Solve problems involving addition and subtraction
Up and down
Working with directed numbers is very common in real-life situations. We can think of the terms positive and negative in situations such as:
- before (-) and after (+) a certain time
- up (+) or down (-)
- forward (+) and back (-)
- receiving money, spending money
In Video 1, we look at a building with a moving lift, and think about how directed numbers could be used in this example. We also see how to write an expression to describe the movement of the lift. (By the way, you can just rewind the video if you want to see the lift moving up and down a few times!)
The context of our problem
In Video 2, we look at an example where you may need to calculate the 'time remaining', in a situation such as missing a bus. Sometimes you might need to work out how much time has already passed, or how long between events. In any of these situations, thinking of time as being similar to a number line can help. Looking out for the words that tell us whether we need to add or subtract is important, so that we can write our actual problem, or contextual problem, out as a number problem.
The order of operations needs to be followed, so when you have only addition and subtraction in your number problem, working from left to right is often the best way.
Worked Examples
Question 1
The planet Athas experiences drastic changes in temperature over the course of the day. On one day it reached a minimum temperature of$-270$−270°F, but then warmed up to a maximum temperature of $-140$−140°F.
What was the temperature change that day?
Question 2
The next flight to Los Angeles is scheduled to be in $64$64 minutes, however there is a $34$34 minute delay. After $23$23 minutes pass, how long will it be before the plane departs?
Question 3
A bus departs the depot with $20$20 passengers on it.
At the first stop, $8$8 people got off and $12$12 people got on. At the second stop, a further $3$3 people got off, and $19$19 more got on.
How many people are on the bus as it leaves the second stop?