Describe personal mental mathematics strategies that could be used to determine a given basic fact, such as:

• doubles (e.g., for 6 + 8, think 7 + 7)
• doubles plus one (e.g., for 6 + 7, think 6 + 6 + 1)
• doubles take away one (e.g., for 6 + 7, think 7 + 7 – 1)
• doubles plus two (e.g., for 6 + 8, think 6 + 6 + 2)
• doubles take away two (e.g., for 6 + 8, think 8 + 8 – 2)
• making 10 (e.g., for 6 + 8, think 6 + 4 + 4 or 8 + 2 + 4)
• commutative property (e.g., for 3 + 9, think 9 + 3)
• addition to subtraction (e.g., for 13 – 7, think 7 + ? = 13)

Observe and generalize personal strategies from different types of representations for adding 2-digit quantities (given concrete materials, pictures, and symbolic decompositions) such as:

• Adding from left to right (e.g., for 23 + 46 think 20 + 40 and 3 + 6)
• Taking one or both addends to the nearest multiple of 5 or 10 (e.g., for 28 + 47, think 30 + 47 - 2, 50 + 28 – 3, or 30 + 50 – 2 – 3)
• Using doubles (e.g., for 24 + 26, think 25 + 25, or for 25 + 26, think 25 + 25 + 1).

Observe and generalize personal strategies for subtracting 2-digit quantities (given concrete materials, pictures, and symbolic decompositions) such as:

• Taking the subtrahends to the nearest multiple or 10 (e.g., for 48 - 19, think 48 – 20 + 1)
• Thinking of addition (e.g., 62 – 45, think 45 + 5, 50 + 12 to get from 45 to 62, so the difference is 5 + 12)
• Using doubles (e.g., for 25 - 12, think 12 + 12 = 24 and 24 is one less than 25, so difference is 12 + 1).

Apply and explain personal mental mathematics strategies to determine the sums and differences of two-digit quantities.

Create a situational question that involves either addition or subtraction and that has a given quantity as the solution.

Model (concretely or pictorially) a process for the addition of two or more given quantities (with a sum less than 1000) and record the process symbolically.

Model (concretely or pictorially) a process for the subtraction of two or more quantities (less than 1000) and record the process symbolically.

Generalize (orally, in writing, concretely, or pictorially) personal strategies for estimating the sum or difference of two 2-digit quantities.

Extend personal mental mathematics strategies to determine sums and differences (of quantities less than 1000) and explain the reasoning used.

Transfer knowledge of the basic addition facts up to 18 and the related subtraction facts to determine the sums and differences of quantities less than 1000.

Generalize rules for the addition and subtraction of zero.

Provide examples to show why knowing about place value is useful when adding and subtracting quantities.