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Properties of Addition & Subtraction

1st Grade

Alabama Course of Study Standards: 3

Apply properties of operations as strategies to add and subtract.
Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known (commutative property of addition). To add 2 + 6 + 4, the second and third numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12 (associative property of addition).
When adding 0 to a number, the result is the same number (identity property of zero for addition).

Arizona Academic Standards: 1.OA.B.3

Apply properties of operations (commutative and associative properties of addition) as strategies to add and subtract within 20. (Students need not use formal terms for these properties.)

Common Core State Standards: 1.OA.B.3

Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)

Georgia Math and ELA Standards: 1.NR.2.3

Recognize the inverse relationship between subtraction and addition within 20 and use this inverse relationship to solve authentic problems.

Massachusetts Curriculum Frameworks: 1.OA.B.3

Apply properties of operations to add. 6 For example, when adding numbers order does not matter. If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known (Commutative property of addition). To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12 (Associative property of addition). When adding zero to a number, the result is the same number (Identity property of zero for addition).

North Carolina - Standard Course of Study: 1.OA.3

Apply the commutative and associative properties as strategies for solving addition problems.

New York State Next Generation Learning Standards: 1.OA.3

Apply properties of operations as strategies to add and subtract.
e.g.,
  • If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.)
  • To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)
Note: Students need not use formal terms for these properties.

Ohio's Learning Standards: 1.OA.3

Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) Students need not use formal terms for these properties.

Tennessee Academic Standards: 1.OA.B.3

Apply properties of operations (additive identity, commutative, and associative) as strategies to add and subtract. (Students need not use formal terms for these properties.)

Wisconsin Academic Standards: 1.OA.B.3

Apply properties of operations as strategies to add and subtract.
Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Informal use of the commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Informal use of the associative property of addition.)

Alabama Course of Study Standards: 4

Explain subtraction as an unknown-addend problem.
Example: subtracting 10 - 8 by finding the number that makes 10 when added to 8

Arizona Academic Standards: 1.OA.B.4

Understand subtraction as an unknown-addend problem within 20 (e.g., subtract 10 - 8 by finding the number that makes 10 when added to 8).

Common Core State Standards: 1.OA.B.4

Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8.

Georgia Math and ELA Standards: 1.NR.2.7

Apply properties of operations as strategies to solve addition and subtraction problem situations within 20.

North Carolina - Standard Course of Study: 1.OA.4

Solve an unknown-addend problem, within 20, by using addition strategies and/or changing it to a subtraction problem.

New York State Next Generation Learning Standards: 1.OA.4

Understand subtraction as an unknown-addend problem within 20.
e.g., Subtract 10 – 8 by finding the number that makes 10 when added to 8.

Tennessee Academic Standards: 1.OA.B.4

Understand subtraction as an unknown-addend problem. For example, to solve 10 – 8 = ___, a student can use 8 + ___ = 10.

Alabama Course of Study Standards: 6

Add and subtract within 20.
  1. Demonstrate fluency with addition and subtraction facts with sums or differences to 10 by counting on.
  2. Demonstrate fluency with addition and subtraction facts with sums or differences to 10 by making ten
  3. Demonstrate fluency with addition and subtraction facts with sums or differences to 10 by decomposing a number leading to a ten.
    Example: 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9
  4. Demonstrate fluency with addition and subtraction facts with sums or differences to 10 by using the relationship between addition and subtraction.
    Example: Knowing that 8 + 4 = 12, one knows 12 - 8 = 4.
  5. Demonstrate fluency with addition and subtraction facts with sums or differences to 10 by creating equivalent but easier or known sums.
    Example: adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13

Arizona Academic Standards: 1.OA.C.6

Fluently add and subtract within 10.

Common Core State Standards: 1.OA.C.6

Tennessee Academic Standards: 1.OA.C.5

Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

Georgia Math and ELA Standards: 1.NR.2.4

Fluently add and subtract within 10 using a variety of strategies.

Louisiana Academic Standards: 1.OA.C.6

Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use mental strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

North Carolina - Standard Course of Study: 1.OA.6

Add and subtract, within 20, using strategies such as:
  • Counting on
  • Making ten
  • Decomposing a number leading to a ten
  • Using the relationship between addition and subtraction
  • Using a number line
  • Creating equivalent but simpler or known sums

New York State Next Generation Learning Standards: 1.OA.6

  1. Add and subtract within 20. Use strategies such as:
    • counting on;
    • making ten;
      e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14
    • decomposing a number leading to a ten;
      e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9
    • using the relationship between addition and subtraction; and
      e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4
    • creating equivalent but easier or known sums.
      e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13
  2. Fluently add and subtract within 10.

Ohio's Learning Standards: 1.OA.6

Add and subtract within 20, demonstrating fluencyG with various strategies for addition and subtraction within 10. Strategies may include counting on; making ten, e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14; decomposing a number leading to a ten, e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9; using the relationship between addition and subtraction, e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4; and creating equivalent but easier or known sums, e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13.

Wisconsin Academic Standards: 1.OA.C.6

Use multiple strategies to add and subtract within 20.
  1. Flexibly and efficiently add and subtract within 10 using strategies that may include mental images and composing and decomposing up to 10.
  2. Add and subtract within 20 using objects, drawings, or equations. Use multiple strategies that may include counting on; making a ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

Pennsylvania Core Standards: CC.2.1.1.B.3

Use place-value concepts and properties of operations to add and subtract within 100.

Pennsylvania Core Standards: CC.2.2.1.A.1

Represent and solve problems involving addition and subtraction within 20.

Pennsylvania Core Standards: CC.2.2.1.A.2

Understand and apply properties of operations and the relationship between addition and subtraction.

Florida - Benchmarks for Excellent Student Thinking: MA.1.AR.1.1

Apply properties of addition to find a sum of three or more whole numbers.

Florida - Benchmarks for Excellent Student Thinking: MA.1.AR.2.1

Restate a subtraction problem as a missing addend problem using the relationship between addition and subtraction

Georgia Math and ELA Standards: 1.NR.2.3

Recognize the inverse relationship between subtraction and addition within 20 and use this inverse relationship to solve authentic problems.

Georgia Math and ELA Standards: 1.NR.2.7

Apply properties of operations as strategies to solve addition and subtraction problem situations within 20.

Arkansas Academic Standards: 1.CAR.3

Apply properties of operations to add and subtract within 20.

Arkansas Academic Standards: 1.CAR.5

Demonstrate the relationship between addition and subtraction by solving problems, using an inverse operation.
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