Order of operations (age 10+)
Look for and use mathematical structure: exploit the hierarchy of 2-D shapes to deduce properties; use order of operations and algebraic structure to simplify expressions; connect fraction–decimal–percentage equivalences; use ratio structure to solve proportion problems efficiently
What a learner can do afterwards
- Use the property that all rectangles are parallelograms to deduce missing angle facts
- Recognise that 3 × (n + 5) = 3n + 15 by applying distributive structure
- Use the equivalence 1/8 = 0.125 = 12.5% flexibly to solve a comparison problem
The lesson
Look at 2 + 3 × 4. If you work left to right, you get 2 + 3 = 5, then 5 × 4 = 20. But if you multiply first, you get 3 × 4 = 12, then 2 + 12 = 14. Two different answers is a problem, so mathematicians agreed on one order to always use.
The order is: brackets first, then multiply and divide (left to right), then add and subtract (left to right). Follow this order every time and everyone gets the same answer.
Priya compares 1/8 of a pizza with 12% of a cake. She remembers that 1/8 = 0.125 = 12.5%. Since 12.5% is more than 12%, the pizza slice is the bigger piece.
Look for structure everywhere. 3 × (n + 5) is the same as 3n + 15, because the 3 multiplies both parts inside the brackets. Spotting patterns like this, in numbers or shapes, helps you work faster and check your answers.
Do brackets first, then multiply and divide, then add and subtract, and keep an eye out for patterns like this in every part of maths.
Watch it
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.