This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.
A PDF of the student activity is included.
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add and subtract integers
FIO, Level 4+, Number, Book Six, Video Viewing, page 16
This activity requires the addition and subtraction of positive and negative numbers, as on the previous page, but it also requires the students to keep in mind that they are working with clock time. This means that 60 becomes a crucial number for both seconds and minutes. For example, as soon as a figure goes beyond 60 seconds, it becomes an extra minute and the seconds start again.
The activity is reasonably challenging, and the students should approach it in a considered and methodical way. Again, a number line may be a very useful way to tackle these problems, but, as indicated above, it will need to show time rather than the usual integers. The students, as a class, could discuss and draw such a time number line. It would be something like the one below, although considerably extended.
The students could draw two time lines, the second showing much larger intervals of time. This would be useful for question 4, where 2 minute and 15 minute periods need to be calculated. For example:
The notes for the previous page explain the principles of adding and subtracting integers. The students should be able to apply that learning to the questions on this page.
For example, for question 2b, the students need to add 4 minutes and 19 seconds to the -0:02:37 given in the previous question, that is, -0:02:37 + -0:04:19. One way to show this is:
They could also show this as a number line:
This activity will help the students to recognise that there are realistic circumstances in our lives where we need to be able to work with negative numbers. It could also be helpful to encourage them to discuss other circumstances where this is so, for example, students’ older family members may have overdrafts or bank loans, mortgages on houses or property, or loans for vehicles and household appliances. The students may find it interesting that a person who has very little money may be much better off than someone who has a loan to repay.
Answers to Activity
1. a. 33 min. and 46 s
b. -0:33:28
c. -0:29:03
2 . a. 26 min. and 26 s
b. 0:01:42
3. a. 2 hrs, 1 min., and 15 s
b. 
(0:29:00 will occur during the next 15 minute
viewing period.)