Addition And Subtraction Properties
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1st Grade Math › Addition And Subtraction Properties
If $8+3=11$, what is $3+8$ (order doesn’t change the sum)?
5
8
9
11
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.
Which is easier using the commutative property: $2+9$ or $9+2$?
You must subtract
They are not equal
$9+2$
$2+9$
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 the order of numbers doesn't matter when adding: a + b = b + a. For example, if we know that 2 + 9 = 11, we also know that 9 + 2 = 11, and starting with the larger number can make counting on easier. The problem asks which is easier using the commutative property: 2 + 9 or 9 + 2. Choice B is correct because the commutative property allows us to reorder to 9 + 2, which is easier by counting on from the larger number. Choice C is a common error where students don't understand that order doesn't affect the sum, this happens because properties are abstract concepts and need concrete examples. To help students: Provide many concrete examples showing both orders give same answer; use physical objects to demonstrate commutative property; practice with equations side by side (2+9=11, 9+2=11); use visual models like ten-frames; emphasize 'order doesn’t matter' for commutative; connect to efficient mental math strategies like counting on from larger.
Which way is easier to add, using order doesn't matter: $2+9$ or $9+2$?
$2+9$
You cannot change the order.
$9+2$
They are different answers.
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, adding 9 + 2 might be easier than 2 + 9 because we can start with the larger number and count on, making mental math quicker. The problem asks which way is easier to add, 2 + 9 or 9 + 2, using the idea that order doesn't matter. Choice B is correct because 9 + 2 allows starting with the larger number, making it easier to compute using the commutative property. Choice A is a common error where students choose a harder order, which happens because the connection between property and strategy isn't automatic and must be explicitly taught. To help students: Provide many concrete examples showing both orders give the same answer; use physical objects to demonstrate commutative property; explicitly teach starting with the larger number for easier addition; practice with equations side by side; use visual models like ten-frames; emphasize 'order doesn't matter' for commutative; connect properties to efficient mental math strategies like counting on from larger.
Which two equations show the same sum because order doesn't matter?
$8+6=14$ and $8+6=13$
$8+6=14$ and $8+5=14$
$8+6=14$ and $6+8=14$
$8+6=14$ and $6+8=12$
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 8 + 6 = 14, we also know that 6 + 8 = 14 without having to calculate again, which is useful because we can choose to add in the easier order, like starting with the larger number. The problem asks which two equations show the same sum because order doesn't matter. Choice A is correct because 8 + 6 = 14 and 6 + 8 = 14 demonstrate the commutative property with the same sum. Choice B is a common error where students don't recognize that order doesn't affect the sum and make a calculation error, 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 commutative property (count group A then B, or B then A—same total); practice with equations side by side (8+6=14, 6+8=14); use visual models like ten-frames; emphasize 'order doesn't matter' for commutative; connect properties to efficient mental math strategies.
Which shows associative property for $7+3+4$ to make 10 first?
$7+(3+4)=7+7$
$7+3+4=7+3$
$(7+3)+4=10+4$
$(7+4)+3=11+3$
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 to make computation much easier. The problem asks which expression shows the associative property for 7 + 3 + 4 to make 10 first. Choice C is correct because (7 + 3) + 4 = 10 + 4, grouping to make 10 first and demonstrating the associative property. Choice D is a common error where students make a calculation error by incomplete addition, 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 different groupings giving the same total; provide many examples 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.
Complete using commutative property: $7+5=12$. So $5+7=, $.
2
7
10
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 7 + 5 = 12, we also know that 5 + 7 = 12 without recalculating, which helps in choosing an easier order like starting with the larger number. The problem gives 7 + 5 = 12 and asks to complete 5 + 7 = __ using the commutative property. Choice C is correct because the commutative property tells us 5 + 7 gives the same sum as 7 + 5, which is 12. Choice A is a common error where students might add incorrectly or think of a different property, 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 (7+5=12, 5+7=12); use visual models like ten-frames; emphasize 'order doesn't matter' for commutative; connect properties to efficient mental math strategies.
To add $2+6+4$, which two should you add first to make 10?
2 and 4
2 and 6
6 and 2
6 and 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 2 + 6 + 4, we can group 6 + 4 first to make 10, then add 2 to get 12. Choosing the right grouping makes computation much easier. The problem asks which two to add first to make 10 in 2 + 6 + 4. Choice C is correct because grouping 6 and 4 first gives 10, and 10 + 2 = 12, making the calculation easier. Choice B is a common error where students don't recognize that grouping two numbers that make 10 is easier, perhaps choosing two smaller numbers instead. This happens because the making 10 strategy must be explicitly taught. 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.
Use grouping to make 10: $(7+3)+4$ equals ____.
12
13
14
15
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. The problem asks for the value of (7 + 3) + 4 using grouping to make 10. Choice D 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 make a calculation error, perhaps adding all without grouping, this happens because students need extensive experience with many examples. 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 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.
Which shows the commutative property: $6+4=10$ and ____ ?
$4+6=10$
$6+6=12$
$10+0=10$
$6+4=11$
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, which is useful because we can choose to add in the easier order, like starting with the larger number. The problem asks which equation shows the commutative property paired with 6 + 4 = 10. Choice A is correct because the commutative property tells us 4 + 6 gives the same sum as 6 + 4, which is 10. Choice D is a common error where students make a calculation mistake, thinking 6 + 4 = 11 instead of 10, 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 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; 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.
Look: $3+7=10$ and $7+3=10$. Why are they the same?
Because $3+7$ is different from $7+3$
Because you always subtract
Because bigger numbers change the sum
Because order doesn’t matter when adding
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.