How long on the bus?
0
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
At Scarborough School most of the children travel to school on one of several buses.
Task administration:
This task can be completed with pencil and paper or online (with auto marking displayed to students).
Level:
3
Curriculum info:
Keywords:
Description of task:
Students work out how much time some bus trips take.
Curriculum Links:
This resource can help to identify students' understanding of calculating with time for the Measurement objective and additive strategies (Number strategies).
Learning Progression Frameworks
This resource can provide evidence of learning associated with within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.Answers/responses:
| Y6 (11/2015) | ||
| a) | 35 minutes | very easy |
| b) | 45 minutes | moderate |
| c) | 65 minutes or 1 hour and 5 minutes or 1:05 | moderate |
| d) | 100 minutes or 1 hour and 40 minutes or 1:40 | difficult |
Based on results of 25 Year 6 students
Teaching and learning:
This assessment resource is about calculating with time which involves adding and subtracting using minutes and hours. A critical aspect of this task is how students add and subtract time over the hour boundary.
Diagnostic and formative information:
| Common error | Likely strategy | |
|
b)
d)
|
15 or 75
80
|
"Won't go" error in the minutes
Subtracts the larger number of minutes from the smaller number (because 30 - 45 "won't go")
|
|
b)
c)
|
55
75
|
Renaming error (subtraction error)
Crosses the single-minutes boundary without renaming it in the minutes.
|
|
b)
d)
|
85
140 or 180 or 200
|
Performs the subtraction as if there are 100 minutes per hour.
Does a "correct" subtraction based upon renaming an hour as 100 minutes.
|
|
c)
d)
|
105
140
|
Assumes 100 minutes per hour - Incorrect interpretation of time in hours and minutes
This error involves treating 1 hour as 100 minutes, rather than 60 minutes, and adding the extra minutes. For example, 1 hour and 5 minutes = 105 minutes, and 1 hour and 40 minutes = 140 minutes.
Note: This could also be done by treating a quarter of an hour as as 25 minutes (i.e., 100 minutes in the hour).
|
Next steps:
Subtraction errors - incorrect "renaming", or "won't go" errors
- These students need to do more work on subtraction or missing addend problems with ordinary (base-10) numbers. See, for example, Easy or harder subtractions or Daily timetable.
Time errors - students work as if there are 100 minutes in the hour
- Students are very used to the base 10 place value system of ones, tens, hundreds, etc and can revert back to this amidst their calculations. Another element of this is how time and hours and minutes can be written, for example 105 minutes can be written 65 minutes or, equivalently, 1:05 hours. Sometimes a simple reminder that there are 60 minutes in the hour may be all they need.
- A critical aspect of this task is how students manage addition and subtraction of time over the hour boundary and what happens to the specific base 60 place value for time (minutes and seconds). When students add or subtract over this hour boundary, adding time is much the same as adding any other 2-digit whole numbers. In the case of time, 60 minutes need to be renamed as 1 hour.
- Students could look at: Earth time or Writing time differently to see how we record time (hours in a day, days in a week, etc).
Note: Measurements and recording of times uses many diferent number-base systems which we take for granted:
For example: 7 days in a week | 12 months in a year | 60 minutes in an hour | 60 seconds in a minute | 24 hours in a day. These illustrate base 7, base 12, base 60, and base 24. There are also other ways to group the measures for days (e.g., months, year).
Because students make a range of both subtraction errors and time errors, the range of possible incorrect answers is large.
Encourage students to check if their answers are sensible, or share their answers. The act of sharing or explaining how they got their answers means that students revisit their calculations and check for sense.