) is correct because 38 < 45 since 3 tens < 4 tens, and we don't need to look at the ones. Choice B (Maya) is a common error where students reverse the meaning of 'fewer,' confusing it with 'more,' which happens because the concepts are related but directionally opposite. To help students: Use base-10 blocks to show visual magnitude; emphasize 'compare tens first—that's most important'; practice with number lines showing position; teach symbol direction ('mouth opens to bigger number'); compare numbers with same tens to highlight ones importance; compare numbers with different tens to show tens dominate; provide many examples of 'tricky' cases like 39 vs 41; use place value charts to organize thinking; practice writing comparison statements; connect to real contexts (scores, ages, quantities).

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