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# 6-N-2-1

6.N.2.1 Estimate solutions to addition and subtraction of integers problems in order to assess the reasonableness of results.

In a Nutshell

Integers are the set of numbers that contain the whole numbers, including zero, and their additive inverses (opposites) (i.e., {… , −2, −1, 0, 1, 2, …}). Estimating real-world and mathematical problems that require addition and subtraction of integers involve rounding each number that is being added and subtracted to the nearest integer in order to obtain an estimated solution. Once an estimation is found, it can be used to see if the results for a given problem are reasonable and make sense in the context of the problem.

## Teacher Actions

• Develop problem-solving strategies by discussing and explaining the estimations of sums and differences of integers for given tasks.

• Verify the reasonableness of results in the context of the problem by estimating the sum and difference of integers.  For example, it would be unreasonable to estimate the distance between a point above sea level and a point below sea level to be negative because the calculation represents a distance.
• Pose purposeful questions about whether a student’s estimation to a sum or difference problem involving integers makes sense in the context of the problem.  For example, when finding a person’s total golf score, some possible questions may be “Is it reasonable for the person to have a negative golf score?” and “What is the meaning of a negative score in golf?”

• Implement tasks that promote mathematical reasoning about estimations of sums and differences of integers including tasks that are in different contexts such as temperature, altitude, golf scores, and money.

## Misconceptions

• Understand the estimation of sums and differences of integers can be used to check the reasonableness of results.

• Understand through estimation that the sum for real-world and mathematical problems involving addition can be smaller than the numbers being added together. For example, - 2 + 6 = - 4.
• Understand through estimation that the difference for real-world and mathematical problems involving subtraction can be larger than the numbers being subtracted. For example, -2 - (-6) = 4.

• Think that estimating the sum and difference of integers is not an important step in the problem-solving process in order to check the reasonableness of the answer.

• Think the estimate of the sum of a set of integers should be larger than the integers being added together.

• Think the estimate of the difference of a set of integers should be smaller than the integers being subtracted.

OKMath Framework Introduction