Rich tasks
- These are open-ended activities that require students to create a presentation that explains transformation using a shape, picture or action. Students also develop a pattern using translation, reflection and rotation. Each task can be given at the start of a topic, done as the students gain enough knowledge to complete it, inserted into a topic at an appropriate place. The first task could also be given as a homework project.
- Shape shifting
> More on "Rich tasks for this Chapter"...
1. Shape shifting
- Students should be familiar with the concept of reflection and translation from Level 1 activities relating to position and orientation. Understanding rotation (turn) is the new element of transformation introduced at Level 2 of the NZ curriculum, while enlargement is introduced at Level 3.
- Encourage students to be creative in their presentations. Presenting their ideas using a variety of media will add interest to the sharing back.
- To keep the focus on the mathematical ideas, ensure that all presentations are accompanied by a description (either written, recorded in the presentation, or as part of the sharing process). You could introduce the task by discussing the example in the text, which includes a definition of the type of transformation, and how this has changed the position or orientation of the original shape.
- Teachers can decide whether students should use the same or new shapes or pictures for the patterning part of this Rich Task.
- Students may have been introduced to transformations at Level 1 using more familiar vocabulary of slide, flip and turn. At the beginning of Level 2 the mathematical vocabulary of translation, reflection or rotation are introduced. It is helpful to use the terms together / interchangeably to support this transition.
Translation, reflection and rotation page 270
- Know that when a shape is reflected, its direction is reversed, so that it looks as it would in a mirror, but its size and shape is not changed.
- Know that when a shape is translated, it moves, but its size, shape and orientation are not changed.
- Know that when a shape is rotated, it is moved around a point. The shape may look different, but its size and shape are not changed, only it’s orientation.
- Be able to predict how a shape will look when it has been translated, reflected or rotated.
> More on "Translation, reflection and rotation"...
Teacher notes
- Depending on prior knowledge and experience students will need to practise reflecting, translating, and rotating a variety of shapes using real materials or pictures, before they will be able to manipulate mental images to predict the results of these transformations. This use of materials should be encouraged for as long as necessary.
- Sometimes students notice that the same image may be created using different transformations. Ask students to explore and discuss these assertions to decide whether they are always true e.g. a half turn may look the same as a reflection (but only if the original shape is symmetrical), a ½ turn clockwise will look the same as a ½ turn anticlockwise.
- Remember to work backwards sometimes, for example, if this is the shape after a ¾ turn clockwise, what did it look like beforehand?
Patterns page 274
- Repeat transformations to create a pattern.
- Identify the transformation(s) that has created the pattern and predict the next item in the pattern.
> More on "Patterns"...
Teacher notes
- Encourage students to create reflective patterns using horizontal, vertical and diagonal mirror lines. For example, for a border, students could reflect a picture horizontally down the page and vertically across it.
- You could make or use a selection of tracing templates (that students can quickly draw around) to improve uniformity of shape and speed of completion.
- As students become more confident encourage them to create more interesting patterns with the same shape by alternating two different transformations, for example, reflect, translate, reflect, translate.
- Using digital technology and programmes such as Microsoft Word that can copy and paste more complex and interesting images and rotate and reflect them quickly is an option for students who are digitally capable or have support at home.
- Students may also notice that a pattern begins to repeat. When using technology, students can check if they have selected the core pattern by using the copy and paste function.
- Give opportunity to practise identifying and describing the patterns they are creating.
