This method uses manipulatives so that students can experience the operation in a hands-on way. It emphasizes the fact that opposite integers add to 0. This model can be used to do integers manipulation inexpensively and easily replicated at home. In chip, if you combine a negative and a positive, a zero is obtained. In multiplication, the chip is used to represent the numbers in the question. For example, -2 × -4=, the -2 is read as “take away two groups of,” and then -4 as the size of the group.
The chip model has advantages over the other model in the multiplication and division of integers. This method is more straightforward and more movable as students can see the digits they are manipulating and think it through to make sense of it. This method also allows students to be more creative as they calculate the integers manipulation (Velit, 2020). Students open their minds to visibly understand the concept better. Because it is practical, they easily relate it to the real world, making the teacher interact with the whole class making the lesson interactive. However, this method does not allow a student to do the calculation in their head; a student must physically do all the work to see the calculation through. The other major disadvantage of this method is that one cannot be ascertained that his or her work was right as there is no feedback on whether to prove if one is right or wrong.
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Number Line Model
This model reinforces the idea of opposites and negatives by having students moving left and right directions on the number line. This model also bridges the idea of multiplication as repeated addition. For example, 3 × -1=, the first number shows which direction they will be starting with, and the second number tells us in what direction they will be moving and how far. The first number tells students how many steps they will be taking, and the second number tells how big each step will be. Hence, the answer will be -3.
The number line model has its advantages that one will prefer over other models. The number line model provides immediate feedback making it easier to tell if one4 wrong or right. It also makes the calculations a lot quicker to grasp the concept as it gives a variety of steps to be observed. In addition, this method often provides an explicit connection between symbolic representation and visual representations. However, the number line model limits the teacher's ability to follow the students throughout the calculation, also forces one to think abstractly.
Conclusively, both models of integer multiplication and division have advantages and disadvantages too. One has to be careful to know which model will fit with his workings perfectly. However, on multiplication, I will prefer the chip model over the number line model, and on division, I will prefer the number line model over the chip model.
References
Velit, K. (2020). Training Educators to Integrate Outdoor Education into the Curriculum in order to Support Students with Disabilities.
