Road journeys

Road journeys

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about solving problems involving speed and distance.
 
NOTE: Speed =
 
a) The distance between Auckland and Taupō by road is 278 kilometres. If the time taken for this journey is 4 hours, what is the average speed? (Show your working.)

 
 
 
 
 
b) The Weepu whānau were travelling from Rotorua to Wairoa for a whānau hui. The journey took them 4 hours and their average speed was 55 kilometres per hour. How far is it from Rotorua to Wairoa? (Show your working.)

 
 
 
 
 
c) A group of Year 10 students from Invercargill were going by bus to Milford Sound. The bus company said that the bus would travel at an average speed of 50 kilometres per hour for the journey. The students knew the distance from Invercargill to Milford was 275 km. How long would the journey take? (Show your working.)

 
 
 
 
 
d) A car travelled at an average speed of 45 kilometres per hour for 20 minutes. How far would the car have travelled in this time? ____________________
 
e) If the car travelled 20 km in 15 minutes, what was its average speed? __________ kilometres per hour
 
f) If the car travelled 60 km at an average speed of 90 kilometres per hour, how long would the journey have taken? __________ minutes
Task administration: 
This task is completed with pencil and paper only.
Level:
5
Curriculum info: 
Maths, Number and Algebra, Number Strategies
Key Competencies: 
Using language, symbols, and texts
Keywords: 
physics concepts, speed, distances, time, formulae
Description of task: 
Task: calculate answer to questions about speed, distance, and time. Assessment focus: using a formula.
Curriculum Links: 
Key competencies
This resource involves recording the strategies students use to solve problems involving speed and distance. This relates to the Key Competency: Using language, symbols and text.
For more information see http://nzcurriculum.tki.org.nz/Key-competencies
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Multiplicative thinking, sets 8-9
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
 

Y10 (11/2003)
a)

Any one of:

•    Speed =
•    s =

69.5 kph (or km/h)
correct working - easy
correct answer - moderate
b)   

Any one of:

•    Distance = Speed × Time
•    d = 55 × 4

220 km
correct working - easy
correct answer - easy
c)   

Any one of:

•    Time =
•    s =

51/2 hours
correct working - easy
correct answer - moderate
d)    15 km difficult
e)    80 km/h difficult
f)    40 minutes very difficult
Diagnostic and formative information: 

This resource was trialled by 165 students. A small number of students in the trial appeared to need more practice in correctly determining fractions of an hour. Some thought 5.5 hours would be 5 hours and 5 minutes, or 5 hours and 50 minutes. Many students did not demonstrate the proportional reasoning required for answering questions d) - f).