This question tests understanding division as an unknown-factor problem (CCSS.3.OA.6), specifically recognizing that division can be solved by finding the missing factor in a multiplication equation. Division and multiplication are inverse operations—they undo each other. When you see a division problem like 72÷9, you can think of it as a multiplication question: "What number times 9 equals 72?" or "9 times what number equals 72?" This is the same as solving the equation ?×9=72 or 9×?=72. If you know your multiplication facts, you can use them to divide: Since 8×9=72, then 72÷9=8. The missing factor (8) is the quotient. Fact families show this relationship: 8×9=72, 9×8=72, 72÷8=9, 72÷9=8 are all related. In this problem, we need to find 72÷9 by thinking 9×?=72. Using the missing factor approach: We know 9×8=72 from multiplication facts, so 72÷9=8. Choice C is correct because 8×9=72, so 8 is the missing factor that makes 72 when multiplied by 9, which means 72÷9=8. This demonstrates understanding that division finds the unknown factor in multiplication. Choice D is incorrect because it provides 81, which might come from 9×9=81 instead of using the correct fact; this error occurs when students make calculation errors or use wrong numbers. To help students understand division as missing factor: Explicitly teach the connection—"72÷9 means: what times 9 equals 72?" Practice fact families: if 7×6=42, then 42÷7=6 (division finds the other factor). Use arrays: "9 rows of how many equals 72 total? 9×?=72" Model thinking aloud: "I need to find 56÷7. I think: 7 times what equals 56? I know 7×8=56, so 56÷7=8." Have students write both equations (division and missing factor multiplication) side by side. Check division answers by multiplying (if 72÷9=8, check: does 8×9=72? Yes!). This reinforces the inverse relationship. Watch for students who can multiply but struggle with division—show them they already know division by knowing multiplication facts.

This question tests understanding division as an unknown-factor problem (CCSS.3.OA.6), specifically recognizing that division can be solved by finding the missing factor in a multiplication equation. Division and multiplication are inverse operations—they undo each other. When you see a division problem like 32÷8, you can think of it as a multiplication question: "What number times 8 equals 32?" or "8 times what number equals 32?" This is the same as solving the equation ?×8=32 or 8×?=32. If you know your multiplication facts, you can use them to divide: Since 4×8=32, then 32÷8=4. The missing factor (4) is the quotient. Fact families show this relationship: 4×8=32, 8×4=32, 32÷4=8, 32÷8=4 are all related. In this problem, we need to find 32÷8 for an array with 32 dots in 8 rows, which means finding dots per row as the missing factor in 8×?=32. Using the missing factor approach: Think: what times 8 equals 32? Answer: 4, because 4×8=32. Choice B is correct because 4×8=32, so 4 is the missing factor that makes 32 when multiplied by 8, which means 32÷8=4. This demonstrates understanding that division finds the unknown factor in multiplication. Choice C is incorrect because it provides 8, which is the number of rows (divisor) instead of solving for the missing factor 4; this error occurs when students confuse the roles of the numbers in the equation or don't connect multiplication to division. To help students understand division as missing factor: Explicitly teach the connection—"32÷8 means: what times 8 equals 32?" Practice fact families: if 7×6=42, then 42÷7=6 (division finds the other factor). Use arrays: "8 rows of how many equals 32 total? 8×?=32" Model thinking aloud: "I need to find 56÷7. I think: 7 times what equals 56? I know 7×8=56, so 56÷7=8." Have students write both equations (division and missing factor multiplication) side by side. Check division answers by multiplying (if 32÷8=4, check: does 4×8=32? Yes!). This reinforces the inverse relationship. Watch for students who can multiply but struggle with division—show them they already know division by knowing multiplication facts.

This question tests understanding division as an unknown-factor problem (CCSS.3.OA.6), specifically recognizing that division can be solved by finding the missing factor in a multiplication equation. Division and multiplication are inverse operations—they undo each other. When you see a division problem like 24÷6, you can think of it as a multiplication question: "What number times 6 equals 24?" or "6 times what number equals 24?" This is the same as solving the equation ?×6=24 or 6×?=24. If you know your multiplication facts, you can use them to divide: Since 4×6=24, then 24÷6=4. The missing factor (4) is the quotient. Fact families show this relationship: 4×6=24, 6×4=24, 24÷4=6, 24÷6=4 are all related. In this problem, we need to solve 24÷6 using the missing factor equation 6×?=24. Using the missing factor approach: We know 6×4=24 from multiplication facts, so 24÷6=4. Choice A is correct because 4×6=24, so 4 is the missing factor that makes 24 when multiplied by 6, which means 24÷6=4. This demonstrates understanding that division finds the unknown factor in multiplication. Choice B is incorrect because it provides 6, which is the known factor (divisor) instead of solving for the missing factor 4; this error occurs when students confuse the roles of the numbers in the equation or don't connect multiplication to division. To help students understand division as missing factor: Explicitly teach the connection—"24÷6 means: what times 6 equals 24?" Practice fact families: if 7×6=42, then 42÷7=6 (division finds the other factor). Use arrays: "6 rows of how many equals 24 total? 6×?=24" Model thinking aloud: "I need to find 56÷7. I think: 7 times what equals 56? I know 7×8=56, so 56÷7=8." Have students write both equations (division and missing factor multiplication) side by side. Check division answers by multiplying (if 24÷6=4, check: does 4×6=24? Yes!). This reinforces the inverse relationship. Watch for students who can multiply but struggle with division—show them they already know division by knowing multiplication facts.

This question tests understanding division as an unknown-factor problem (CCSS.3.OA.6), specifically recognizing that division can be solved by finding the missing factor in a multiplication equation. Division and multiplication are inverse operations—they undo each other. When you see a division problem like 35÷7, you can think of it as a multiplication question: "What number times 7 equals 35?" or "7 times what number equals 35?" This is the same as solving the equation ?×7=35 or 7×?=35. If you know your multiplication facts, you can use them to divide: Since 5×7=35, then 35÷7=5. The missing factor (5) is the quotient. Fact families show this relationship: 5×7=35, 7×5=35, 35÷5=7, 35÷7=5 are all related. In this problem, we need to solve 35÷7 by thinking 7×?=35. Using the missing factor approach: We know 7×5=35 from multiplication facts, so 35÷7=5. Choice C is correct because 5×7=35, so 5 is the missing factor that makes 35 when multiplied by 7, which means 35÷7=5. This demonstrates understanding that division finds the unknown factor in multiplication. Choice B is incorrect because it provides 42, which might come from multiplying 7×6=42 instead of using the correct fact; this error occurs when students make calculation errors or use wrong numbers. To help students understand division as missing factor: Explicitly teach the connection—"35÷7 means: what times 7 equals 35?" Practice fact families: if 7×6=42, then 42÷7=6 (division finds the other factor). Use arrays: "7 rows of how many equals 35 total? 7×?=35" Model thinking aloud: "I need to find 56÷7. I think: 7 times what equals 56? I know 7×8=56, so 56÷7=8." Have students write both equations (division and missing factor multiplication) side by side. Check division answers by multiplying (if 35÷7=5, check: does 5×7=35? Yes!). This reinforces the inverse relationship. Watch for students who can multiply but struggle with division—show them they already know division by knowing multiplication facts.

This question tests understanding division as an unknown-factor problem (CCSS.3.OA.6), specifically recognizing that division can be solved by finding the missing factor in a multiplication equation. Division and multiplication are inverse operations—they undo each other. When you see a division problem like 42÷6, you can think of it as a multiplication question: "What number times 6 equals 42?" or "6 times what number equals 42?" This is the same as solving the equation ?×6=42 or 6×?=42. If you know your multiplication facts, you can use them to divide: Since 7×6=42, then 42÷6=7. The missing factor (7) is the quotient. Fact families show this relationship: 7×6=42, 6×7=42, 42÷7=6, 42÷6=7 are all related. In this problem, we need to use the fact family with 6, 7, and 42 to find 42÷6. Using the missing factor approach: From the fact family, since 6×7=42, then 42÷6=7. Choice C is correct because 7×6=42, so 7 is the missing factor that makes 42 when multiplied by 6, which means 42÷6=7. This demonstrates understanding that division finds the unknown factor in multiplication. Choice A is incorrect because it provides 6, which is the divisor instead of solving for the missing factor 7; this error occurs when students confuse the roles of the numbers in the fact family or don't connect multiplication to division. To help students understand division as missing factor: Explicitly teach the connection—"42÷6 means: what times 6 equals 42?" Practice fact families: if 7×6=42, then 42÷7=6 (division finds the other factor). Use arrays: "6 rows of how many equals 42 total? 6×?=42" Model thinking aloud: "I need to find 56÷7. I think: 7 times what equals 56? I know 7×8=56, so 56÷7=8." Have students write both equations (division and missing factor multiplication) side by side. Check division answers by multiplying (if 42÷6=7, check: does 7×6=42? Yes!). This reinforces the inverse relationship. Watch for students who can multiply but struggle with division—show them they already know division by knowing multiplication facts.

This question tests understanding division as an unknown-factor problem (CCSS.3.OA.6), specifically recognizing that division can be solved by finding the missing factor in a multiplication equation. Division and multiplication are inverse operations—they undo each other. When you see a division problem like 56÷8, you can think of it as a multiplication question: "What number times 8 equals 56?" or "8 times what number equals 56?" This is the same as solving the equation ?×8=56 or 8×?=56. If you know your multiplication facts, you can use them to divide: Since 7×8=56, then 56÷8=7. The missing factor (7) is the quotient. Fact families show this relationship: 7×8=56, 8×7=56, 56÷7=8, 56÷8=7 are all related. In this problem, we need to find 56÷8 using the missing factor 8×?=56. Using the missing factor approach: We know 8×7=56 from multiplication facts, so 56÷8=7. Choice C is correct because 7×8=56, so 7 is the missing factor that makes 56 when multiplied by 8, which means 56÷8=7. This demonstrates understanding that division finds the unknown factor in multiplication. Choice D is incorrect because it multiplies 8×8=64 instead of dividing or finding the correct missing factor; this error occurs when students confuse operations or use wrong numbers. To help students understand division as missing factor: Explicitly teach the connection—"56÷8 means: what times 8 equals 56?" Practice fact families: if 7×6=42, then 42÷7=6 (division finds the other factor). Use arrays: "8 rows of how many equals 56 total? 8×?=56" Model thinking aloud: "I need to find 56÷7. I think: 7 times what equals 56? I know 7×8=56, so 56÷7=8." Have students write both equations (division and missing factor multiplication) side by side. Check division answers by multiplying (if 56÷8=7, check: does 7×8=56? Yes!). This reinforces the inverse relationship. Watch for students who can multiply but struggle with division—show them they already know division by knowing multiplication facts.

This question tests understanding division as an unknown-factor problem (CCSS.3.OA.6), specifically recognizing that division can be solved by finding the missing factor in a multiplication equation. Division and multiplication are inverse operations—they undo each other. When you see a division problem like 42÷6, you can think of it as a multiplication question: "What number times 6 equals 42?" or "6 times what number equals 42?" This is the same as solving the equation ?×6=42 or 6×?=42. If you know your multiplication facts, you can use them to divide: Since 7×6=42, then 42÷6=7. The missing factor (7) is the quotient. Fact families show this relationship: 7×6=42, 6×7=42, 42÷7=6, 42÷6=7 are all related. In this problem, we need to find 42÷6 for 42 stickers in 6 equal groups, which means finding stickers per group as the missing factor in 6×?=42. Using the missing factor approach: Think: what times 6 equals 42? Answer: 7, because 7×6=42. Choice A is correct because 7×6=42, so 7 is the missing factor that makes 42 when multiplied by 6, which means 42÷6=7. This demonstrates understanding that division finds the unknown factor in multiplication. Choice B is incorrect because it provides 6, which is the number of groups (divisor) instead of solving for the missing factor 7; this error occurs when students confuse the roles of the numbers in the equation or don't connect multiplication to division. To help students understand division as missing factor: Explicitly teach the connection—"42÷6 means: what times 6 equals 42?" Practice fact families: if 7×6=42, then 42÷7=6 (division finds the other factor). Use arrays: "6 rows of how many equals 42 total? 6×?=42" Model thinking aloud: "I need to find 56÷7. I think: 7 times what equals 56? I know 7×8=56, so 56÷7=8." Have students write both equations (division and missing factor multiplication) side by side. Check division answers by multiplying (if 42÷6=7, check: does 7×6=42? Yes!). This reinforces the inverse relationship. Watch for students who can multiply but struggle with division—show them they already know division by knowing multiplication facts.

This question tests understanding division as an unknown-factor problem (CCSS.3.OA.6), specifically recognizing that division can be solved by finding the missing factor in a multiplication equation. Division and multiplication are inverse operations—they undo each other. When you see a division problem like 48÷6, you can think of it as a multiplication question: "What number times 6 equals 48?" or "6 times what number equals 48?" This is the same as solving the equation ?×6=48 or 6×?=48. If you know your multiplication facts, you can use them to divide: Since 8×6=48, then 48÷6=8. The missing factor (8) is the quotient. Fact families show this relationship: 8×6=48, 6×8=48, 48÷8=6, 48÷6=8 are all related. In this problem, we need to identify which multiplication equation helps solve 48÷6 as a missing factor. Using the missing factor approach: The equation 6×?=48 directly represents the division 48÷6. Choice A is correct because the equation 6×8=48 directly represents the division 48÷6 as a missing factor problem. This demonstrates understanding that division finds the unknown factor in multiplication. Choice B is incorrect because it multiplies 48×6=288 but rearranges the numbers incorrectly and doesn't solve for the missing factor; this error occurs when students confuse operations or use wrong numbers. To help students understand division as missing factor: Explicitly teach the connection—"48÷6 means: what times 6 equals 48?" Practice fact families: if 7×6=42, then 42÷7=6 (division finds the other factor). Use arrays: "6 rows of how many equals 48 total? 6×?=48" Model thinking aloud: "I need to find 56÷7. I think: 7 times what equals 56? I know 7×8=56, so 56÷7=8." Have students write both equations (division and missing factor multiplication) side by side. Check division answers by multiplying (if 48÷6=8, check: does 8×6=48? Yes!). This reinforces the inverse relationship. Watch for students who can multiply but struggle with division—show them they already know division by knowing multiplication facts.

This question tests understanding division as an unknown-factor problem (CCSS.3.OA.6), specifically recognizing that division can be solved by finding the missing factor in a multiplication equation. Division and multiplication are inverse operations—they undo each other. When you see a division problem like 32÷8, you can think of it as a multiplication question: "What number times 8 equals 32?" or "8 times what number equals 32?" This is the same as solving the equation ?×8=32 or 8×?=32. If you know your multiplication facts, you can use them to divide: Since 4×8=32, then 32÷8=4. The missing factor (4) is the quotient. Fact families show this relationship: 4×8=32, 8×4=32, 32÷4=8, 32÷8=4 are all related. In this problem, we need to find 32÷8 by thinking what times 8 equals 32. Using the missing factor approach: Think: what times 8 equals 32? Answer: 4, because 4×8=32. Choice B is correct because 4×8=32, so 4 is the missing factor that makes 32 when multiplied by 8, which means 32÷8=4. This demonstrates understanding that division finds the unknown factor in multiplication. Choice A is incorrect because it provides 8, which is the known factor (divisor) instead of solving for the missing factor 4; this error occurs when students confuse the roles of the numbers in the equation or don't connect multiplication to division. To help students understand division as missing factor: Explicitly teach the connection—"32÷8 means: what times 8 equals 32?" Practice fact families: if 7×6=42, then 42÷7=6 (division finds the other factor). Use arrays: "8 rows of how many equals 32 total? 8×?=32" Model thinking aloud: "I need to find 56÷7. I think: 7 times what equals 56? I know 7×8=56, so 56÷7=8." Have students write both equations (division and missing factor multiplication) side by side. Check division answers by multiplying (if 32÷8=4, check: does 4×8=32? Yes!). This reinforces the inverse relationship. Watch for students who can multiply but struggle with division—show them they already know division by knowing multiplication facts.

This question tests understanding division as an unknown-factor problem (CCSS.3.OA.6), specifically recognizing that division can be solved by finding the missing factor in a multiplication equation. Division and multiplication are inverse operations—they undo each other. When you see a division problem like $32 \div 8$ (apples per row), you can think of it as a multiplication question: 'What number times 8 equals 32?' or '8 times what number equals 32?' This is the same as solving the equation $? \times 8 = 32$ or $8 \times ? = 32$. If you know your multiplication facts, you can use them to divide: Since $4 \times 8 = 32$, then $32 \div 8 = 4$. The missing factor (4) is the quotient. Fact families show this relationship: $4 \times 8 = 32$, $8 \times 4 = 32$, $32 \div 4 = 8$, $32 \div 8 = 4$ are all related. In this problem, we need to find how many apples per row with 32 apples in 8 rows, using $8 \times ? = 32$. Using the missing factor approach: Think: what times 8 equals 32? Answer: 4, because $4 \times 8 = 32$. Choice A is correct because $4 \times 8 = 32$, so 4 is the missing factor that makes 32 when multiplied by 8, which means $32 \div 8 = 4$ apples per row. This demonstrates understanding that division finds the unknown factor in multiplication. Choice C is incorrect because it provides 40, which might come from addition ($32 + 8 = 40$) instead of multiplication/division. This error occurs when students confuse operations. To help students understand division as missing factor: Explicitly teach the connection—'32÷8 means: what times 8 equals 32?' Practice fact families: if $7 \times 6 = 42$, then $42 \div 7 = 6$ (division finds the other factor). Use arrays: '8 rows of how many equals 32 total? $8 \times ? = 32$' Model thinking aloud: 'I need to find $56 \div 7$. I think: 7 times what equals 56? I know $7 \times 8 = 56$, so $56 \div 7 = 8$.' Have students write both equations (division and missing factor multiplication) side by side. Check division answers by multiplying (if $32 \div 8 = 4$, check: does $4 \times 8 = 32$? Yes!). This reinforces the inverse relationship. Watch for students who can multiply but struggle with division—show them they already know division by knowing multiplication facts.