Order of Operations

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Hima Bindu

Objective: Use conventional method to prioritize order of operations.

Why do we need order of operations?

What is the answer to this.

Did you get 20 ?

Did you also see how the answer could be 16 ?

There are two possible ways to do this …

So which of the above answers do you think is correct?

Lets see few real life situations to answer this question

Lets see another example ?

Concept 1:  If a girl buys 4 pencils costing Rs 15 each , how much will she get back if she gives Rs 100?

Concept 2

Pencils come in packs of 10. I have 4 full packs and 3 extra pencils. How many pencils do I have ?

Strategies:

  1. I have 4 packs of 10 pencils plus 3 extra..so .. 4 x 10 + 3 =   43
  2. Its also 5 packs of 10 pencils with 7 missing so …. 5 x 10 – 7 = 43
  3. I have 3 pencils plus 4 packs of 10 so I do….  3 + 4 x10 = 43

In the last example teacher must emphasize that 3 shouldn’t be added to 4 because it doesn’t make sense…The context of the question helps them to understand this

The above two contexts would ensure pupils that multiplication would have to be carried out before subtraction. ( Teacher can go back and help students answer Q1)

Announcement of the Topic…BODMAS

Powerful Operations …

Students should know that mathematicians needed a standard order of operations for consistency. The most powerful operations should be completed first – Exponentiation increases or decreases at a greater rate than multiplication, which on the other hand increases or decreases at a greater rate than addition.

Sometimes we want to use a different order, so we use grouping symbols to signify “do this first” when its not the most powerful operation.

Possible Approaches for Teacher

  1. Introduce the Topic using examples
  • Emphasize DM ( as per priority left to Right) and AS ( as per priority left to right).
  • Precision and clarity in explanation and notes.
  • Questions that draw out misconceptions.
  • Numerous carefully chosen examples.

Common Misconceptions and Difficulties

  • The big misconception is thinking that addition comes before subtraction (eg.. answerin 0 for the question below)

     5 – 3 + 2

  • Failing to apply left to right Theory …
  • In algebra, failing to apply the order of operations ( eg answering 36 for the question below)
  • Misinterpretation of notation.
  •  Unsure what to do in unfamiliar examples ( eg those involving roots, fractions or multiple set of brackets)