All questions
Question 1
Maria has 8 stickers. She wants to give away 3 stickers to her friends. Instead of subtracting, Maria decides to count backwards from 8 to find how many stickers she will have left. Which counting pattern should Maria use?
- 8,7,6,5 and she will have 5 stickers left (correct answer)
- 8,7,6 and she will have 6 stickers left
- 8,9,10,11 and she will have 11 stickers left
- 8,5 and she will have 5 stickers left immediately
Explanation: To subtract 3 by counting backwards, Maria starts at 8 and counts back 3 numbers: 8→7 (back 1), 7→6 (back 2), 6→5 (back 3). She lands on 5, so she will have 5 stickers left. Choice B stops counting after only 2 steps back. Choice C counts forward instead of backward. Choice D jumps directly without showing the counting process.
Question 2
Chen adds 9+5 by counting on: start at 9 and say 10, 11, 12, 13, 14. What is the sum?
- 13
- 14 (correct answer)
- 15
- 9
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.
Question 3
To subtract 10−2, start at 10 and count back 2: 9, 8. What is the answer?
- 6
- 9
- 8 (correct answer)
- 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 miscount by one, such as stopping after the first count back; 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 direction of counting; practice with small subtrahends (1-5) first; connect counting to written subtraction equations; compare to counting on for addition.
Question 4
Sofia has 6 stickers and gets 4 more. Start at 6 and count on 4. How many now?
- 9
- 10 (correct answer)
- 11
- 6
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 6+4, start at 6 and count forward 4 numbers: '7, 8, 9, 10'—the last number you say (10) is the answer. The problem asks to add by counting on from 6 after Sofia gets 4 more stickers. Choice B is correct because starting at 6 and counting on 4 gives '7, 8, 9, 10,' so the total is 10. Choice A is a common error where students start counting from the wrong number or miscount by one, perhaps by including the starting number as a count; this happens because distinguishing between the starting point and the counts requires practice. 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. Question 5
To add 13+4, start at 13 and count on 4: 14, 15, 16, 17. What is the answer?
- 16
- 17 (correct answer)
- 18
- 13
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 13 + 4, start at 13 and count forward 4 numbers: '14, 15, 16, 17'—the last number you say (17) is the answer. The problem asks to add 13 + 4 by counting on from 13. Choice B is correct because starting at 13 and counting on 4 gives '14, 15, 16, 17,' so the answer is 17. Choice A is a common error where students stop counting too early, perhaps by miscounting the 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.
Question 6
To subtract 13−4, start at 13 and count back 4: 12, 11, 10, 9. What is the answer?
- 8
- 9 (correct answer)
- 10
- 13
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 13 - 4, start at 13 and count back 4: '12, 11, 10, 9'—the last number you say (9) is the answer. The problem asks to subtract 13 - 4 by counting back from 13. Choice B is correct because starting at 13 and counting back 4 gives '12, 11, 10, 9,' so the answer is 9. Choice A is a common error where students count back one extra, landing on 8; 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 direction of counting; practice with small subtrahends (1-5) first; connect counting to written subtraction equations; encourage verbalizing each step.
Question 7
Sarah is teaching her little brother how to use counting for 6−3. She shows him two methods. Method 1: "Start at 6, count back 3: 5,4,3". Method 2: "Start at 3, count up to 6: 4,5,6, which is 3 steps". Why do both methods give the correct answer of 3?
- Both methods use the same numbers, so they must give the same answer always
- Both methods count the same distance between 3 and 6 on the number line (correct answer)
- Both methods start with 3, which is the answer to the subtraction problem
- Both methods count exactly 3 numbers, which matches the number being subtracted
Explanation: When you see subtraction problems solved with counting methods, think about what's really happening on the number line. Both of Sarah's methods are finding the distance between two numbers, just from different starting points.
Method 1 starts at 6 and counts backward 3 steps to reach 3. Method 2 starts at 3 and counts forward until it reaches 6, which takes 3 steps. Both methods are measuring the same gap on the number line - the distance between 3 and 6. This distance is always 3, no matter which direction you count. It's like measuring the length of a stick - you get the same measurement whether you start from the left end or the right end.
Choice A is incorrect because using the same numbers doesn't guarantee the same answer unless you're measuring the same thing. Choice C is wrong because Method 1 starts with 6, not 3 - the starting numbers are different. Choice D misses the point because while both methods do count 3 steps, that's the result of measuring the distance, not the reason why both methods work.
The key insight is that subtraction finds the distance between numbers. Whether you count up from the smaller number or count back from the larger number, you're measuring the same distance on the number line.
Remember: When solving subtraction with counting, both "counting back" and "counting up" work because they measure the same distance between two points. Question 8
Sofia has 12 balloons and gives away 5; start at 12 and count back 5. How many balloons now?
- 8
- 17
- 7 (correct answer)
- 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 12−5 by counting back from 12 in a word problem context. Choice C is correct because starting at 12 and counting back 5 gives '11, 10, 9, 8, 7,' so the answer is 7. Choice A is a common error where students count back one too few, perhaps by miscounting the steps; 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. Question 9
Chen has 14 apples and eats 5; start at 14 and count back 5. What number is left?
- 10
- 9 (correct answer)
- 11
- 14
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 14−5, start at 14 and count back 5: '13, 12, 11, 10, 9'—the last number you say (9) is the answer. The problem asks to subtract 14−5 by counting back from 14 in a story context. Choice B is correct because starting at 14 and counting back 5 gives '13, 12, 11, 10, 9,' so the answer is 9. Choice A is a common error where students count back only four steps, landing on 10; 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 direction of counting; practice with small subtrahends (1−5) first; connect counting to written subtraction equations; use story problems to make it relatable. Question 10
To add 7+5, start at 7 and count on 5: 8, 9, 10, 11, 12. What is the sum?
- 13
- 12 (correct answer)
- 11
- 7
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 7 + 5, start at 7 and count forward 5 numbers: '8, 9, 10, 11, 12'—the last number you say (12) is the answer. The problem asks to add 7 + 5 by counting on from 7 and find the sum. Choice B is correct because starting at 7 and counting on 5 gives '8, 9, 10, 11, 12,' so the sum is 12. Choice A is a common error where students stop counting too early, perhaps by miscounting the 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.
Question 11
Carlos has 9 toy cars and gives 1 away. Start at 9 and count back 1: 8. What is the answer?
- 9
- 7
- 10
- 8 (correct answer)
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 9 - 1, start at 9 and count back 1: '8'—the last number you say (8) is the answer. The problem asks to subtract 9 - 1 by counting back from 9 after Carlos gives away 1 toy car. Choice D is correct because starting at 9 and counting back 1 gives '8,' so the answer is 8. Choice A is a common error where students might confuse with addition or start from the wrong number; 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.
Question 12
Carlos has 15 toy cars and loses 2; start at 15 and count back 2: 14, 13. How many left?
- 12
- 17
- 13 (correct answer)
- 15
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. Question 13
Maya has 6 stickers and gets 4 more; start at 6 and count on 4. How many now?
- 9
- 10 (correct answer)
- 6
- 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.
Question 14
To add 8+3, start at 8 and count on 3: 9, 10, 11. What is the answer?
- 10
- 11 (correct answer)
- 8
- 5
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.
Question 15
To add 8+3, start at 8 and count on 3: 9, 10, 11. What is the sum?
- 10
- 11 (correct answer)
- 8
- 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.
Question 16
To subtract 14−4, start at 14 and count back 4: 13, 12, 11, 10. What is the answer?
- 11
- 18
- 10 (correct answer)
- 9
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 14 - 4 by counting back from 14. Choice C is correct because starting at 14 and counting back 4 gives '13, 12, 11, 10,' so the answer is 10. Choice A is a common error where students stop one count early, perhaps by not tracking the full number of steps; 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.
Question 17
Jamal starts at 15 and counts back 4: 14, 13, 12, 11. What number does he land on?
- 12
- 10
- 11 (correct answer)
- 15
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 - 4, start at 15 and count back 4: '14, 13, 12, 11'—the last number you say (11) is the answer. The problem asks to count back 4 from 15 and find the landing number. Choice C is correct because starting at 15 and counting back 4 gives '14, 13, 12, 11,' so the answer is 11. Choice A is a common error where students stop too early, such as counting only three steps; this happens because tracking counts while saying numbers is cognitively demanding. 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 direction of counting; practice with small subtrahends (1-5) first; connect counting to written subtraction equations; encourage verbalizing each step.
Question 18
Jamal has 14 apples and eats 3. Start at 14 and count back 3: 13, 12, 11. Answer?
- 11 (correct answer)
- 12
- 17
- 3
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 14 - 3, start at 14 and count back 3: '13, 12, 11'—the last number you say (11) is the answer. The problem asks to subtract 14 - 3 by counting back from 14 after Jamal eats 3 apples. Choice A is correct because starting at 14 and counting back 3 gives '13, 12, 11,' so the answer is 11. Choice B is a common error where students count back one too few, perhaps by stopping too early or miscounting the steps; 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.
Question 19
Jamal has 9 apples and eats 3; start at 9 and count back 3: 8, 7, 6. How many left?
- 5
- 6 (correct answer)
- 12
- 7
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. Question 20
To add 9+2, start at 9 and count on 2: 10, 11. What is the sum?
- 10
- 12
- 11 (correct answer)
- 9
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 9 + 2, start at 9 and count forward 2 numbers: '10, 11'—the last number you say (11) is the answer. The problem asks to add 9 + 2 by counting on from 9. Choice C is correct because starting at 9 and counting on 2 gives '10, 11,' so the answer is 11. Choice A is a common error where students stop after the first count, landing on 10; 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.