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Elementary and Middle School Mathematics

Order Instructions:

After reading Chapters 15 – 18 from Kiss My Math (McKellar, 2009) and reading chapter 23 from
Elementary and Middle School Mathematics: Teaching Developmentally (Van de Walle et al., 2013),
discuss one of the following.

What strategies do you use to help students understand and appropriately use the order of
operations? How might order of operations be taught in a way that is more than just memorizing the
order? In addition, integers must be connected to real contexts and to linear and quantity models.
What contexts might be used to connect to a quantity approach to integers? How can teachers build
on students� understanding of the meaning of operations as they operate within integer contexts?


Address common student misconceptions about exponents. Students easily confuse some exponent
values. Two of the most common cases are listed below. For each example:

  • Explain how the values are different in meaning.
  • Draw a representation to show how they are different.
  • Describe what investigation you would plan to help students see the differences in these values.

Example 1: 2^3 and 2 x 3 and 3^2
Example 2: 2^n and n^2 and 2n


In the order of operations, it is important to emphasize to the students to comprehend
the rules. The first strategy focuses on the use of PEMDAS (Parenthesis, exponents, multiply,
divide, addition, and subtraction) to explain the application of rules in simple calculations.
The movement of operations occurs from left to right (McKelllar, 2009). When the students
understand the simple calculations, then we can progress to the complex calculations.
Furthermore, the use of real-life context in the order of operations reduces
memorization and enhances comprehension of the order. The teacher has the responsibility of
selecting suitable contexts. This enables the students to use their knowledge to comprehend
abstract concepts (McKellar, 2009).
According to Van de Walle, (2013), there are two contexts that might be used to
connect quantity approach to integers. They are positive and negative counters and the
number line and arrows. The contexts create a plausible scenario. They make it easier for the

association of mathematical concepts to the integers. In the integers analysis, the rule of
operations forms the basis of all calculations.
Finally, introduction of integers in problem form provides the students with an
opportunity to combine the concepts of integers and operations. The teachers can show the
student one example and then provide them with an opportunity to work on another problem
form. The students need to work on the various concepts on their own and then compare
answers. The students who have got the correct answers can explain their approach to the
other students (Van de Walle et al., 2013). The involvement of students makes it easier for
them to comprehend the concepts.
In conclusion, the various strategies discussed in the essay help the students apply the
order of operations when working with integers. Moreover, the use of real-life context and
students’ participation in class activities reduces memorization and enhances comprehension
of the order of operations.



McKellar. D. (2009). Kiss my math: showing pre-algebra who’s boss. Penguin.
Van de Walle, J. A., Karp, K.S., & Bay-Williams, J. M. (2013). Elementary and Middle
School Mathematics: Teaching developmentally (8th.ed). Boston, MA: Pearson Education

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