Powers, roots and the rules of the road

Maths has its own shorthand and its own road rules. Once you know them, you can read and write calculations that anyone in the world will understand in the same way.

Powers and roots

A power is a quick way to write repeated multiplication. 5² (five squared) means 5 × 5 = 25. 2³ (two cubed) means 2 × 2 × 2 = 8. The small raised number is called the exponent. A square root goes backwards: √25 = 5, because 5 × 5 = 25. A cube root does the same for cubes: ∛8 = 2.

Below zero

Negative numbers are numbers less than zero. On a thermometer, zero degrees Celsius is where water freezes. The coldest temperature ever recorded in New Zealand was −25.6°C at Ranfurly in Central Otago. In winter at Scott Base in Antarctica it is often colder than −30°C. For heights, sea level is zero. Aoraki/Mt Cook is 3,724 metres above it, and the Kermadec Trench, north-east of Aotearoa, is about 10,000 metres below it.

To find the gap between a negative and a positive number, count up to zero and then keep going. From −25.6°C to 20°C is 25.6 + 20 = 45.6 degrees. A number line makes this easy to see.

The order of operations

What is 3 + 4 × 2? If you add first you get 14. If you multiply first you get 11. Mathematicians agreed long ago to use one order, so everyone gets 11. Your curriculum uses the word GEMA to help remember it:

Engineers, nurses working out medicine doses and computer programmers all rely on this order. A calculation done in the wrong order can give a very wrong answer.