Elementary School Math Quiz: Addition And Subtraction Properties
20 questions · exam conditions
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Addition And Subtraction PropertiesQuestion 1 of 20

Maria knows that 4+5=94 + 5 = 9. She needs to solve 5+45 + 4 but forgot the answer. What is the best way for Maria to find 5+45 + 4 without counting?

She should know that 5+4=95 + 4 = 9 because addition works the same when numbers switch places
She should count on her fingers starting from 5 and adding 4 more to get the answer
She should subtract 1 from 9 to get 8 because the numbers are in different order
She should add 1 to 9 to get 10 because 5 is bigger than 4 in this problem
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Elementary School Math Quiz

Elementary School Math Quiz: Addition And Subtraction Properties

Practice Addition And Subtraction Properties in Elementary School Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Addition And Subtraction Properties, giving you a quick way to practice the rules, question types, and explanations that matter most for Elementary School Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

Maria knows that 4+5=94 + 5 = 9. She needs to solve 5+45 + 4 but forgot the answer. What is the best way for Maria to find 5+45 + 4 without counting?

  1. She should know that 5+4=95 + 4 = 9 because addition works the same when numbers switch places (correct answer)
  2. She should count on her fingers starting from 5 and adding 4 more to get the answer
  3. She should subtract 1 from 9 to get 8 because the numbers are in different order
  4. She should add 1 to 9 to get 10 because 5 is bigger than 4 in this problem
Explanation: 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.

Question 2

Complete using grouping: (6+4)+5=6+(4+ ).

  1. 4
  2. 5 (correct answer)
  3. 6
  4. 9
Explanation: 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.

Question 3

Use grouping to make 10: (7+3)+4=(7+3)+4= what? (Grouping doesn't change the sum.)

  1. 12
  2. 14 (correct answer)
  3. 10
  4. 11
Explanation: 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 group 7 + 3 first to make 10, then add 4 to get 14. Choosing the right grouping makes computation much easier. The problem gives the grouped equation (7 + 3) + 4 and asks for the sum, emphasizing using grouping to make 10. Choice B is correct because grouping 7 and 3 first gives 10, and 10 + 4 = 14, demonstrating the associative property. Choice C is a common error where students stop after making 10 and don't add the remaining number. This happens because students need extensive experience with many examples to complete the addition after grouping. To help students: Provide many concrete examples showing both groupings give same answer; use physical objects to demonstrate; explicitly teach making-10 pairs and how to use them with associative property; practice with equations side by side; use visual models like ten-frames; emphasize 'we can make 10 first' for associative; connect properties to efficient mental math strategies; practice identifying pairs that make 10 in three-number problems.

Question 4

If 9+4=139+4=13, what is 4+94+9 (same sum)?

  1. 17
  2. 5
  3. 13 (correct answer)
  4. 9
Explanation: 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 gives 9 + 4 = 13 and asks for 4 + 9, noting same sum. Choice C is correct because the commutative property tells us 4 + 9 gives the same sum as 9 + 4, which is 13. Choice A is a common error where students might think reversing order changes the sum or make a calculation error, often because they don't recognize the property. To help students: Provide many concrete examples showing both orders give same answer; use physical objects to demonstrate; 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.

Question 5

Look: 6+4=106+4=10 and 4+6=104+6=10. Which property is shown?

  1. Order doesn't matter when adding (correct answer)
  2. You must subtract to switch numbers
  3. The sum changes when you switch numbers
  4. You can only add the bigger number
Explanation: 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.

Question 6

If 8+3=118+3=11, what is 3+83+8 (order doesn't change the sum)?

  1. 5
  2. 8
  3. 11 (correct answer)
  4. 9
Explanation: 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 C is correct because the commutative property tells us 3 + 8 gives the same sum as 8 + 3, which is 11. Choice A is a common error where students think reversing the order changes the sum, perhaps by subtracting instead of adding when order is reversed; 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); 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.

Question 7

Which is easier using the commutative property: 2+92+9 or 9+29+2?

  1. 2+92+9
  2. 9+29+2 (correct answer)
  3. They are equally easy
  4. Neither is easier
Explanation: Starting with the larger number, 9, and adding 2 more is easier to count on from, so 9+29+2 is the easier way to think about it. 2+92+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+29+2 is the more efficient way to add these two numbers.

Question 8

Look: 6+4=106+4=10 and 4+6=104+6=10. Which property is shown?​

  1. Order doesn't matter when adding (correct answer)
  2. You must add left to right only
  3. Adding in a new order changes the sum
  4. You should subtract to check
Explanation: 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.

Question 9

Sofia adds 7+3+47+3+4. Which grouping makes it easiest by making 1010?

  1. 7+(3+4)7+(3+4)
  2. (7+4)+3(7+4)+3
  3. (7+3)+4(7+3)+4 (correct answer)
  4. 3+(7+4)3+(7+4)
Explanation: 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.

Question 10

If 8+3=118+3=11, what is 3+83+8? (Order doesn't change the sum.)

  1. 8
  2. 11 (correct answer)
  3. 5
  4. 9
Explanation: 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.

Question 11

If 8+3=118+3=11, what is 3+83+8 using the commutative property?

  1. 9
  2. 5
  3. 11 (correct answer)
  4. 8
Explanation: 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 8 + 3 = 11, we also know that 3 + 8 = 11 without recalculating, which helps in choosing an easier order like starting with the larger number. The problem gives 8 + 3 = 11 and asks for the value of 3 + 8 using the commutative property. Choice C is correct because the commutative property tells us 3 + 8 gives the same sum as 8 + 3, which is 11. Choice A is a common error where students might subtract instead of adding when the order is reversed, 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 (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.

Question 12

If 9+4=139+4=13, what is 4+94+9 (same sum, new order)?

  1. 13 (correct answer)
  2. 5
  3. 9
  4. 12
Explanation: 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.

Question 13

Why do 3+93+9 and 9+39+3 have the same answer?

  1. Because order doesn't matter when adding (correct answer)
  2. Because you always add the smaller number first
  3. Because switching numbers means subtracting
  4. Because the sum changes when you switch numbers
Explanation: 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 3 + 9 = 12, we also know that 9 + 3 = 12 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 asks why 3 + 9 and 9 + 3 have the same answer. Choice A is correct because the commutative property tells us order doesn't matter when adding. Choice C is a common error where students think switching numbers means subtracting, perhaps confusing operations. 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 (3+9=12, 9+3=12); use visual models like ten-frames; emphasize 'order doesn't matter' for commutative; connect properties to efficient mental math strategies.

Question 14

Look: 3+7=103+7=10 and 7+3=107+3=10. Why are they the same?

  1. Because order doesn't matter when adding (correct answer)
  2. Because you always subtract
  3. Because bigger numbers change the sum
  4. Because 3+73+7 is different from 7+37+3
Explanation: 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 3 + 7 = 10, we also know that 7 + 3 = 10 without recalculating, which helps in mental math. The problem shows 3 + 7 = 10 and 7 + 3 = 10, asking why they are the same. Choice A is correct because the commutative property explains that order doesn't matter when adding, so the sums are equal. Choice D is a common error where students think reversing the order changes the sum, this happens because properties are abstract and students need extensive experience with 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 (3+7=10, 7+3=10); use visual models like ten-frames; emphasize 'order doesn't matter' for commutative; connect properties to efficient mental math strategies.

Question 15

If 9+4=139+4=13, what is 4+94+9 using the commutative property?

  1. 13 (correct answer)
  2. 5
  3. 9
  4. 12
Explanation: 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.

Question 16

If 9+4=139 + 4 = 13, then what does 13−413 - 4 equal, and why?

  1. 13−4=813 - 4 = 8 because you subtract 1 more than you added originally
  2. 13−4=413 - 4 = 4 because 4 appears in both the addition and subtraction
  3. 13−4=913 - 4 = 9 because subtraction undoes addition with the same numbers (correct answer)
  4. 13−4=1013 - 4 = 10 because you take away 4 from the sum and get close to 9
Explanation: 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=913 - 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=913 - 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=913 - 4 = 9 and explains why: subtraction undoes addition when you use the same numbers. Remember this fact family pattern: if a+b=ca + b = c, then c−b=ac - b = a. Learning these number relationships will make addition and subtraction much faster and easier.

Question 17

To add 2+6+42+6+4, which two should you add first to make 1010?

  1. 2 and 6
  2. 6 and 4 (correct answer)
  3. 2 and 4
  4. 2, 6, and 4
Explanation: Adding 6 and 4 first makes 10, which makes the rest of the problem easier to finish. 2 and 6 make 8, not 10, so that pair doesn't help make a ten first. 2 and 4 make 6, not 10, so that pair doesn't help either. Adding all three numbers at once skips the strategy of making a ten first. Only 6 and 4 combine to make exactly 10.

Question 18

If 8+3=118+3=11, what is 3+83+8?

  1. 9
  2. 11 (correct answer)
  3. 5
  4. 8
Explanation: 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 8 + 3 = 11, we also know that 3 + 8 = 11 without recalculating, which helps in choosing an easier order like starting with the larger number. The problem gives 8 + 3 = 11 and asks for the value of 3 + 8, noting that order doesn't change the sum. Choice B is correct because the commutative property tells us 3 + 8 gives the same sum as 8 + 3, which is 11. Choice A is a common error where students might add incorrectly or think reversing order increases the sum, often because properties are abstract and need concrete examples to understand. 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 (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.

Question 19

To add 8+2+58+2+5, which grouping makes 10 first?

  1. 8+(2+5)8+(2+5)
  2. (8+2)+5(8+2)+5 (correct answer)
  3. (8+5)+2(8+5)+2
  4. 8+2+5=8+28+2+5=8+2
Explanation: 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 8 + 2 + 5, we can group 8 + 2 first to make 10, then add 5 to get 15. The problem asks which grouping for 8 + 2 + 5 makes 10 first. Choice B is correct because grouping (8 + 2) + 5 gives 10 + 5 = 15, making the calculation easier. Choice A is a common error where students don't recognize that grouping two numbers that make 10 is easier, this happens because making 10 strategy must be explicitly taught. To help students: Provide many concrete examples showing both groupings give same answer; explicitly teach making-10 pairs and how to use them with associative property; use physical objects to demonstrate; practice identifying pairs that make 10 in three-number problems; use visual models like ten-frames; emphasize 'we can make 10 first' for associative; connect properties to efficient mental math strategies.

Question 20

What is true about 4+74+7 and 7+47+4?

  1. They have the same sum because order doesn't matter (correct answer)
  2. Adding backward means subtracting
  3. The sums are different because 77 is bigger than 44
  4. The sum changes when you switch the numbers around
Explanation: 4+74+7 and 7+47+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.