Transformations
In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:
GM 3-4: Represent objects with drawings and models.
GM 3-6: Describe the transformations (Reflection, rotation, translation or enlargement) that have mapped an object onto another.
GM 4-6: Relate three-dimensional models to two-dimensional representations and vice versa.
GM 4-8: Use the invariant properties of figures and objects under transformations (reflection, rotation, translation or enlargement)
GM 5-9: Define and use transformations and describe the invariant properties of figures and objects under these transformations.
GM 3-4: Represent objects with drawings and models.
GM 3-6: Describe the transformations (Reflection, rotation, translation or enlargement) that have mapped an object onto another.
GM 4-6: Relate three-dimensional models to two-dimensional representations and vice versa.
GM 4-8: Use the invariant properties of figures and objects under transformations (reflection, rotation, translation or enlargement)
GM 5-9: Define and use transformations and describe the invariant properties of figures and objects under these transformations.
In this unit you will Learn:
1. Reflection. 2. Symmetry 3. Rotation 4. Translation 5. Enlargement 6. Tessellations |
Homework Book Pages for this Unit:
Dragon Maths 6: 88 - 92 nuLake Level 3/4: 76 - 82 nuLake Level 4: 74 - 80 nuLake 5: 98 - 106 |
What are transformations?
When a shape is transformed, it is changed in some way. This change often leads to an attractive pattern or design. Many cultures use transformations to decorate their objects and buildings.
- A shape can be transformed more than once to make a combined transformation.
- A combined transformation can be described in different ways.
- A combined transformation can give the same result as a single one.
A kowhaiwhai design can use different transformations. Hone and Tere are looking at this kowhaiwhai. Hone says he thinks translation and rotation have been used. Tere says he thinks reflection has been used. Tane say they both could be correct. Discuss.
Reflection
- Reflection is the movement or flip of a shape or pattern across a mirror line.
- Any point touching the mirror line stays in the same place after reflection.
- After an object is reflected, the shape is called an image.
- A shape has line symmetry if it has at least one mirror line.
- A line of symmetry is the fold line or mirror line for a shape that is the same on both sides of the line.
Symmetry
Rotation
- Rotation involves turning around a centre of rotation.
- The angle of rotation tells us the size of the turn.
- After being rotated, the object is called an image.
- A full turn means the image is back where the object started from.
- Rotational symmetry is how many times a shape overlaps itself in one full turn (360 degrees).
- Every shape has rotational symmetry of at least i.
Translation
Enlargement
Tessellations
- A tessellation is the covering of a surface by shapes so there are no gaps or overlaps.
- Tessellation is also called tiling.
- A tessellation can be made by repeating the same shape or by repeating different shapes.