Excellent Math Performers have a habit to predict possible answers or think about reasonable answers. If you are working out the side length of a triangle and you get a negative answer – you might have made a mistake somewhere, because lengths should be positive. Here are some common logical arguments that might help you in reasoning about answers and predicting possible outcomes:
- Lengths are positive
- The term number of a number pattern is always positive – I can’t find the (-10 th) term.
- I can’t divide by zero
- I can’t find the square root of a negative number…. Also if I square something – it should be positive (bigger than or equal to 0)
- If I’m working out the height of a building – 0.3 metres and 120 km are ridiculous answers. 2.7 Metres is a perfectly acceptable answer.
- If I’m working with a number of students, animals, books, etc. decimal numbers are not valid answers – I need a positive integer as an answer, so if I get 2,6 students, I’ll answer 3 students.
- Similarly – if I predict the outcome on a dice – it should be a positive integer between 1 and 6. It can’t be 8 or 12,4 or -4
- The answers of sin and cos should lie between -1 and 1. Pi is 3,14… and is not a valid answer. If sin(x) gives an answer of 3pi, I’ll check my calculator settings. You also can’t find if x is smaller than -1 or bigger than 1.