Addition And Subtraction Properties - 1st Grade Math

1. To add $4+7+3$, which way uses commutative then associative to make 10?
   Answer: $7+3+4=(7+3)+4$ This question tests 1st grade understanding of properties of operations as addition strategies (CCSS.1.OA.3). The commutative property allows reordering, and associative property allows regrouping: together, they help in making 10, like reordering to group friendly numbers. For example, in $4 + 7 + 3$, we can reorder to $7 + 3 + 4$ using commutative, then group $(7 + 3) + 4 = 10 + 4 = 14$ using associative. The problem asks which way to add $4 + 7 + 3$ uses commutative then associative to make 10. Choice C is correct because it reorders to $7 + 3 + 4$ using commutative, then groups $(7 + 3) + 4$ to make $10 + 4 = 14$. Choice B is a common error where students use associative without commutative, missing the reordering step, this happens because the connection between properties and strategy isn't automatic. To help students: Provide many concrete examples showing reordering and regrouping; explicitly teach combining commutative and associative for making 10; use physical objects to demonstrate; practice identifying pairs that make 10; use visual models like ten-frames; emphasize reordering then grouping; connect properties to efficient mental math strategies.
2. To add $2+6+4$, which two numbers add first to make 10?
   Answer: 6 and 4 This question tests 1st grade understanding of properties of operations as addition strategies (CCSS.1.OA.3). The associative property of addition means that when adding three numbers, we can group them in different ways and get the same answer: (a + b) + c = a + (b + c). This is especially useful for making 10: in 2 + 6 + 4, we can group 6 + 4 first to make 10, then add 2 to get 12, choosing the right grouping to make computation much easier. The problem asks which two numbers to add first in 2 + 6 + 4 to make 10. Choice B is correct because grouping 6 and 4 first gives 10, and then adding 2 gives 12, demonstrating the associative property for easier addition. Choice C is a common error where students choose a harder grouping rather than an easier one, which happens because the making-10 strategy must be explicitly taught and the connection between property and strategy isn't automatic. To help students: Explicitly teach making-10 pairs and how to use them with associative property; practice identifying pairs that make 10 in three-number problems; use physical objects to demonstrate groupings; provide many examples where grouping to make 10 simplifies addition; use visual models like ten-frames; emphasize 'we can make 10 first' for associative; connect properties to efficient mental math strategies.
3. If $9 + 4 = 13$, then what does $13 - 4$ equal, and why?
   Answer: $13 - 4 = 9$ because subtraction undoes addition with the same numbers When you see addition and subtraction problems using the same numbers, you're working with fact families - number relationships that help you solve problems quickly. Let's think about what happens step by step. You start with 9, add 4, and get 13. Now when you subtract 4 from 13, you're taking away the exact same amount you just added. This brings you right back to where you started: 9. Addition and subtraction are opposite operations, so when you use the same numbers, one undoes the other. Think of it like walking 4 steps forward, then 4 steps backward - you end up exactly where you began. Choice A is incorrect because $13 - 4 = 9$, not 8. The reasoning about "subtracting 1 more" doesn't make sense - you're subtracting the exact same amount (4) that you originally added. Choice B gives the wrong answer of 4. While it's true that 4 appears in both problems, that doesn't mean 4 is the answer to the subtraction. Choice D is incorrect because $13 - 4 = 9$, not 10. The phrase "close to 9" should be a red flag - in math, we need exact answers, not approximations. Choice C correctly identifies that $13 - 4 = 9$ and explains why: subtraction undoes addition when you use the same numbers. Remember this fact family pattern: if $a + b = c$, then $c - b = a$. Learning these number relationships will make addition and subtraction much faster and easier.
4. Complete using grouping: (6+4)+5=6+(4+____).
   Answer: 5 This question is testing the associative property of addition — a rule that says when you're adding three numbers, it doesn't matter how you group them with parentheses. The sum stays the same! The parentheses just tell you which two numbers to add together first. Look carefully at both sides of the equation. On the left, you have (6+4)+5. On the right, you have 6+(4+____). Notice that the same three numbers appear: 6, 4, and 5. Only the grouping has moved. The 6 stayed in its spot, the 4 stayed in its spot, so the number that must go in the blank is the leftover number — 5. To check: the left side gives 10+5=15, and the right side gives 6+(4+5)=6+9=15. Both equal 15, so the grouping didn't change the answer. Now let's see why the other choices don't fit. Choosing 4 repeats a number that's already sitting outside the blank, which would leave the 5 missing entirely. Choosing 6 pulls the 6 into the wrong place — it already belongs at the front of the right side. Choosing 9 is a trap: 9 is the sum of 4+5, not one of the original numbers you're regrouping; you're asked to fill in a single addend, not the total. A helpful tip: when you see the same numbers on both sides with parentheses moved, just match up the numbers you can already see, and the blank is always the "missing" one from the set.
5. What is true about $4+7$ and $7+4$?
   Answer: They have the same sum because order doesn't matter $4+7$ and $7+4$ have the same sum because changing the order of the numbers being added doesn't change the total. Saying adding backward means subtracting confuses two completely different operations. Saying the sums are different because 7 is bigger than 4 mistakenly assumes size affects the outcome of reordering. Saying the sum changes when you switch the numbers is incorrect, since both expressions equal 11. Order doesn't matter when adding, so both expressions have the same sum.
6. Look: $6+4=10$ and $4+6=10$. Which property is shown?
   Answer: Order doesn't matter when adding This question tests 1st grade understanding of properties of operations as addition strategies (CCSS.1.OA.3). The commutative property of addition means that order doesn't matter when adding two numbers: a + b = b + a. For example, if we know that 6 + 4 = 10, we also know that 4 + 6 = 10 without having to calculate again. This is useful because we can choose to add in the easier order, like starting with the larger number. The problem shows 6 + 4 = 10 and 4 + 6 = 10 and asks which property is shown. Choice A is correct because the commutative property tells us order doesn't matter when adding, demonstrating that both equations equal 10. Choice C is a common error where students don't recognize that grouping two numbers that make 10 is easier and instead think order changes the sum; this happens because the connection between property and strategy isn't automatic. To help students: Provide many concrete examples showing both orders/groupings give same answer; use physical objects to demonstrate commutative property (count group A then B, or B then A—same total); explicitly teach making-10 pairs and how to use them with associative property; practice with equations side by side (8+3=11, 3+8=11); use visual models like ten-frames; emphasize 'order doesn't matter' for commutative, 'we can make 10 first' for associative; connect properties to efficient mental math strategies; practice identifying pairs that make 10 in three-number problems.
7. Complete using commutative property: 7+5=12. So 5+7= ____.
   Answer: 12 When you see a question about the commutative property of addition, remember this special rule: you can swap the order of the numbers you're adding, and the total stays exactly the same. Think of it like this — if you have 7 apples and add 5 more, or you have 5 apples and add 7 more, either way you end up with the same pile of apples! So since you already know that 7+5=12, you can flip the numbers around to get 5+7, and the answer must still be 12. That's why 12 is correct — swapping the order never changes the sum. Now let's look at why the other choices don't work. The answer 10 is what you'd get if you added 5+5, but that's not our problem — we need a 7 and a 5. The answer 11 is one too few; you might land here if you accidentally counted 7 and 4, or lost a number while counting. The answer 13 is one too many, which can happen if you count a number twice while adding on your fingers. Only 12 keeps the sum the same after the swap. Here's a tip to remember: whenever you see two addition problems with the same two numbers in a different order, don't recalculate — the answer is always identical. Spotting that "flip" instantly saves you time and helps you avoid counting mistakes.
8. To make adding easier, which grouping helps you add $5+8+2$?
   Answer: $5+(8+2)$ Grouping $8+2$ first makes 10, and then adding 5 more is easy. $(4+7)+3$ uses different numbers than the problem asks about. $5+(8-2)$ changes subtraction into the problem instead of just regrouping the addition. $5+8=13$ only solves part of the problem and isn't a way of grouping all three numbers. Only $5+(8+2)$ correctly groups the numbers to make adding easier.
9. Jamal adds $4+7+3$. Which change makes it easier to get to $10$ first?
   Answer: $4+(7+3)$ Grouping $7+3$ first makes 10, and then adding 4 more is easy. Grouping $4+7$ first makes 11, which doesn't lead to a ten as the first step. Changing the 3 to a 2 changes the problem instead of just regrouping it. Saying $4+7=10$ is simply incorrect, since $4+7$ equals 11. Only grouping $7+3$ first correctly makes 10 to simplify the rest of the problem.
10. Which shows the same sum as $5+8$, just in a different order?
    Answer: $8+5$ Switching the order of 5 and 8 gives $8+5$, which has the same sum as $5+8$. $5+5$ uses the wrong second number and doesn't match the original problem. $8+8$ also uses the wrong number and changes the sum. $5+3$ changes both numbers and gives a completely different sum. Only $8+5$ reorders the exact same numbers from the original problem.
11. Look: $6+4=10$ and $4+6=10$. Which property is shown?
    Answer: Order doesn't matter when adding This question tests 1st grade understanding of properties of operations as addition strategies (CCSS.1.OA.3). The commutative property of addition means that order doesn't matter when adding two numbers: a + b = b + a. For example, if we know that 6 + 4 = 10, we also know that 4 + 6 = 10 without having to calculate again. This is useful because we can choose to add in the easier order, like starting with the larger number. The problem shows 6 + 4 = 10 and 4 + 6 = 10 and asks which property is shown. Choice A is correct because the commutative property tells us order doesn't matter when adding, demonstrating that switching the numbers gives the same sum. Choice C is a common error where students think the sum changes when you switch numbers, perhaps confusing addition with subtraction. This happens because properties are abstract concepts and students need extensive experience with many examples. To help students: Provide many concrete examples showing both orders give same answer; use physical objects to demonstrate commutative property (count group A then B, or B then A—same total); practice with equations side by side (6+4=10, 4+6=10); use visual models like ten-frames; emphasize 'order doesn't matter' for commutative; connect properties to efficient mental math strategies.
12. Which two equations show the same sum because order doesn't matter?
    Answer: $8+6=14$ and $6+8=14$ Swapping the order of 8 and 6 still gives 14, which shows that order doesn't change the sum. $9+5$ also equals 14, but it uses different addends, not the same two numbers reordered. $7+7$ equals 14 too, but again with different addends, not a reorder of 8 and 6. $6+9=15$ uses the same digits but changes one number, so it isn't a true reordering. Only $6+8=14$ reorders the exact same addends and keeps the same sum.
13. If $8+3=11$, what is $3+8$? (Order doesn't change the sum.)
    Answer: 11 This question tests 1st grade understanding of properties of operations as addition strategies (CCSS.1.OA.3). The commutative property of addition means that order doesn't matter when adding two numbers: a + b = b + a. For example, if we know that 8 + 3 = 11, we also know that 3 + 8 = 11 without having to calculate again. This is useful because we can choose to add in the easier order, like starting with the larger number. The problem shows the equation 8 + 3 = 11 and asks for 3 + 8. Choice B is correct because the commutative property tells us 3 + 8 gives the same sum as 8 + 3, which is 11. Choice C is a common error where students think reversing the order changes the sum, perhaps by subtracting like 8 - 3 = 5. This happens because properties are abstract concepts and students need extensive experience with many examples. To help students: Provide many concrete examples showing both orders give same answer; use physical objects to demonstrate commutative property (count group A then B, or B then A—same total); practice with equations side by side (8+3=11, 3+8=11); use visual models like ten-frames; emphasize 'order doesn't matter' for commutative; connect properties to efficient mental math strategies.
14. Which expression shows starting at 9 and counting on 3 more?
    Answer: $9+3$ 9 + 3 writes 9 first. Start at 9 and count on 3: 10, 11, 12. 3 + 9 also makes 12. You can use the bigger number to help with either addition problem.
15. Which is easier using the commutative property: $2+9$ or $9+2$?
    Answer: $9+2$ Starting with the larger number, 9, and adding 2 more is easier to count on from, so $9+2$ is the easier way to think about it. $2+9$ starts with the smaller number, which takes more counting steps. Saying they are equally easy ignores that starting with the bigger number makes counting on simpler. Saying neither is easier avoids answering the question directly. $9+2$ is the more efficient way to add these two numbers.
16. Emma is solving $6 + 4 + 8$. She says, "I'll do $6 + 4 = 10$, then $10 + 8 = 18$." Ben says, "I'll do $4 + 8 = 12$, then $6 + 12 = 18$." What is true about their methods?
    Answer: Both methods are correct because you can group addition problems in different ways This tests the associative property of addition. Both (6 + 4) + 8 = 18 and 6 + (4 + 8) = 18 are correct because addition can be grouped in different ways. Choice C correctly identifies that both methods work. Choice A incorrectly suggests order matters in addition. Choice B incorrectly suggests size determines the method. Choice D incorrectly rejects both correct solutions.
17. Sofia adds $7+3+4$. Which grouping makes it easiest by making $10$?
    Answer: $(7+3)+4$ This question tests 1st grade understanding of properties of operations as addition strategies (CCSS.1.OA.3). The associative property of addition means that when adding three numbers, we can group them in different ways and get the same answer: (a + b) + c = a + (b + c). This is especially useful for making 10: in 7 + 3 + 4, we can group 7 + 3 first to make 10, then add 4 to get 14. Choosing the right grouping makes computation much easier. The problem asks which grouping for 7 + 3 + 4 makes it easiest by making 10. Choice C is correct because grouping (7 + 3) + 4 gives 10 + 4 = 14, demonstrating the associative property. Choice A is a common error where students make a calculation error and don't recognize that grouping two numbers that make 10 is easier; this happens because students need extensive experience with many examples. To help students: Provide many concrete examples showing both orders/groupings give same answer; use physical objects to demonstrate commutative property (count group A then B, or B then A—same total); explicitly teach making-10 pairs and how to use them with associative property; practice with equations side by side (8+3=11, 3+8=11); use visual models like ten-frames; emphasize 'order doesn't matter' for commutative, 'we can make 10 first' for associative; connect properties to efficient mental math strategies; practice identifying pairs that make 10 in three-number problems.
18. If $9+4=13$, what is $4+9$ (same sum, new order)?
    Answer: 13 This question tests 1st grade understanding of properties of operations as addition strategies (CCSS.1.OA.3). The commutative property of addition means that order doesn't matter when adding two numbers: a + b = b + a. For example, if we know that 9 + 4 = 13, we also know that 4 + 9 = 13 without having to calculate again. This is useful because we can choose to add in the easier order, like starting with the larger number. The problem shows the equation 9 + 4 = 13 and asks for 4 + 9. Choice A is correct because the commutative property tells us 4 + 9 gives the same sum as 9 + 4, which is 13. Choice B is a common error where students subtract instead of add when order is reversed; this happens because properties are abstract concepts. To help students: Provide many concrete examples showing both orders give same answer; use physical objects to demonstrate commutative property (count group A then B, or B then A—same total); explicitly teach making-10 pairs and how to use them with associative property; practice with equations side by side (8+3=11, 3+8=11); use visual models like ten-frames; emphasize 'order doesn't matter' for commutative, 'we can make 10 first' for associative; connect properties to efficient mental math strategies; practice identifying pairs that make 10 in three-number problems.
19. Maria knows that $4 + 5 = 9$. She needs to solve $5 + 4$ but forgot the answer. What is the best way for Maria to find $5 + 4$ without counting?
    Answer: She should know that $5 + 4 = 9$ because addition works the same when numbers switch places This tests the commutative property of addition. Since Maria knows 4 + 5 = 9, she can use the fact that addition gives the same result regardless of order, so 5 + 4 = 9. Choice A correctly identifies this strategy. Choice B suggests counting, which doesn't use the known fact. Choices C and D incorrectly assume the order change affects the sum by adding or subtracting 1.
20. If $9+4=13$, what is $4+9$ using the commutative property?
    Answer: 13 This question tests 1st grade understanding of properties of operations as addition strategies (CCSS.1.OA.3). The commutative property of addition means that the order of numbers doesn't matter when adding: a + b = b + a. For example, if we know that 9 + 4 = 13, we also know that 4 + 9 = 13 without recalculating, which helps in choosing an easier order like starting with the larger number. The problem gives 9 + 4 = 13 and asks for the value of 4 + 9 using the commutative property. Choice A is correct because the commutative property tells us 4 + 9 gives the same sum as 9 + 4, which is 13. Choice D is a common error where students don't understand that order doesn't affect the sum and might subtract or miscalculate, which happens because properties are abstract concepts and students need extensive experience with many examples. To help students: Provide many concrete examples showing both orders give the same answer; use physical objects to demonstrate the commutative property (count group A then B, or B then A—same total); practice with equations side by side (9+4=13, 4+9=13); use visual models like ten-frames; emphasize 'order doesn't matter' for commutative; connect properties to efficient mental math strategies.

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