Crawling ant problem

Crawling ant problem

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about faces, edges and vertices of a 3-dimensional shape.
Crawling ant and 3-d shape
An ant crawls along the edges of this shape (it is a tetrahedron). The ant does not crawl along any edge twice.
 
a)     What is the greatest number of edges the ant can crawl along? ______
 
b)     Draw arrows on the shape to show the ant's journey.
 
c)     How many different vertices does this shape have? _______
 
Task administration: 
This task can be completed by pencil and paper only.
Level:
4
Curriculum info: 
Maths, Geometry and Measurement, Shape
Keywords: 
3-dimensional shapes, tetrahedrons, edges, vertices
Description of task: 
Students answer questions about the journey of an ant along the edge of a tetrahedron.
Curriculum Links: 
This resource can help to identify students' understanding of properties of 3-dimensional shapes.
 
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Geometric thinking, sets 4-5
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
 

Y9 (04/1998)
a) 5 moderate
b) Accept if a path along 5 edges is shown.
or accept if they show the number of paths in their answer to a).

NOTE:

•    Accept different starting points.
•    The journey must be valid,
i.e., the flow/direction the ant is walking must make sense.
easy
c) 4 moderate
Diagnostic and formative information: 
  Student response Likely reason
a)
c)		 4
3		 Fails to recognise the fifth edge.
c) 6 Confuses edge and vertex.
Next steps: 
Extend student thinking by asking: How many different routes can the ant take?