Integer Operations

Addition and subtraction of integers are typically taught using the following methods.

Number Line

Addition

Subtraction

Pros:
Some students can visualize the number line and direction.

Cons:
This method is not helpful if students do not have a clear understanding of an abstract number line.

Errors and next steps: If students are often off by 1 when adding or subtracting integers, they may not have made the transition from a number chart to a number line. In other words, students are counting the numbers themselves rather than the spaces between the numbers.

Links for practice and review:

http://www.mathsisfun.com/positive-negative-integers.html

http://www.coolmath.com/prealgebra/08-signed-numbers-integers

Using Rules

Addtion

• If the signs are the same, add the absolute value of the numbers. The sum is the same sign as the numbers.

Subtraction

• If the signs are different, find the difference of the absolute value of the numbers. The sign of the sum is the same as the sign of the number with the larger absolute value.

Pros: Some students find this straightforward.

Cons: Students memorizing the rules will lack the understanding needing and will often confuse these "rules" with rules for multiplication and division.

Errors and next steps: If students cannot explain how they got their answer, you might suspect they are confusing the addition and subtraction rules with multiplication and division rules. Using rules to add and subtract integers is not recommended for students to be successful in math.

Links for practice and review:

http://www.virtualnerd.com/tutorials/?id=PreAlg_01_02_0003

Making Zero Pairs

Addition

3 + –8

+   +   +
–    –   –   –   –   –   –   –


Solution is –5

Subtraction

Pros: Discrete and visual which is helpful to many students.

Cons: May be difficult to write out for larger numbers. Can cause confusion with subtraction.

Errors and next steps:

Links for Practice and Review:
Chef's Soup - Hot and Cold Cubes

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What does subtraction mean?

To subtract means to take something out or take something away. Using a vertical number line (with balloons and weights) or using the zero pairs (with hot and cold cubes in the chef''s soup) are good methods to help with understanding. For example, if a chef wants to make the soup cooler, the chef can put in a cold cube or take out a hot cube. If a hot air balloon must go higher, you can add another balloon or take away a weight from the balloon.

Students who count by ones

Students who struggle with the number line

Students off by 1 when using the number line may not understand the spaces between numbers must be counted rather than the spaces themselves. You can determine if this is true for your high school students by asking them to describe their counting. Students might say they do not know which number to start on when subtracting.