Crossing the river

Crossing the river

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Further Resources
This task is about using problem-solving strategies to explore situations mathematically.
crossing-the-river-people-canoe.png
 
Two men and two children want to cross a river. None of them can swim, but they can paddle a canoe.
They only have one canoe, which will only hold one man at a time or two children. The boat can only go across the river if someone is in it. 
 
How do both the men and both the children get across the river in the least number of trips?
  • Cut out the people and the canoe from your River template sheet.
  • Cut a slit in the canoe where shown so that you can place people 'in' the canoe.
  • Use the figures, the canoe, and the River template sheet to solve this question.
  • In the table below write down who is in the canoe on each trip and the order in which the trips are made.
Trip number
Who is in the canoe?
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
River template sheet
 
 
crossing-river-river-crocodiles.png
 
crossing-river-cutout-people-canoe.png
Task administration: 
This task can be completed with pencil and paper and other equipment.
 
Equipment
Scissors, one River template sheet per student. 
 
This assessment activity can be carried out with one student at a time or by observing a small group of students working independently.
Level:
3
Key Competencies: 
Keywords: 
Description of task: 
Students use problem-solving strategies to work out how to carry two men and two children across a river using one canoe. Students record their solution on a sheet provided.
Answers/responses: 
NOTE: Other ways of solving are possible (e.g., working from the last trip backwards). 
First pattern of 4 trips, 
Trip 1 – 2 children
Trip 2 – 1 child 
Trip 3 – 1 man 
Trip 4 – 1 child
 
For repeating the first pattern of trips,
Trip 5 – 2 children
Trip 6 – 1 child 
Trip 7 – 1 man
Trip 8 – 1 child 
Trip 9 – 2 children
or
for saying that the pattern repeats (for the second adult). For everyone across the river successfully. 
 
NOTE: This mark is given regardless of any other answers that are incorrect.