Time Intervals: 4.0
Supporting materials
Indicator of Progress
Students can work out how long it is between two given times, whether using clock time or dates.
Initially, students can calculate the time between two dates within the same month and between two times within one hour. In both cases, these are like calculations with whole numbers.
Next, students can calculate intervals across months, and across hours and across days. This is more complicated. The main difficulty arises when students try to apply an addition or subtraction algorithm. It is better that they solve such problems by working in stages (e.g. first building to next hour, then a whole number of hours, then adding the final minutes etc.).
Illustration 1: Diagnostic task
This task can be used to check students' skills in reading timetables. One of the main difficulties in such questions is reading the timetable in the first place. Be sure to begin by checking that students can 'see' the two trains on this timetable.
Parts a) and b) are straightforward and can be solved using subtraction, and should be readily solved by all students well before Level 4.
Part c) is an important real life application. Observing the same 20 min difference between starting and finishing times makes the question easy.
Part d) is more difficult. It is better for the students to use a strategy such as calculating how long from 12:48 to 1:00 as a first step, then calculating how long from 1:00 to 1:30. At this level, students should be working towards solving this mentally, as is normally required in everyday life.
Part of the timetable for two trains from Hurstbridge reads as follows:
|
|
P.M. |
P.M. |
|
Greensborough |
12:28 |
12:48 |
|
Watsonia |
12:31 |
12:51 |
|
Macleod |
12:35 |
12:55 |
|
|
|
|
|
Clifton Hill |
12:55 |
1:15 |
|
|
|
|
|
Southern Cross |
1:10 |
1:30 |
a) How long does the first train take to travel from Greensborough to Macleod?
b) How long is it between the times the two trains stop at Greensborough?
c) Do the two trains take the same time from Greensborough to Southern Cross?
d) How long does the second train take to travel from Greensborough to Southern Cross?
Illustration 2
Examples of the types of tasks that would be illustrative of understanding time, aligned from the Mathematics Online Interview:
- Question 41 - Calendar tasks
- Question 42 - Duration tasks using digital time
Teaching Strategies
The main teaching and learning strategy is to pose tasks that cannot be solved easily, and allow students to devise their own intuitive methods for a solution. Most of the intuitive methods will be working in stages (e.g. days to end of month, then from that month to target, then add final number of days).
In reviews of such tasks, the teacher has an opportunity to highlight important issues such as estimating, encouraging students to use their own ways to work out an answer, and emphasising the importance of explaining what they did. A written record that enables students to check their work is important.
Personalised questions are highly motivating for students, so will feature prominently in these tasks. For example, students may find out how old they are in seconds. However, a pedagogical and management issue for teachers is to check the work of students when they are working on their own questions. Teachers will not know the right answers (although they will have a good estimate), so the answer alone is not enough. Some suggestions include: getting students to write an account of what they did; getting students to explain their methods to other students; asking students direct questions about a part of their work (e.g. how did you work out how many whole months?); conducting a discussion and sharing of methods.
Activity 1: Sample questions and tasks provides a range of sample tasks on hours and minutes. Simpler calculations should be done mentally at this level.
Activity 2: Questions involving dates provides samples of more substantial time calculations involving dates.
Activity 1: Sample questions and tasks
Sample questions and tasks are suggested below for various contexts involving time.
Sample questions for clock times (be sure to ask these questions at different times on different days, to prompt students to use different strategies).
- How long is it from now until the end of this lesson?
- How long is it from now until the end of school?
At lower levels, these may be written questions. By this level, many students should be able to do these mentally.
Sporting matches
- Create a fixture and timetable for a basketball tournament with 8 teams if you have 2 courts (include realistic requirements for change over time etc)
- How long is a football game? (Mental calculation at this level)
Timetables
Get some copies of local bus or train timetables, and ask questions on time intervals relevant to the students using the timetables. Include long distance buses that travel overnight.
Activity 2: Questions involving dates
Sample questions for dates
- How long is it until your birthday? (Teachers to consider how the accuracy of each student's work can be monitored adequately.)
- How long is it until Christmas next year?
- What will be the date 100 days (100 weeks) from now?
- How long until the total of the ages of students in your class is a special number (e.g., 200, 250, 300 etc.)? When will be that special class birthday?
Choose some situations that include calculations with leap years.
Further Resources
The following resource contains sections that may be useful when designing learning experiences:
Digilearn object *
Journey Planner: quickest route 1 – students help two children travel around town. They look at a map, then check bus and train timetables. They choose the fastest route.
(https://www.eduweb.vic.gov.au/dlr/_layouts/dlr/Details.aspx?ID=4900)
Journey Planner: quickest route 2 – students help two children travel around town. They look at a map, then check bus and train timetables. They choose the fastest route.
(https://www.eduweb.vic.gov.au/dlr/_layouts/dlr/Details.aspx?ID=3306)
* Note that Digilearn is a secure site; DEECD login required.