Snail Trails


This is a Level 3 Geometry activity from the Figure It Out Series.

A PDF of the student activity is included.

Achievement Objectives
GM3-3: Classify plane shapes and prisms by their spatial features.
GM3-5: Use a co-ordinate system or the language of direction and distance to specify locations and describe paths.
Student Activity

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Specific Learning Outcomes
  • Describe two dimensional shapes.
  • Describe a pathway.
Required Resource Materials
  • Square dot paper
  • FIO, Level 3, Geometry, Snail Trails, page 4
  • Ruler

The aim of this activity is for students to begin to recognise that each sequence is either a rotation, a slide (translation), or a combination of both.
To reinforce the idea, students could use a two-dimensional model of a rectangle and complete the rotations and slides. This will reinforce their ability to visualise and make predictions.
A rotation occurs when an object is turned about a fixed point, called the centre of rotation. (See the notes for page 19.) A translation occurs when a shape slides horizontally or vertically without turning. The shape does not change its size or orientation.
In question 2, although Snitch the Snail travels clockwise, the rotation of his trail is 90 degrees in an anticlockwise direction. The trail he leaves has an angle of rotation of 90 degrees.


Question 3a shows a slide or translation left and down:


Question 3b shows a rotation of 90 degrees in a clockwise direction.


Question 3c shows a rotation of 180 degrees in a clockwise direction.

Snitch’s trail fits onto itself twice in a full turn of 360 degrees (order of rotation of 2).
In question 3d, although Snitch travels clockwise, the rotation of his trail is 90 degrees in an anticlockwise direction. Note the centre of rotation:


The shapes in questions 2 and 3b, 3c, and 3d have rotational symmetry, that is, they fit onto themselves exactly when rotated about a centre point. For example:
The order of rotation is 4. The shape fits onto itself four times in a full turn of 360 degrees.

Answers to Activity



4. Discussion points will vary.


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