Addition And Subtraction Fluency
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1st Grade Math › Addition And Subtraction Fluency
Use counting on to solve $9+3$. What is the answer?
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Explanation
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.
If $8+4=12$, what is $12-8$?
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Explanation
This question tests 1st grade fluency in addition and subtraction within 20, with emphasis on strategies (CCSS.1.OA.6). Fact families show the relationship between addition and subtraction. For example, if 8 + 4 = 12, then 12 - 8 = 4 and 12 - 4 = 8. The problem asks to use the fact that 8 + 4 = 12 to find 12 - 8. Choice C is correct because using the known addition fact, 12 - 8 = 4 since 8 + 4 = 12. Choice A is a common error where students use the wrong operation or make a calculation error; 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; provide daily practice with mixed strategies; help students select appropriate strategy for each problem type.
How many apples now? Mia has 7 apples and gets 2 more; count on.
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Explanation
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.
Solve $6+7$ using doubles plus 1. What is the sum?
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Explanation
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.
Solve $15-7$ by decomposing to ten: $15-5-2$.
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Explanation
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 15 - 7, we think: 15 to 10 is 5, so break 7 into 5 + 2, then 15 - 7 = (15 - 5) - 2 = 10 - 2 = 8. The problem asks to solve 15 - 7 by decomposing to ten: 15 - 5 - 2. Choice C is correct because decomposing to 10: 15 - 5 - 2 = 10 - 2 = 8. Choice A is a common error where students don't decompose correctly and get a wrong answer like 9; this happens because decomposing numbers flexibly is challenging. To help students: For decomposing to 10 in subtraction, practice with many examples showing the 'get to 10 first' step; use ten-frames to visualize; provide daily practice with mixed strategies; help students select appropriate strategy for each problem type.
If $8+4=12$, what is $12-8$? Use the related fact.
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Explanation
This question tests 1st grade fluency in addition and subtraction within 20, with emphasis on strategies (CCSS.1.OA.6). Using related addition and subtraction facts helps solve problems through fact families. For example, if 8 + 4 = 12, then the related subtraction is 12 - 8 = 4. The problem asks if 8 + 4 = 12, what is 12 - 8, using the related fact. Choice B is correct because using the known addition fact, 12 - 8 = 4 since 8 + 4 = 12. Choice A is a common error where students use the wrong operation or make a calculation error, getting 3; 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.
Solve $6+7$ using doubles plus 1. What is the sum?
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Explanation
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.
Mia has 7 stickers and gets 6 more; make ten to find how many.
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Explanation
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 7 + 6 using making ten in a word problem context. Choice C is correct because following making-10: 7 + 6 = 7 + 3 + 3 = 10 + 3 = 13. Choice A is a common error where students make a calculation error, such as forgetting to add the remainder; this happens because keeping track of parts while combining them is cognitively demanding. 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.
Complete the subtract-to-10 step: $15-7=15-5-\underline{\ \ }$.
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Explanation
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 complete the subtract-to-10 step for 15 - 7 = 15 - 5 - _. Choice B is correct because to get to 10 from 15 is subtracting 5, and the remaining part of 7 is 2 (since 7 = 5 + 2). Choice A is a common error where students confuse which number to decompose, such as thinking it's 1 instead; this happens because decomposing numbers flexibly is challenging. 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.
Solve $9+2$ using counting on. Start at 9 and count 2.
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Explanation
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).