There are various approaches to solving problems requiring integer multiplication and division. In the Chip Model, Positive and negative integers are represented by multiple colored chips (+ or -), which helps determine each product. One of the disadvantages of utilizing the chip model is that sure students may struggle to understand the depiction, which may cause them to become confused. The chip approach has the advantage of providing students with hands-on learning through the use of manipulative skills.
In the Number Line Model, Positive integers correspond to move to the right, while negative integers correspond to movements on the left. One problem is that it does not help students comprehend how to read an abstract number line. This strategy has the advantage of allowing children to connect repetitive addition to multiplication.
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Integers are multiplied and divided in the same way as whole numbers are. According to Wilson (2020,) the main distinction is that one must use caution and keep track of the signs. When multiplying or dividing signed numbers, start with the absolute values and use these rules to identify the sign of the result. When two integers with the same sign are multiplied, the result is always positive. Multiply the absolute values to get a positive result. When you multiply two integers with opposite signs, however, the result is always negative (Wilson, 2020). Multiply the fundamental values and subtract the result. The multiplication and changes in the signs of the integers are shown in the table below.
| Positive | x | Positive | = | Positive |
| negative | x | negative | = | Positive |
| Positive | x | negative | = | negative |
| negative | x | Positive | = | negative |
Similarly, the same applies when dividing integers, as illustrated in the table below.
| Positive | ÷ | Positive | = | Positive |
| negative | ÷ | negative | = | Positive |
| Positive | ÷ | negative | = | negative |
| negative | ÷ | Positive | = | negative |
Although the number line model is straightforward for students to grasp, all methods should be used in the classroom since each student learns differently. It is better to provide all students with the opportunity to understand integer multiplication and division laws through the various available models.
References
Wilson, R. (2020). 2. Multiplying and dividing. Number Theory: A Very Short Introduction , 14-37. https://doi.org/10.1093/actrade/9780198798095.003.0002
