Determine Unknown Whole Numbers
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1st Grade Math › Determine Unknown Whole Numbers
What number goes in the blank: $ + 3 = 10$?
3
6
7
13
Explanation
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 ? + b = c), we work backwards by subtracting the known addend from the result: c - b = ?. We can check by adding the found number back: ? + b should equal c. The equation is ___ + 3 = 10. Choice C is correct because subtracting 10 - 3 = 7, and we can verify: 7 + 3 = 10. Choice A is a common error where students add the given numbers instead of subtracting, like 10 + 3 = 13, which happens because working backwards is less intuitive and they may try the wrong operation. To help students: Teach each unknown position explicitly (result, addend, start); show how to check answer by substituting back into equation; for start unknown, explicitly teach 'work backwards' by subtracting known addend from result; use part-part-whole diagrams to visualize relationships; practice with concrete examples using objects; show related fact families (if 7 + 3 = 10, then 10 - 3 = 7); emphasize checking: substitute answer back into equation to verify it's true; provide many examples with unknowns in all positions.
Complete the equation: $\square - 2 = 8$
6
8
10
12
Explanation
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 minuend in subtraction (like in ? - b = c), we work backwards by adding the subtrahend to the result: c + b = ?. We can check by subtracting: ? - b should equal c. The equation is □ - 2 = 8. Choice A is correct because adding 8 + 2 = 10, and we can verify: 10 - 2 = 8. Choice D is a common error where students multiply or use a different operation, like 8 x 2 - something leading to 12, which happens because working backwards is less intuitive. To help students: Teach each unknown position explicitly (result, addend, start); show how to check answer by substituting back into equation; for minuend unknown, explicitly teach 'work backwards' by adding subtrahend to result; use part-part-whole diagrams to visualize relationships; practice with concrete examples using objects; show related fact families (if 10 - 2 = 8, then 8 + 2 = 10); emphasize checking: substitute answer back into equation to verify it's true; provide many examples with unknowns in all positions.
What number makes this equation true: $18 - 9 = ?$
8
9
10
27
Explanation
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.
Solve: $\square - 5 = 7$. What is $\square$?
2
7
12
13
Explanation
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 minuend in subtraction (like in ? - b = c), we work backwards by adding the subtrahend to the result: c + b = ?. We can check by subtracting: ? - b should equal c. The equation is □ - 5 = 7. Choice B is correct because 7 + 5 = 12, and we can verify: 12 - 5 = 7. Choice A is a common error where students subtract instead of adding, getting 7 - 5 = 2; this happens because working backwards is less intuitive and they don't use the inverse operation. To help students: Teach each unknown position explicitly (result, subtrahend, minuend); show how to check answer by substituting back into equation; for minuend unknown, explicitly teach 'work backwards' by adding subtrahend to result; use part-part-whole diagrams to visualize relationships; practice with concrete examples using objects; show related fact families (if 12-5=7, then 7+5=12); emphasize checking: substitute answer back into equation to verify it's true.
What number goes in the blank: $\square + 8 = 13$?
5
6
8
21
Explanation
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.
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?
$$15 - 9 = ?$$
$$? + 15 = 9$$
$$9 - ? = 15$$
$$9 + ? = 15$$
Explanation
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.
Sarah had 14 crayons. She lost some crayons and now has 6 crayons left. What number belongs in the box? $$14 - \square = 6$$
7
8
9
20
Explanation
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.
Emma writes the equation $$6 + 4 = 5 + ?$$. What number makes both sides equal?
4
5
6
10
Explanation
The left side equals 6 + 4 = 10. For the equation to be true, the right side must also equal 10. So 5 + ? = 10, which means ? = 5. Choice A (4) gives 5 + 4 = 9. Choice C (6) gives 5 + 6 = 11. Choice D (10) gives 5 + 10 = 15.
Ben has 7 toy cars. His sister has some toy cars too. Together they have 13 toy cars. Which two equations both show how many cars Ben's sister has?
$$7 + ? = 13$$ and $$13 - 7 = ?$$
$$7 + ? = 13$$ and $$7 - ? = 13$$
$$? + 13 = 7$$ and $$13 + 7 = ?$$
$$? - 7 = 13$$ and $$13 + ? = 7$$
Explanation
Ben has 7 cars, sister has ? cars, total is 13. This gives us 7 + ? = 13. We can also write this as 13 - 7 = ? (total minus Ben's cars equals sister's cars). Both equations find the same unknown. Choice B mixes addition and subtraction incorrectly. Choice C has the wrong relationships. Choice D uses incorrect operations.
Maria has some stickers. She gives 4 stickers to her friend and has 7 stickers left. Which equation shows how many stickers Maria had at the start?
$$? - 4 = 7$$
$$7 - 4 = ?$$
$$? + 4 = 7$$
$$4 + 7 = ?$$
Explanation
Maria started with some unknown number of stickers (?), gave away 4, and had 7 left. This gives us ? - 4 = 7. Choice A incorrectly adds instead of subtracts. Choice C finds the total after giving away, not the original amount. Choice D finds how many were given away, not the original amount.