Travelling from Wellington to Auckland

Travelling from Wellington to Auckland

Auto-markingPencil and paperOnline interactive
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about percentages and fractions of distance.

route-wn-ak.png

 

Distances from Wellington in Kilometres
 
Wellington to Sanson Wellington to Tūrangi Wellington to Rotorua Wellington to Auckland
140 km 330 km 460 km 700 km

 

Jade and Tim are travelling from Wellington to Auckland.

Use the table to answer the questions below.

Question 1Change answer

a)  When they reach Sanson, what percentage of the trip have they completed?
       %

Question 1Change answer

b)  How many kilometres have Jade and Tim travelled when they have completed 65% of the journey?
       km

Question 1Change answer

c)  They are one-quarter of the way between Tūrangi and Rotorua when they realise Tim has
      left his wallet in a shop in Tūrangi, so they turn around and go back.
 
      How many kilometres does this now make their trip from Wellington to Auckland?
       km
Task administration: 
This task is completed with pencil and paper and online (WITH automarking).
Level:
5
Curriculum info: 
Maths, Number and Algebra, Number Strategies
Keywords: 
percentages
Description of task: 
Students express a distance as a percentage of the distance of a whole journey, and calculate percentages or fractions of parts of the journey.
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: 
 

Y9 (05/1997)

Y10 (05/1997)
a) 20 difficult moderate
b) 455 very difficult difficult
c) 765 very difficult difficult

 

Diagnostic and formative information: 
  Common error Likely calculation Likely reason
b) 460   Estimation rather than calculation or rounding the answer to the nearest 10 km.
c) 732.5 700 + 1/4 (460 - 330) Add only 1 part rather than the both of the extra distances.
c) 830 700 + 130 Add too much extra distance.