The learning goals for this section are for students to understand the need for (1) brackets in expressions and (2) assigning an order to operations.
I found this section difficult to plan for, because of how much background knowledge is required before students can successfully complete the problems proposed in the textbook. It was challenging to find a way to build the necessary understanding into each example that would allow students to feel successful with the next. I am still not entirely sure I succeeded, and I would appreciate feedback.
The first example reviews the concept of brackets, and shows what effect they can have on an expression containing only addition and subtraction. The second example adds a small amount of complexity, but sticks to addition and subtraction. The third example introduces multiplication and division. The fourth combines multiplication with addition, and explains that multiplication is simply shorthand for repeated addition.
Next, we use the acronym BEDMAS (Brackets and Exponents, Division and Multiplication, Addition and Subtraction) to state the order of operations. I am unsure if this is still the best way to present the order of operations, for the following reason. Ideally, students should understand that:
- Brackets define a priority
- Powers (exponents) are simply repeated multiplication (or division)
- Multiplication is simply repeated addition (or subtraction)
With that understanding, students should be able to comprehend intuitively what the order of operations has to be. In this lesson, it would be up to the teacher to ensure that students make that connection.
The final example puts it all together and introduces the square root symbol, which (depending on your interpretation and the level of your students), could be categorized (correctly) as an exponent or (less correctly) as a type of bracket.
To view or print the PDF, click here: 2014-09-06 1.8 Order of Operations.pdf
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