Addition And Subtraction Fluency - 1st Grade Math

1. If $7+5=12$, what is $12-7$? Use the fact family.
   Answer: 5 This question tests 1st grade fluency in addition and subtraction within 20, with emphasis on strategies (CCSS.1.OA.6). Fact families show related addition and subtraction facts. For example, for 7 + 5 = 12, the family includes 5 + 7 = 12, 12 - 7 = 5, 12 - 5 = 7. The problem asks to use the fact family for 7 + 5 = 12 to find 12 - 7. Choice B is correct because using the known addition fact, 12 - 7 = 5 since 7 + 5 = 12. Choice C is a common error where students use the wrong operation or confuse which number to subtract, like thinking 12 - 6; this happens because the connection between addition and subtraction facts must be explicitly taught. To help students: For fact families, show all four related facts together; emphasize that facts within 10 should be automatic (fluent); provide daily practice with mixed strategies; help students select appropriate strategy for each problem type.
2. Solve $9+2$ using counting on. Start at 9 and count 2.
   Answer: 11 This question tests 1st grade fluency in addition and subtraction within 20, with emphasis on strategies (CCSS.1.OA.6). Counting on is a strategy for addition where you start with the first number and count forward by the second number. For example, for 9 + 2, start at 9 and count: 10, 11. The problem asks to use counting on to solve 9 + 2, starting at 9 and counting 2. Choice B is correct because 9 + 2: starting at 9, count on two: 10, 11. Choice C is a common error where students make a calculation error like counting one extra to 12; this happens because students may try to compute without using the strategy systematically. To help students: Practice counting on with small numbers first; use number lines or fingers to visualize; provide daily practice with mixed strategies; emphasize that facts within 10 should be automatic (fluent).
3. Complete the making-ten step: 8+6=8+2+____.
   Answer: 4 The make-a-ten strategy is a clever way to add numbers when one of them is close to 10. The idea is to break apart the smaller number so you can first build a friendly, easy-to-work-with 10, then add whatever is left over. Whenever you see a problem like this, ask yourself: "How many more do I need to turn 8 into 10?" Here, you start with 8+6. To make 8 into a 10, you need to add 2 — that's why the problem already shows 8+2. But you can't just add 2 out of nowhere; you have to take that 2 from the 6. Since 6 = 2 + 4, once you use up the 2, there are 4 left. So 8+6 = 8+2+4 = 10+4 = 14. The missing number is 4. Now look at the traps. The choice 2 repeats the number already used to make the ten, but that 2 is spoken for — it can't appear twice. The choice 6 is just the original number you were adding; if you added the full 6 again, you'd be adding way too much. The choice 8 is the first number in the problem, not part of splitting the 6 at all — it's there to tempt you into grabbing a familiar number. Remember this pattern: when you split the second number to make ten, the two pieces must add back up to the original number. Here 2+4=6, which checks out perfectly.
4. David solved $6 + 7$ by making it into $6 + 6 + 1$. Then he said $6 + 6 = 12$, so $6 + 7 = 13$. Which two strategies did David combine?
   Answer: Making equivalent sums and using known doubles facts When you see a problem about math strategies, look carefully at what the student actually did step-by-step to identify which methods they used. Let's trace David's work: He changed $6 + 7$ into $6 + 6 + 1$. This is called making equivalent sums - he broke apart the 7 into $6 + 1$ to create a problem that's easier to solve but gives the same answer. Then he recognized that $6 + 6 = 12$, which is using doubles facts - those special addition problems where you add a number to itself. So David combined making equivalent sums with doubles facts, which is answer C. Let's check why the other answers don't fit: Answer A mentions "making ten," but David never made 10 - he made 12 using doubles. Answer B talks about "counting on," but David didn't count up from one number; he used the doubles fact $6 + 6$. Answer D also mentions "making ten," which again isn't what happened here, plus there weren't really "leftover parts" in the way this strategy typically works. The key insight is that David transformed $6 + 7$ into $6 + 6 + 1$ specifically because he knew the doubles fact $6 + 6 = 12$. This made the problem much easier to solve. Remember: When identifying math strategies, focus on the actual steps taken. Look for keywords like "doubles" (adding a number to itself), "making ten" (creating groups of 10), and "equivalent" (same value, different form).
5. Solve $14-6$ by decomposing to ten: $14-4-2$.
   Answer: 8 This question tests 1st grade fluency in addition and subtraction within 20, with emphasis on strategies (CCSS.1.OA.6). For subtraction across 10, decompose the subtrahend to first reach 10, then subtract the rest. For example, for 13 - 4, we think: 13 to 10 is 3, so break 4 into 3 + 1, then 13 - 4 = (13 - 3) - 1 = 10 - 1 = 9. The problem asks to solve 14 - 6 by decomposing to ten as 14 - 4 - 2. Choice D is correct because decomposing to 10: 14 - 4 = 10, then 10 - 2 = 8. Choice B is a common error where students make 10 but forget to subtract the remainder, stopping at 10; this happens because these strategies require multiple steps and practice. To help students: For decomposing to 10 in subtraction, practice with many examples showing the 'get to 10 first' step; use ten-frames; provide daily practice with mixed strategies; help students select appropriate strategy for each problem type.
6. Solve $13-4$ by subtracting to 10. What is the answer?
   Answer: 9 This question tests 1st grade fluency in addition and subtraction within 20, with emphasis on strategies (CCSS.1.OA.6). For subtraction across 10, decompose the subtrahend to first reach 10, then subtract the rest. For 13 - 4, we think: 13 to 10 is 3, so break 4 into 3 + 1. Then: 13 - 4 = (13 - 3) - 1 = 10 - 1 = 9. The problem asks to solve 13 - 4 by subtracting to 10. Choice C is correct because decomposing to 10: 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9. Choice A is a common error where students don't apply the strategy systematically, such as subtracting all at once and miscounting; this happens because these strategies require multiple steps and practice. To help students: For decomposing to 10 in subtraction, practice with many examples showing the 'get to 10 first' step; use ten-frames; provide daily practice with mixed strategies; emphasize that facts within 10 should be automatic.
7. Use counting on to solve $8+3$. Start at 8 and count on.
   Answer: 11 This question tests 1st grade fluency in addition and subtraction within 20, with emphasis on strategies (CCSS.1.OA.6). Counting on is a strategy for addition where you start with the first number and count forward by the second number. For example, for 8 + 3, start at 8 and count: 9, 10, 11. The problem asks to use counting on to solve 8 + 3, starting at 8 and counting on. Choice B is correct because 8 + 3: starting at 8, count on three: 9, 10, 11. Choice C is a common error where students make a calculation error like counting one extra to 12; this happens because keeping track of parts while combining them is cognitively demanding. To help students: Practice counting on with small numbers first; use number lines or fingers to visualize; provide daily practice with mixed strategies; emphasize that facts within 10 should be automatic (fluent).
8. Carlos wants to find $16 - 8$ using an addition fact he knows. He remembers that $8 + 8 = 16$. How does this help Carlos solve the subtraction problem?
   Answer: Since $8 + 8 = 16$, then $16 - 8 = 8$ When you see a subtraction problem, you can use addition facts you already know to help solve it! Addition and subtraction are related - they're called "fact families" because they work together. Carlos knows that $8 + 8 = 16$. This addition fact tells him that when he puts 8 and 8 together, he gets 16. Now, if he starts with 16 and takes away one of those 8s, he'll be left with the other 8. So $16 - 8 = 8$. Think of it like having 16 toys that are made up of two groups of 8 toys each. If you take away one group of 8 toys, you're left with the other group of 8 toys. Choice A says the answer is 0, but that would only be true if Carlos subtracted all 16 from 16, not just 8. Choice B says the answer is 16, but when you subtract something from a number, you get less than what you started with, not the same amount. Choice D says 24, but that's what you'd get if you added 16 + 8 instead of subtracting. The correct answer is C because $16 - 8 = 8$. Remember this helpful trick: when you know an addition fact, you automatically know two subtraction facts! Since $8 + 8 = 16$, you know that $16 - 8 = 8$. This connection between addition and subtraction will make math much easier for you.
9. How many apples now? Mia has 7 apples and gets 2 more; count on.
   Answer: 9 This question tests 1st grade fluency in addition and subtraction within 20, with emphasis on strategies (CCSS.1.OA.6). Counting on is a strategy for addition where you start with the larger number and count up by the smaller number. For example, for 7 + 2, start at 7 and count on two more: 8, 9, so the total is 9. The problem asks how many apples Mia has now after starting with 7 and getting 2 more, using count on. Choice B is correct because starting at 7 and counting on 2 gives 8, 9. Choice C is a common error where students make a calculation error or count on too many, getting 10; this happens because keeping track of parts while combining them is cognitively demanding. To help students: Practice counting on with concrete objects like fingers or counters; emphasize starting with the larger number; provide daily practice with mixed strategies; help students select appropriate strategy for each problem type.
10. Solve $6+7$ using doubles plus 1. What is the sum?
    Answer: 13 This question tests 1st grade fluency in addition and subtraction within 20, with emphasis on strategies (CCSS.1.OA.6). Creating equivalent sums using doubles helps with near-doubles. For 6 + 7, we recognize these are close to the double 6 + 6. We think: 6 + 7 = 6 + 6 + 1 = 12 + 1 = 13. The problem asks to solve 6 + 7 using doubles plus 1. Choice C is correct because using doubles: 6 + 7 = 6 + 6 + 1 = 12 + 1 = 13. Choice A is a common error where for near-doubles, students forget to add the +1; this happens because students may try to compute without using the strategy. To help students: For doubles, ensure all doubles facts are memorized (6+6, 7+7, 8+8, 9+9); for near-doubles, practice thinking 'double plus/minus 1'; provide daily practice with mixed strategies; help students select appropriate strategy for each problem type.
11. Tom knows that $6 + 8 = 14$. Which subtraction problem can Tom solve using this same fact?
    Answer: $14 - 6 = ?$ Since addition and subtraction are inverse operations, knowing that 6 + 8 = 14 means Tom can solve 14 - 6 = 8 or 14 - 8 = 6. Choice A is correct because 14 - 6 = 8. Choice B uses the addends but not the sum. Choice C reverses the addends incorrectly. Choice D uses 8 but with the wrong sum (16 instead of 14).
12. Create an easier sum: $9+6$ can be $10+5$. What is $9+6$?
    Answer: 15 This question tests 1st grade fluency in addition and subtraction within 20, with emphasis on strategies (CCSS.1.OA.6). Creating an easier sum, like compensating, adjusts numbers to make addition simpler. For example, for 9 + 6, we can think of it as 10 + 5 by adding 1 to 9 and subtracting 1 from 6, so 10 + 5 = 15. The problem asks to create an easier sum: 9 + 6 can be 10 + 5, and find 9 + 6. Choice B is correct because 9 + 6 = 10 + 5 = 15. Choice A is a common error where students make a calculation error in compensation, getting 14; this happens because keeping track of parts while combining them is cognitively demanding. To help students: Practice compensation by adjusting pairs to make 10; use ten-frames to visualize; provide daily practice with mixed strategies; help students select appropriate strategy for each problem type.
13. Ben solved $7 + 8$ by thinking: '$7 + 7 = 14$, and $8$ is one more than $7$, so $7 + 8 = 15$.' What strategy did Ben use?
    Answer: Making equivalent but easier sums using known facts When you encounter math strategy questions, focus on identifying exactly what mental process the student used to solve the problem. Let's trace Ben's thinking step by step. He started with $7 + 8$ but didn't solve it directly. Instead, he thought about $7 + 7 = 14$, which he already knew. Then he recognized that since $8$ is one more than $7$, he could add one more to get $7 + 8 = 15$. Ben transformed the original problem into an equivalent but easier problem using a math fact he already knew well. This makes answer D correct - Ben made an equivalent but easier sum using known facts. He replaced the unfamiliar $7 + 8$ with the familiar $7 + 7$, then adjusted. Answer A is wrong because Ben didn't use subtraction at all - he only used addition throughout his strategy. Answer B is incorrect because Ben didn't count "8, 9, 10, 11, 12, 13, 14, 15" by ones from 7. Instead, he jumped directly to 14 using his known fact, then added just one more. Answer C is wrong because Ben didn't break apart the second number (8) into smaller parts to make ten - he used doubling instead. When you see strategy questions, pay attention to the specific steps the student takes. Look for key phrases like "I know that..." which often signal the use of known facts, or step-by-step counting, which indicates different strategies.
14. Solve $9+7$ by making ten. What is the sum?
    Answer: 16 This question tests 1st grade fluency in addition and subtraction within 20, with emphasis on strategies (CCSS.1.OA.6). The making-10 strategy helps add numbers that cross 10. To use it, decompose the second number into the amount needed to make 10, plus the remainder. For example, for 8 + 6, we think: 8 needs 2 more to make 10, so break 6 into 2 + 4, then 8 + 6 = 8 + (2 + 4) = (8 + 2) + 4 = 10 + 4 = 14. The problem asks to solve 9 + 7 using the making-10 strategy. Choice B is correct because following making-10: 9 + 7 = 9 + 1 + 6 = 10 + 6 = 16. Choice A is a common error where students don't decompose correctly and get a wrong answer like adding without strategy, such as 9 + 6 = 15, forgetting the full decomposition; this happens because these strategies require multiple steps and practice. To help students: For making-10, explicitly teach pairs that make 10 (1+9, 2+8, 3+7, 4+6, 5+5) and practice decomposing; use ten-frames to visualize making 10; provide daily practice with mixed strategies; help students select appropriate strategy for each problem type.
15. Use counting on to solve $9+3$. What is the answer?
    Answer: 12 This question tests 1st grade fluency in addition and subtraction within 20, with emphasis on strategies (CCSS.1.OA.6). Counting on is a strategy where you start from the larger number and count up by the smaller number. For example, for 9 + 3, start at 9 and count on three: 10, 11, 12. This is efficient for small addends. The problem asks to use counting on to solve 9 + 3. Choice B is correct because counting on from 9 by 3 gives 10, 11, 12. Choice A is a common error where students make a calculation error, such as starting from 8 instead of 9; this happens because keeping track of parts while combining them is cognitively demanding. To help students: Practice counting on with small numbers first; use number lines or fingers to visualize; provide daily practice with mixed strategies; help students select appropriate strategy for each problem type, like counting on for addends less than 4.
16. Complete: 8+6=8+2+____. What number goes in the blank?
    Answer: 4 This question is really about a clever math idea: breaking numbers apart. When you see 8+6, you can split the 6 into two smaller pieces. Notice that the right side already shows 8+2+____. So the 6 has been broken into 2 and something else. Ask yourself: "2 plus what makes 6?" Since 2 + 4 = 6, the missing piece must be 4. You can double-check by adding both sides: the left side is 8+6=14, and the right side is 8+2+4 = 10+4 = 14. They match, so 4 is correct. The choice 2 is a trap because that number is already written in the problem — but 2+2 only makes 4, not the 6 you need. The choice 6 is wrong because it repeats the original number you were supposed to split; using it would give 8+2+6=16, which is too big. The choice 8 just copies the first number in the problem; 8+2+8=18 is far too large. Only 4 keeps both sides equal. A smart trick to remember: when a number gets split into parts, all the parts must add back up to the whole. Here the whole is 6, one part is 2, so the other part fills in the gap. Whenever both sides of an equal sign should match, add each side up and make sure they land on the same total.
17. Solve $7+6$ by making a ten.
    Answer: 13 Making a ten from 7 and part of 6 leaves 3 more to add, giving 7 plus 6 equals 13. 12 is one less than the correct sum. 14 is one more than the correct sum. 11 is two less than the correct sum. Only 13 correctly shows the sum of 7 and 6.
18. To solve $15-7$, first subtract $5$: $15-5=10$. What should you subtract next?
    Answer: $2$ After subtracting 5 to reach 10, there are 2 left of the original 7 still to subtract, so the next step is to subtract 2. Subtracting 1 doesn't account for all of the remaining amount. Subtracting 5 again would subtract too much, more than the original 7. Subtracting 7 again repeats the whole amount instead of just what's left. Only subtracting 2 correctly finishes taking away the full 7.
19. What is $7+8$?
    Answer: 15 Adding 7 and 8 together gives a sum of 15. 16 is one more than the correct sum. 14 is one less than the correct sum. 13 is two less than the correct sum. Only 15 correctly shows the sum of 7 and 8.
20. Lisa has 15 marbles. She gives away 5 marbles, then gives away 2 more marbles. How many marbles does Lisa have left?
    Answer: $8$ Lisa starts with 15 marbles, gives away 5 to leave 10, then gives away 2 more to leave 8. 10 stops after only the first step instead of finishing both steps. 13 comes from adding instead of subtracting the marbles she gave away. 7 mixes up the total marbles given away with the marbles left. Only 8 correctly shows how many marbles Lisa has after giving away 5 and then 2 more.

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