Determine Unknown Whole Numbers - 1st Grade Math

1. What number makes this equation true: $8 + 8 = ?$
   Answer: 16 This question tests 1st grade ability to determine the unknown whole number in an addition or subtraction equation (CCSS.1.OA.8). When the unknown is the result in an addition equation (like in a + b = ?), we simply add the two known numbers to find the sum. We can use counting on, objects, or mental math to compute it directly. The equation is 8 + 8 = ?. Choice A is correct because 8 + 8 = 16, so ? = 16. Choice B is a common error where students make a calculation mistake, like 8 + 7 = 15 instead of 8 + 8; this happens because they may select a number close but not verify. To help students: Teach each unknown position explicitly (result, addend, start); show how to check answer by substituting back into equation; for result unknown, it's direct computation; use part-part-whole diagrams to visualize relationships; practice with concrete examples using objects; show related fact families (if 8+8=16, then 16-8=8); emphasize checking: substitute answer back into equation to verify it's true.
2. What number makes this equation true: $8 + \ ? = 13$?
   Answer: 5 This question tests 1st grade ability to determine the unknown whole number in an addition or subtraction equation (CCSS.1.OA.8). When the unknown is an addend (like in a + ? = c), we need to find what number added to a equals c, which we can do by subtracting: c - a = ?. We can also count on from a to c and count how many steps—that gives the unknown. The equation is 8 + ? = 13. Choice A is correct because when we add 8 + 5 = 13, so the unknown is 5, or subtracting 13 - 8 = 5. Choice B is a common error where students add the two given numbers, like 8 + 13 = 21, which happens because they don't recognize they need to use the inverse operation. To help students: Teach each unknown position explicitly (result, addend, start); show how to check answer by substituting back into equation; for addend unknown, connect to subtraction and 'unknown addend' thinking (covered in CCSS.1.OA.4); use part-part-whole diagrams to visualize relationships; practice with concrete examples using objects; show related fact families (if 8 + 5 = 13, then 13 - 8 = 5); emphasize checking: substitute answer back into equation to verify it's true; provide many examples with unknowns in all positions.
3. Solve: $15 - 6 = \ ?$
   Answer: 9 This question tests 1st grade ability to determine the unknown whole number in an addition or subtraction equation (CCSS.1.OA.8). When finding the result in a subtraction equation (like in 15 - 6 = ?), we simply compute the operation by subtracting the second number from the first. We can think of it as taking away 6 from 15, counting backwards or using manipulatives. The equation is 15 - 6 = ?. Choice B is correct because 15 - 6 = 9, so ? = 9. Choice A is a common error where students might add instead of subtracting, getting 15 + 6 = 21, but subtraction requires understanding removal. To help students: Teach result unknown in subtraction as direct computation; use objects to model taking away; practice with number lines; emphasize checking by adding back (9 + 6 = 15); provide varied examples.
4. Find the unknown number: $12 - \square = 7$.
   Answer: 5 This question tests 1st grade ability to determine the unknown whole number in an addition or subtraction equation (CCSS.1.OA.8). When the unknown is the subtrahend (like in 12 - ? = 7), we find what number subtracted from 12 gives 7, which can be done by subtracting: 12 - 7 = 5. We can also think of it as addition: what plus 7 equals 12, so 7 + 5 = 12. The equation is 12 - □ = 7. Choice B is correct because 12 - 5 = 7, so the unknown is 5. Choice A is a common error where students add instead, getting 12 + 7 = 19, not recognizing the need for inverse operations. To help students: Teach subtrahend unknown by connecting to addition; use fact families (12 - 5 = 7, 7 + 5 = 12); practice checking by substituting; use manipulatives; emphasize different unknown positions.
5. Which number makes this equation true? $12 = ? + 5$
   Answer: 7 We need to find what number plus 5 equals 12. Since 7 + 5 = 12, the answer is 7. Choice A (8) gives 8 + 5 = 13. Choice B (17) gives 17 + 5 = 22. Choice C (6) gives 6 + 5 = 11.
6. What number makes this equation true: $18 - 9 = ?$
   Answer: 9 This question tests 1st grade ability to determine the unknown whole number in an addition or subtraction equation (CCSS.1.OA.8). When the unknown is the result in a subtraction equation (like in a - b = ?), we simply subtract the subtrahend from the minuend to find the difference. We can use counting back, objects, or number lines to compute it directly. The equation is 18 - 9 = ?. Choice C is correct because 18 - 9 = 9, so ? = 9. Choice D is a common error where students add the numbers instead of subtracting, getting 18 + 9 = 27; this happens because they may misread the operation or not recognize the need for subtraction. To help students: Teach each unknown position explicitly (result, subtrahend, minuend); show how to check answer by substituting back into equation; for result unknown in subtraction, it's direct computation; use part-part-whole diagrams to visualize relationships; practice with concrete examples using objects; show related fact families (if 18-9=9, then 9+9=18); emphasize checking: substitute answer back into equation to verify it's true.
7. What number goes in the blank: $\square + 8 = 13$?
   Answer: 5 This question tests 1st grade ability to determine the unknown whole number in an addition or subtraction equation (CCSS.1.OA.8). When the unknown is the starting number in addition (like in ? + 8 = 13), we work backwards by subtracting the known addend from the result: 13 - 8 = 5. We can check by adding: 5 + 8 = 13. The equation is □ + 8 = 13. Choice C is correct because subtracting 13 - 8 = 5, and we can verify: 5 + 8 = 13. Choice A is a common error where students add the numbers instead of subtracting, getting 8 + 13 = 21, not using the inverse operation. To help students: Explicitly teach 'work backwards' for start unknown; use part-part-whole models; practice substitution to verify; connect to fact families; use concrete examples with objects.
8. Solve: $6 + \ ? = 14$. What is $?$
   Answer: 8 This question tests 1st grade ability to determine the unknown whole number in an addition or subtraction equation (CCSS.1.OA.8). When the unknown is an addend (like in a + ? = c), we need to find what number added to a equals c, which we can do by subtracting: c - a = ?. We can also count on from a to c and count how many steps—that gives the unknown. The equation is 6 + ? = 14. Choice B is correct because when we add 6 + 8 = 14, so the unknown is 8, or subtracting 14 - 6 = 8. Choice C is a common error where students add the two given numbers instead of subtracting, like 6 + 14 = 20, which happens because they don't recognize they need to use the inverse operation. To help students: Teach each unknown position explicitly (result, addend, start); show how to check answer by substituting back into equation; for addend unknown, connect to subtraction and 'unknown addend' thinking (covered in CCSS.1.OA.4); use part-part-whole diagrams to visualize relationships; practice with concrete examples using objects; show related fact families (if 6 + 8 = 14, then 14 - 6 = 8); emphasize checking: substitute answer back into equation to verify it's true; provide many examples with unknowns in all positions.
9. Sarah had 14 crayons. She lost some crayons and now has 6 crayons left. What number belongs in the box? $14 - \square = 6$
   Answer: 8 Sarah started with 14 crayons and has 6 left, so she lost 14 - 6 = 8 crayons. We can check: 14 - 8 = 6 ✓. Choice A (20) gives 14 - 20 = -6. Choice B (9) gives 14 - 9 = 5. Choice D (7) gives 14 - 7 = 7.
10. Find the missing number: 9 - 4 = ____.
    Answer: 5 When you see a subtraction problem like 9 - 4, you're being asked: "If I start with 9 things and take away 4, how many are left?" One great way to solve this is to count backward from the bigger number. Start at 9 and count back 4 steps: 9 → 8 → 7 → 6 → 5. After taking away 4, you land on 5. You can also check your work by adding: 5 + 4 = 9, which matches the number you started with. That confirms 5 is correct! Now let's look at why the other answers don't work. The choice 4 is the number you were subtracting, not the amount left over — it's easy to accidentally repeat a number from the problem. The choice 6 happens if you only count back 3 steps instead of 4, so you stopped one number too early. The choice 13 comes from adding 9 + 4 = 13 instead of subtracting — remember, the minus sign (-) means take away, so the answer should be smaller than 9, not bigger. A helpful strategy: whenever you subtract, the answer should be less than the number you started with. If your answer is bigger, you probably added by mistake. And you can always double-check subtraction by adding your answer back — if it returns you to the starting number, you got it right!
11. Ben has 7 toy cars. His sister has some toy cars. Together they have 13 toy cars. Which pair of equations could you use to find how many toy cars Ben's sister has?
    Answer: $7 + ? = 13$ and $13 - 7 = ?$ Both $7+?=13$ and $13-7=?$ correctly represent finding the missing number of cars Ben's sister has. $7+?=13$ and $7-?=13$ pairs a correct equation with one that uses the wrong operation. $?+13=7$ and $13+7=?$ both set up the total incorrectly. $?-7=13$ and $13+?=7$ also set up the relationship between the numbers incorrectly. Only the first pair correctly shows the missing amount using both addition and subtraction.
12. Find the missing number: 4 + ____ = 9.
    Answer: 5 When you see a problem like 4 + ____ = 9, you're being asked to find the missing part of an addition sentence. The trick is to think: "I have 4, and I want to get to 9. How many more do I need to count up?" One great way to solve this is to count up from 4 until you reach 9: 5, 6, 7, 8, 9 — that's 5 numbers, so you need to add 5. You can check your work by putting it back into the sentence: 4 + 5 = 9. It works! Now let's look at why the other answers don't fit. Choosing 4 repeats the number already in the problem, but 4 + 4 = 8, which is too small. Choosing 6 overshoots, since 4 + 6 = 10, one too many. Choosing 13 is what you get if you accidentally add the two numbers you see (4 + 9 = 13) instead of finding the missing piece — but 13 is even bigger than 9, so it can't be right when you're building up to 9. A helpful tip: whenever a number is missing in an addition sentence, you can count up from the number you have to the total, or think about subtraction — the missing number is 9 - 4 = 5. Always plug your answer back in to make sure both sides equal the same amount!
13. Jake needs to find the missing number: $\square - 3 = 9$. He says the missing number is 6, because $9 - 3 = 6$. Is Jake correct?
    Answer: No, Jake is wrong and the missing number is $12$ 12 − 3 = 9, so the missing number is 12 and Jake is wrong. 6 − 3 = 3, 9 − 3 = 6, and 27 − 3 = 24. None of those makes 9. You can find the missing number by adding 9 + 3 = 12.
14. Solve: $11 = ? + 2$. What is $?$
    Answer: 9 This question tests 1st grade ability to determine the unknown whole number in an addition or subtraction equation (CCSS.1.OA.8). When the unknown is an addend (like in ? + b = c), we need to find what number added to b equals c; we can think of this as subtraction: c - b = ?. Or we can count on from b to c and count how many—that's the unknown. The equation is 11 = ? + 2, which is the same as ? + 2 = 11. Choice B is correct because when we add 9 + 2 = 11, so the unknown is 9. Choice A is a common error where students add the two given numbers instead of subtracting, getting 11 + 2 = 13; this happens because finding unknowns in different positions requires different strategies and the inverse relationship between operations must be understood. To help students: Teach each unknown position explicitly (result, addend, start); show how to check answer by substituting back into equation; for addend unknown, connect to subtraction and 'unknown addend' thinking (covered in CCSS.1.OA.4); use part-part-whole diagrams to visualize relationships; practice with concrete examples using objects; show related fact families (if 9+2=11, then 11-2=9); emphasize checking: substitute answer back into equation to verify it's true.
15. Tom counted 9 birds in a tree. Then some more birds flew to the tree. Now there are 15 birds total. Which equation can help find how many birds flew to the tree?
    Answer: $9 + ? = 15$ Tom started with 9 birds, some unknown number (?) flew to the tree, and now there are 15 total. This gives us 9 + ? = 15. Choice B solves the problem but doesn't show the unknown. Choice C incorrectly suggests adding 15 to get 9. Choice D incorrectly uses subtraction when birds were added.
16. Find the missing number: $12 - \ ? = 7$
    Answer: 5 This question tests 1st grade ability to determine the unknown whole number in an addition or subtraction equation (CCSS.1.OA.8). When the unknown is the subtrahend in subtraction (like in a - ? = c), we find what number subtracted from a gives c by subtracting: a - c = ?. We can check by verifying a - ? = c. The equation is 12 - ? = 7. Choice D is correct because 12 - 5 = 7, so the unknown is 5. Choice A is a common error where students add instead of subtract, like 12 + 7 = 19, which happens because they may confuse the operation or not understand the inverse relationship. To help students: Teach each unknown position explicitly (result, addend, start); show how to check answer by substituting back into equation; for subtrahend unknown, connect to addition (if 12 - 5 = 7, then 7 + 5 = 12); use part-part-whole diagrams to visualize relationships; practice with concrete examples using objects; show related fact families; emphasize checking: substitute answer back into equation to verify it's true; provide many examples with unknowns in all positions.
17. Solve: $6 + ? = 14$. What is $?$
    Answer: 8 This question tests 1st grade ability to determine the unknown whole number in an addition or subtraction equation (CCSS.1.OA.8). When the unknown is an addend (like in a + ? = c), we need to find what number added to a equals c; we can think of this as subtraction: c - a = ?. Or we can count on from a to c and count how many—that's the unknown. The equation is 6 + ? = 14. Choice A is correct because when we add 6 + 8 = 14, so the unknown is 8. Choice B is a common error where students add the two given numbers instead of subtracting, getting 6 + 14 = 20; this happens because finding unknowns in different positions requires different strategies and the inverse relationship between operations must be understood. To help students: Teach each unknown position explicitly (result, addend, start); show how to check answer by substituting back into equation; for addend unknown, connect to subtraction and 'unknown addend' thinking (covered in CCSS.1.OA.4); use part-part-whole diagrams to visualize relationships; practice with concrete examples using objects; show related fact families (if 6+8=14, then 14-6=8); emphasize checking: substitute answer back into equation to verify it's true.
18. Find the missing number: $9 + \square = 14$.
    Answer: 5 This question tests 1st grade ability to determine the unknown whole number in an addition or subtraction equation (CCSS.1.OA.8). When the unknown is an addend (like in 9 + ? = 14), we need to find what number added to 9 equals 14, which can be done by subtracting: 14 - 9 = 5. We can also count on from 9 to 14 (10, 11, 12, 13, 14) and count the steps—that's 5. The equation is 9 + □ = 14. Choice A is correct because when we add 9 + 5 = 14, so the unknown is 5. Choice C is a common error where students might select the total instead of finding the missing part, not recognizing they need to use the inverse operation. To help students: Teach addend unknown by connecting to subtraction (CCSS.1.OA.4); use part-part-whole diagrams; practice checking by substituting; provide examples with objects; show fact families like if 9 + 5 = 14, then 14 - 9 = 5.
19. What number makes this equation true: $7 + 5 = \square$?
    Answer: 12 This question tests 1st grade ability to determine the unknown whole number in an addition or subtraction equation (CCSS.1.OA.8). When finding the result in an addition equation (like in a + b = ?), we simply compute the sum by adding the two addends together. We can use counting on or known facts to find the total efficiently. The equation is 7 + 5 = □. Choice B is correct because 7 + 5 = 12, so □ = 12. Choice A is a common error where students make a calculation mistake, such as adding 7 + 4 = 11 instead of 7 + 5, which happens because they may miscount or confuse the numbers. To help students: Teach each unknown position explicitly (result, addend, start); show how to check answer by substituting back into equation; for result unknown, it's direct computation; use part-part-whole diagrams to visualize relationships; practice with concrete examples using objects; emphasize checking: substitute answer back into equation to verify it's true; provide many examples with unknowns in all positions.
20. Complete the equation: $6 + \ ? = 10$.
    Answer: 4 This question tests 1st grade ability to determine the unknown whole number in an addition or subtraction equation (CCSS.1.OA.8). When the unknown is an addend (like in 6 + ? = 10), we find what number added to 6 equals 10 by subtracting: 10 - 6 = 4. Counting on from 6 to 10 (7,8,9,10) gives 4 steps. The equation is 6 + ? = 10. Choice C is correct because 6 + 4 = 10, so ? = 4. Choice B is a common error where students add the numbers, getting 6 + 10 = 16, instead of subtracting. To help students: Connect addend unknown to subtraction (CCSS.1.OA.4); use diagrams and objects; teach checking by substitution; practice fact families; vary unknown positions.

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