Relate Counting To Addition And Subtraction
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1st Grade Math › Relate Counting To Addition And Subtraction
Chen adds $9+5$ by counting on: start at 9 and say 10, 11, 12, 13, 14. What is the sum?
9
13
14
15
Explanation
This question tests 1st grade ability to relate counting to addition and subtraction (CCSS.1.OA.5). Counting on is an efficient strategy for addition. Instead of counting from 1, start at one of the addends and count forward by the other addend. For example, to solve 8 + 3, start at 8 and count forward 3 numbers: '9, 10, 11'—the last number you say (11) is the answer. The problem asks to add 9 + 5 by counting on from 9. Choice B is correct because starting at 9 and counting on 5 gives '10, 11, 12, 13, 14,' so the answer is 14. Choice A is a common error where students count one too few, perhaps by stopping at the fourth count instead of fifth; this happens because tracking counts while saying numbers is cognitively demanding. To help students: Model counting on with number lines showing clear starting point and forward jumps; use fingers to track counts while saying numbers aloud; emphasize NOT starting at 1 for counting on; practice with physical objects (start with group, add more by counting on); compare efficiency of counting on vs counting all from 1; practice with small addends (1-5) first; connect counting to written addition equations.
To add $7+2$, start at 7 and count on 2: 8, 9. What number do you end at?
7
8
9
10
Explanation
This question tests 1st grade ability to relate counting to addition and subtraction (CCSS.1.OA.5). Counting on is an efficient strategy for addition. Instead of counting from 1, start at one of the addends and count forward by the other addend. For example, to solve 8 + 3, start at 8 and count forward 3 numbers: '9, 10, 11'—the last number you say (11) is the answer. The problem asks to add 7 + 2 by counting on from 7. Choice D is correct because starting at 7 and counting on 2 gives '8, 9,' so the answer is 9. Choice C is a common error where students add one extra or miscount by including the starting number; this happens because tracking counts while saying numbers is cognitively demanding. To help students: Model counting on with number lines showing clear starting point and forward jumps; use fingers to track counts while saying numbers aloud; emphasize NOT starting at 1 for counting on; practice with physical objects (start with group, add more by counting on); compare efficiency of counting on vs counting all from 1; practice with small addends (1-5) first; connect counting to written addition equations.
Carlos has 15 toy cars and loses 2; start at 15 and count back 2: 14, 13. How many left?
12
13
15
17
Explanation
This question tests 1st grade ability to relate counting to addition and subtraction (CCSS.1.OA.5). Counting back is a strategy for subtraction. Start at the first number (minuend) and count backward by the second number (subtrahend). For example, to solve $10 - 2$, start at 10 and count back 2: '9, 8'—the last number you say (8) is the answer. The problem asks to subtract $15 - 2$ by counting back from 15 in a word problem context. Choice C is correct because starting at 15 and counting back 2 gives '14, 13,' so the answer is 13. Choice A is a common error where students count back too many, perhaps by miscounting or going an extra step; this happens because counting back is more challenging than counting forward for many students. To help students: Demonstrate counting back with number line showing backward movement; use fingers to track counts while saying numbers aloud; practice with physical objects (start with group, remove by counting back); emphasize the last number said is the answer; practice with small subtrahends ($1-5$) first; connect counting to written subtraction equations.
Maya has 6 stickers and gets 4 more; start at 6 and count on 4. How many now?
6
9
10
11
Explanation
This question tests 1st grade ability to relate counting to addition and subtraction (CCSS.1.OA.5). Counting on is an efficient strategy for addition. Instead of counting from 1, start at one of the addends and count forward by the other addend. For example, to solve 8 + 3, start at 8 and count forward 3 numbers: '9, 10, 11'—the last number you say (11) is the answer. The problem asks to add 6 + 4 by counting on from 6 in a word problem context. Choice B is correct because starting at 6 and counting on 4 gives '7, 8, 9, 10,' so the answer is 10. Choice A is a common error where students count one too few, perhaps by starting to count from the next number but forgetting one step; this happens because counting on requires not starting at 1, which is different from early counting. To help students: Model counting on with number lines showing clear starting point and forward jumps; use fingers to track counts while saying numbers aloud; emphasize NOT starting at 1 for counting on; practice with physical objects (start with group, add more by counting on); compare efficiency of counting on vs counting all from 1; practice with small addends (1-5) first; connect counting to written addition equations.
To subtract $10-2$, start at 10 and count back 2: 9, 8. What is the answer?
2
8
9
12
Explanation
This question tests 1st grade ability to relate counting to addition and subtraction (CCSS.1.OA.5). Counting back is a strategy for subtraction. Start at the first number (minuend) and count backward by the second number (subtrahend). For example, to solve 10 - 2, start at 10 and count back 2: '9, 8'—the last number you say (8) is the answer. The problem asks to subtract 10 - 2 by counting back from 10. Choice C is correct because starting at 10 and counting back 2 gives '9, 8,' so the answer is 8. Choice B is a common error where students count back one too few, perhaps by including the starting number as a count or stopping at the first backward step; this happens because counting back is more challenging than counting forward for many students. To help students: Demonstrate counting back with number line showing backward movement; use fingers to track counts while saying numbers aloud; practice with physical objects (start with group, remove by counting back); emphasize the last number said is the answer; compare to counting on for addition; practice with small subtrahends (1-5) first; connect counting to written subtraction equations.
Maya has 15 beads and loses 5. Start at 15 and count back 5. What number do you land on?
9
10
11
20
Explanation
This question tests 1st grade ability to relate counting to addition and subtraction (CCSS.1.OA.5). Counting back is a strategy for subtraction. Start at the first number (minuend) and count backward by the second number (subtrahend). For example, to solve $15 - 5$, start at 15 and count back 5: '14, 13, 12, 11, 10'—the last number you say (10) is the answer. The problem asks to subtract 15 - 5 by counting back from 15 and identify the landing number after Maya loses 5 beads. Choice C is correct because starting at 15 and counting back 5 gives '14, 13, 12, 11, 10,' so you land on 10. Choice B is a common error where students count back one too few, perhaps by stopping too early; this happens because counting back is more challenging than counting forward for many students. To help students: Demonstrate counting back with number line showing backward movement; use fingers to track counts while saying numbers aloud; practice with physical objects (start with group, remove by counting back); emphasize the last number said is the answer; compare to counting on for addition; practice with small subtrahends (1-5) first; connect counting to written subtraction equations.
To add $11+3$, start at 11 and count on 3: 12, 13, 14. What is the sum?
11
13
14
15
Explanation
This question tests 1st grade ability to relate counting to addition and subtraction (CCSS.1.OA.5). Counting on is an efficient strategy for addition. Instead of counting from 1, start at one of the addends and count forward by the other addend. For example, to solve 8 + 3, start at 8 and count forward 3 numbers: '9, 10, 11'—the last number you say (11) is the answer. The problem asks to add 11 + 3 by counting on from 11. Choice B is correct because starting at 11 and counting on 3 gives '12, 13, 14,' so the answer is 14. Choice C is a common error where students stop one count early, perhaps by not tracking the full steps; this happens because tracking counts while saying numbers is cognitively demanding. To help students: Model counting on with number lines showing clear starting point and forward jumps; use fingers to track counts while saying numbers aloud; emphasize NOT starting at 1 for counting on; practice with physical objects (start with group, add more by counting on); compare efficiency of counting on vs counting all from 1; practice with small addends (1-5) first; connect counting to written addition equations.
To add $8+3$, start at 8 and count on 3: 9, 10, 11. What is the sum?
8
10
11
12
Explanation
This question tests 1st grade ability to relate counting to addition and subtraction (CCSS.1.OA.5). Counting on is an efficient strategy for addition. Instead of counting from 1, start at one of the addends and count forward by the other addend. For example, to solve 8 + 3, start at 8 and count forward 3 numbers: '9, 10, 11'—the last number you say (11) is the answer. The problem asks to add 8 + 3 by counting on from 8. Choice B is correct because starting at 8 and counting on 3 gives '9, 10, 11,' so the answer is 11. Choice A is a common error where students stop counting too early, such as counting only two steps instead of three; this happens because tracking counts while saying numbers is cognitively demanding. To help students: Model counting on with number lines showing clear starting point and forward jumps; use fingers to track counts while saying numbers aloud; emphasize NOT starting at 1 for counting on; practice with physical objects (start with group, add more by counting on); compare efficiency of counting on vs counting all from 1; practice with small addends (1-5) first; connect counting to written addition equations.
Jamal has 9 apples and eats 3; start at 9 and count back 3: 8, 7, 6. How many left?
5
6
7
12
Explanation
This question tests 1st grade ability to relate counting to addition and subtraction (CCSS.1.OA.5). Counting back is a strategy for subtraction. Start at the first number (minuend) and count backward by the second number (subtrahend). For example, to solve $10 - 2$, start at 10 and count back 2: '9, 8'—the last number you say (8) is the answer. The problem asks to subtract $9 - 3$ by counting back from 9 in a word problem context. Choice B is correct because starting at 9 and counting back 3 gives '8, 7, 6,' so the answer is 6. Choice A is a common error where students count back one too many, perhaps by miscounting the steps or starting incorrectly; this happens because counting back is more challenging than counting forward for many students. To help students: Demonstrate counting back with number line showing backward movement; use fingers to track counts while saying numbers aloud; practice with physical objects (start with group, remove by counting back); emphasize the last number said is the answer; practice with small subtrahends (1-5) first; connect counting to written subtraction equations.
To add $8+3$, start at 8 and count on 3: 9, 10, 11. What is the answer?
5
8
10
11
Explanation
This question tests 1st grade ability to relate counting to addition and subtraction (CCSS.1.OA.5). Counting on is an efficient strategy for addition. Instead of counting from 1, start at one of the addends and count forward by the other addend. For example, to solve 8 + 3, start at 8 and count forward 3 numbers: '9, 10, 11'—the last number you say (11) is the answer. The problem asks to add 8 + 3 by counting on from 8. Choice B is correct because starting at 8 and counting on 3 gives '9, 10, 11,' so the answer is 11. Choice A is a common error where students stop counting too early, perhaps by miscounting the steps or including the starting number as one of the counts; this happens because tracking counts while saying numbers is cognitively demanding. To help students: Model counting on with number lines showing clear starting point and forward jumps; use fingers to track counts while saying numbers aloud; emphasize NOT starting at 1 for counting on; practice with physical objects (start with group, add more by counting on); compare efficiency of counting on vs counting all from 1; practice with small addends (1-5) first; connect counting to written addition equations.