GM3-6: Describe the transformations (reflection, rotation, translation, or enlargement) that have mapped one object onto another.
This means students will explore and describe transformations. “Transformation” is a generic term used to describe actions on shapes that result in some form of pattern, usually symmetric. A reflection is the image of a shape as seen through a mirror line either inside or outside the shape, sometimes called a “flip”. A rotation is the image of the shape turned about a point either inside or outside the shape. A translation is the image of a shift of the shape along a line, and an enlargement is the image of the shape made bigger or smaller by some scale factor. At Level Three students should be able to compare the image of a shape with the original and describe the transformation. This can include a sequence of two transformations. For example:
A' is the image of A
B' is the image of B
C' is the image of C
- Students will be able to demonstrate an understanding of tessellation through creating a design that uses more than one shape in a tessellated pattern.
- Students will be able to explain how the characteristics of the shapes enabled their ability to tessellate the pattern.
explore patterns (Problem 1)
solve problems involving transformations (Problem 2)
use addition skills to solve problems relating to distances (Problem 3)
solve problems using addition (Problem 4)
explore symmetry and tessellations
use symmetry to solve problems
- Design and make a pattern using reflection, rotation or translation.
use addition and multiplication to solve problems (Problems 1 and 4)
explore different two dimensional shapes (Problem 2)
explore reflections with paper folding (Problem 3)
explore symmetry and transformations
use addition and a systematic approach to solve problems (Problem 1)
use addition strategies in the context of calendar problems (Problem 2)
use transformations to make triominoes (Problem 3)
use addition facts to solve capacity problems (Problem 4)
use addition and a systematic approach to solve problems (Problems 1 and 2)
explore features of two dimensional shapes (Problem 3)
explore symmetry (Problem 4)
explore tessellations with shapes (Problem 2)
use operation signs to make equations (Problem 3)
- Recognise changes in properties with enlargement.
- Demonstrate why a given tessellation will cover the plane.
- Create regular tessellations.
solve problems involving sequential patterns (Problems 1 and 4)
use simple multiplicative strategies to solve problems (Problem 2)
solve problems involving enlargements (Problem 3)
- Find all the lines of reflection symmetry in a given shape.
- Identify the order of rotational symmetry of a given shape (how many times it "maps" onto itself in a full turn).
- Create designs which have reflection symmetry, rotational symmetry (orders 2, 3, 4, 6) and translational symmetry.
identify transformations as translations, reflections or rotations
design patterns that show translations, reflections and rotations
estimate and measure lengths using rulers
compare lengths using estimation and multiplication
explore the relationship between length and area under enlargement (Q5)
use scale factors from a diagram to calculate length
draw an enlargement
interpret three dimensional drawings (Problem 2)
use algebraic thinking to solve problems (Problem 3)
predict the results of paper folding reflections (Problem 4)
use logic to solve equations (Problem 1)
explore tessellations with rectangles (Problem 2)
solve problems using algebraic thinking (Problems 3 and 4)