Thank you once again to the courageous individuals, Dylan and Nathanael, for having a go at the last question. Nathanael’s solution was correct as follows:
(2+3 × 5-3) ÷(6+1)=2
To solve this question, knowledge of order of operation was required. Order of operation requires operations to be completed in the following order:
Brackets
Multiplication and division
Addition and subtraction
Hence
(2+3 × 5-3) ÷(6+1)
= (2+15-3)÷(7) solve the times in the first bracket and the addition in the second bracket
= 14÷7 work from left to right in the first bracket as + and – are on the same level of order of operations
= 2
Earlier this term, stage 4 students completed a test and one of the questions was to solve a number problem that had a mix of operations. I found it surprising when a student called me over and said, “The question doesn’t say to use order of operations. Do I still have to?”
This students’ question certainly made me reflect on my teaching practice and lament the days of old. In my day, calculators were very basic and when I was in my first year at university studying engineering, I used to have to think very carefully how to enter a number calculation to ensure that it was calculated in the correct order. It was time consuming and fraught with the danger of making a mistake so would often involve repeating the process several times.
In fact, it was so frustrating that after the summer holiday between my first and second year at university, when I had worked for a supermarket packing grocery bags (yeah, I didn’t even make it to checkout operator) for $4.17 an hour, I bought a $450 calculator that enabled me to solve order of operation problems more easily.
Calculators of today automatically do order of operations which unfortunately means it is not such a critical skill for students but they will still come unstuck when algebra is involved or when working with negative numbers and powers.
Now for another challenge!
Two small cogs in a drive train mesh. One cog has 28 teeth and the other has 36 teeth. Each cog has one broken tooth. If the broken teeth have just meshed together, how many revolutions of each cog will be required for the broken teeth to meet again?
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