We are learning the rules for the order of operations.
I can use the order of operations rule to solve complex number problems.
If you want your calculator to divide 125 by 5 and the answer shown is 625, there is only one person to blame. A calculator always does what it is asked to do. So, if you press × instead of ÷, it won’t argue with you and ask you if you’re sure that’s what you want. It will multiply 125 × 5.
A calculator ALWAYS does what it has been told to do. However, what if the calculator has been programmed to calculate in a different way than you want it to work?
If you press 2000 + 12 × 2 =, the calculator might begin with 2000 + 12 and then multiply by 2, which equals 4024. A different calculator might multiply 12 x 2, which equals 24, and then add 2000, which equals 2024. It all depends on the way the calculator has been programmed.
G – Grouping
- Anything that is grouped together in a bracket is calculated first. eg. 2 x (3- 1) = 2 x 2 = 4
E – Exponents
- Next comes exponents (and/or square roots) eg. 4 x 4 × 32 = 4 × 9 = 36
M – Multiply and Divide
- Then work from left to right doing division and/or multiplication. eg. 10 + 6 ÷ 2 = 10 + 3 = 13
A – Add and Subtract
- Finally, work from left to right doing addition and/or subtraction. eg. 4 + 2 × 3 = 4 + 6 = 10
In independent practice, we had to use the rules of GEMA to solve the following problems without a calculator.
The first two questions were
1) a. 6 + 21 ÷ 3 = 10
to solve this question, you have to solve division first then the addition, according to GEMA. eg. 21 ÷ 3 = 4 + 6 = 0
b. 3 x 4 – 2 = 10
To solve this question, you have to solve the timetable first and then do the subtraction afterwards. e.g., 3 x 4 = 12 – 2 = 10
On Friday, we had a post-test on the order of operations, and I was honestly feeling a bit nervous about it beforehand. At first, I thought the questions were going to be much harder than they actually were. Whenever I hit a problem that I was struggling with, I grabbed a whiteboard to map out the steps and visualised the math. Taking that extra step to scratch out the work completely changed my confidence level. When I finally finished and saw my results, I was so excited to see that I got a perfect 100%, which was a much higher score than I ever expected to get!
The order of operations is a set of rules that dictates the sequence to follow when solving mathematical expressions with multiple operations. It ensures everyone evaluates equations the same way to arrive at the correct, consistent answer.
Have you learned about this before?