Transformation Units of Work | NZ Maths

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Level 1 Transformation

Achievement Objectives	Learning Outcomes	Unit title
GM1-5	identify lines of symmetry in objects make patterns which have line symmetry describe line symmetry in their own words	Pattern Matching
GM1-5	make patterns that involve translations, reflections, and rotations identify translations, reflections, or rotations in patterns	Making Patterns

Level 2 Transformation

Achievement Objectives	Learning Outcomes	Unit title
GM2-7	make shapes with tessellations investigate shapes that tessellate make geometric patterns by translating, reflecting and rotating	In The Garden
GM2-7 GM2-3	explain in their own language what line symmetry is describe the process of making shapes with line symmetry. name common two-dimensional mathematical shapes describe the differences between common two-dimensional mathematical shapes in relation to number of sides	Fold and Cut
GM2-7	fold paper systematically cut shapes from folded paper find number patterns derived from folding and cutting using a table	Fold and Cut 2
GM2-7	create simple tessellations involving squares and dominoes identify the repeating element(s) in simple tessellations involving squares and dominoes	Tessellating Tiles

Level 3 Transformation

Achievement Objectives	Learning Outcomes	Unit title
GM3-6 GM3-4	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	Logo Licenses
GM3-6	demonstrate why a given tessellation will cover the plane create regular tessellations	Keeping In Shape

Level 4 Transformation

Achievement Objectives	Learning Outcomes	Unit title
GM4-8	recognise when one figure is a reflection of another using variant properties such as perpendicular distance from the mirror line, equalities of lengths, areas and angles, and opposite orientation in relation to the mirror line. recognise the rotational symmetry of a figure including identifying the centre of rotation and the order and angle of rotation. create symmetrical patterns using the properties of translation, reflection, and rotation.	Transformations
GM4-8	alter polygons to create unique shapes that tessellate describe the reflection or rotational symmetry of a shape or tessellation	Tessellating Art
GM4-8 GM4-5	create regular and semi-regular tessellations of the plane demonstrate why a given tessellation will cover the plane	Fitness
GM4-8 GM4-2 NA4-3	follow instructions, in diagram form, to construct two-dimensional mathematical shapes, e.g. triangles, quadrilaterals, pentagons and hexagons enlarge and reduce two-dimensional mathematical shapes by a given scale factor identify invariant properties when enlarging and reducing two-dimensional mathematical shapes convert between mm and cm measurement multiply whole numbers by a decimal	Team Puzzles

Level 5 Transformation

Achievement Objectives	Learning Outcomes	Unit title
GM5-9	find the scale factors for length, area and volume identify the centre point of an enlargement place similar objects to show a negative enlargement	Russian Boxes
GM5-9 GM5-4 NA5-4	use scale factors to investigate areas being enlarged use scale factors to investigate volumes being enlarged solve real life context problems involving scale factors	Scale Factors for Areas and Volumes
GM5-10 NA5-4	measure the lengths of the sides of sets of similar right angled triangles and find the ratio of sides investigate the relationship between these ratios and the angle size use calculators or tables to find the sine, cosine and tangent of angles	Introducing Trigonometry
GM5-10	label right angle triangles with respect to a given angle. use trigonometric ratios to calculate the length of opposite and adjacent sides in right angled triangles use trigonometric ratios to calculate the size of angles in right angled triangles	Using Trigonometry
GM5-10	state and explain Pythagoras' theorem use Pythagoras' theorem to find the unknown sides of right angled triangles	Pythagoras' Theorem
GM5-10	find lengths of objects using Pythagoras' Theorem understand how similar triangles can be used to prove Pythagoras' Theorem understand that Pythagoras' Theorem can be thought of in terms of areas on the sides of the triangle	Gougu Rule or Pythagoras' Theorem
GM5-10	describe and demonstrate how trigonometry can be used to find the height of a tall building or tree describe and demonstrate how trigonometry can be used to find the height of a high hill, or other high object where one cannot stand directly beneath the highest part describe in broad terms how trigonometry might be used to find the distance between the earth and the moon	Trigonometric applications outside the classroom
GM5-10	measure lengths and angles accurately find the height of objects using trigonometry	Dizzy Heights
GM5-10	use cos to solve problems involving right-angled triangles solve equations of the form cos(θ) = a, for a between –180° and 360° state the value of cos(θ) in special cases graph y = cos(θ)	Investigating the Idea of Cos
GM5-10	use sin to solve problems involving right-angled triangles solve equations of the form sin(θ) = a, for a between –180° and 360° state the value of sin(θ) in special cases graph y = sin(θ) describe some of the ways in which the sine, cosine and tangent functions are related	Investigating the Idea of Sin
GM5-10	use tan to solve problems involving right-angled triangles solve equations of the form tan(θ) = a, for a between –180° and 360° state the value of tan(θ) in special cases graph y = tan(θ)	Investigating the Idea of Tan