(Numbers and Operations > Operations with Rationals > Addition and Subtraction > Integers)
For an alternative to the number line model, try our new Integer Addition Using a Chip Model document that has students representing sums of positive and negative integers with marked chips.
The document begins by introducing the addition of two negative integers through students’ familiarity with addition of positive integers.
Early in the lesson, the concept of one positive chip and one negative chip forming a zero is introduced so that students can use this as a basis in evaluating addition expressions on the succeeding pages.
By clicking on positive and negative chips on page 3, students freely explore various addition sentences and the sums they produce. This interactive chips activity allows students to observe patterns leading to a conclusion about when the sums are negative and when they are positive.
Notice how the matching zeros appear lighter when the sum is computed, thus leaving only the remaining chips.
As students use the concept of matching zeros, they determine the sign of the remaining chips and eventually use subtraction to find the number of chips remaining. Informally students are thinking about number of chips versus the sign. This will help later when the absolute value definition and notation are formally presented in one of our other new documents, Absolute Value.
The document continues with students working addition problems by thinking of the chip model as a guide.