1. Home

GM4-5: Identify classes of two- and three-dimensional shapes by their geometric properties.

Thanks for visiting NZMaths.
We are preparing to close this site and currently expect this to be in June 2024
but we are reviewing this timing due to the large volume of content to move and
improvements needed to make it easier to find different types of content on
Tāhūrangi. We will update this message again shortly.

For more information visit https://tahurangi.education.govt.nz/updates-to-nzmaths

Elaboration on this Achievement Objective

This means students will use geometric properties to identify classes of shapes. Classes are categories of two or three-dimensional shapes. Shapes are sorted into classes according to defined geometric properties, such as number and relationship of sides (for example equal and parallel); number and nature of angles (for example four right angles); symmetry, number, nature, and shape of faces and surfaces (for 3-dimensional shapes). Classes can be included within other classes, can intersect or be disjoint, for example all squares are rectangles or no triangles are pentagons. At Level Four students should be familiar with:

  1. classes of polygons defined by the number of sides; triangles (3 sides), quadrilaterals (4 sides), pentagons (5 sides), hexagons (6 sides)...octagons (8 sides)...
  2. classes of 3-dimensional shapes defined by the nature of faces and surfaces; prisms (constant cross-section) and cylinders, pyramids and cones, regular polyhedral (identical faces)
  3. classes of 2-dimensional closed curves and their 3-dimensional equivalents by rotation; circles and spheres, ellipses and ellipsoids
  4. sub-classes that are included within classes: squares within rectangles, rectangles within parallelograms, parallelograms within quadrilaterals, circles within ellipses, cubes within rectangular prisms
  5. classes that are disjoint, scalene and isosceles triangles, prisms and pyramids.

 

 

Teaching resources for this Achievement Objective
Resource logo

Alien Action

Level Four
Geometry and Measurement
Figure It Out activities
This is a level 4 geometry strand activity from the Figure It Out series. A PDF of the student activity is included.

follow instructions expressed in geometric language

Resource logo

Carrie's first cubes

Level Four
Integrated
Problem solving activities
This problem solving activity has a geometry focus.
  • Apply the properties of 3-D shapes to solve a problem.
  • Visualise 3-D objects.
  • Devise and use problem solving strategies to explore situations mathematically (be systematic).
Resource logo

Compass Shapes

Level Four
Geometry and Measurement
Figure It Out activities
This is a level 4 geometry strand activity from the Figure it Out series. A PDF of the student activity is included.

construct shapes and patterns using a compass

Resource logo

Cyclic Quadrilaterals

Level Four
Geometry and Measurement
Rich learning activities
The purpose of this activity is to engage students in considering geometric properties when categorising shapes.
Resource logo

Fitness

Level Four
Geometry and Measurement
Units of Work
This unit examines regular tessellations, that is, tessellations that can be made using only one type of regular polygon, and semi-regular tessellations, where more than one type of regular polygon is involved. Students are required to investigate what properties tessellating shapes must have in...
  • Create regular and semi-regular tessellations of the plane.
  • Demonstrate why a given tessellation will cover the plane.
Resource logo

Hexagon Hunt

Level Four
Geometry and Measurement
Figure It Out activities
This is a level 4 geometry strand activity from the Figure It Out series. A PDF of the student activity is included.

identify attributes of polygons

rotate an object

Resource logo

More of Carrie's cubes

Level Four
Geometry and Measurement
Problem solving activities
This problem solving activity has a geometry focus.
  • Apply the properties of 3-D objects to solve a problem.
  • Visualise 3-D objects.
  • Devise and use problem solving strategies to explore situations mathematically (be systematic).
Resource logo

Pathway Patterns

Level Four
Geometry and Measurement
Figure It Out activities
This is a level 4 geometry strand activity from the Figure It Out series. A PDF of the student activity is included.

explore angle properties of two dimensional shapes

Resource logo

Precision Flying

Level Four
Geometry and Measurement
Figure It Out activities
This is a level 4 geometry strand activity from the Figure It Out series. A PDF of the student activity is included.

use drawing equipment to construct two dimensional shapes

Resource logo

Pyroxene

Level Four
Geometry and Measurement
Rich learning activities
The purpose of this activity is to engage students in evaluating a claim made on the basis of supporting statistics.
Resource logo

Quad Queries

Level Four
Geometry and Measurement
Figure It Out activities
This is a level 4 geometry strand activity from the Figure It Out series. A PDF of the student activity is included.

classify quadrilaterals

describe their features

Resource logo

Quadrilaterals

Level Four
Geometry and Measurement
Units of Work
In this unit we conduct a couple of investigations looking at the relationship between the angle between two diagonals of a quadrilateral, the sides of the quadrilateral, and the type of quadrilateral. The main emphasis is on rectangles.
  • Investigate the relationship between the diagonals and lengths of a rectangle.
  • Investigate the relationship between the angle of the diagonal and length of rectangles sides.
  • Use rulers, compasses and protractors accurately.
Resource logo

Shaping Up

Level Four
Geometry and Measurement
Figure It Out activities
This is a level 4 geometry strand activity from the Figure It Out series. A PDF of the student activity is included.

explore angle properties of two dimensional shapes

Resource logo

Solid Understanding

Level Four
Geometry and Measurement
Units of Work
In this unit students make and investigate various solids, including regular and semi-regular polyhedra, and cylinders and cones. They look for patterns in the numbers of faces, edges and vertices.
  • Construct models of polyhedra using construction materials, like geoshapes or polydrons.
  • Use the terms faces, edges and vertices to describe models of polyhedra and look for relationships between these features.
  • Anticipate the features of the solid created when a Platonic solid is truncated (its300
Resource logo

Tempting Tangrams

Level Four
Geometry and Measurement
Figure It Out activities
This is a level 4 geometry strand activity from the Figure It Out series.

explore geometric properties of tangram pieces

Resource logo

Tessellation, Transformation and Art

Level Four
Geometry and Measurement
Units of Work
In this unit students learn about transformations (translations, rotations, reflections) and tessellations, then apply this knowledge to create a piece of art that creatively demonstrates one or more tessellated transformations.
  • Recognise invariant properties of tessellations.
  • Apply invariant properties to continue and complete given tessellating patterns.
  • Use translations, rotations and reflections to create Escher-type tessellations.
  • Apply knowledge of tessellations to the creation of a piece of art.
Resource logo

Tiling

Level Three
Level Four
Geometry and Measurement
Figure It Out activities
This is a level 3-4 geometry strand activity from the Figure it Out series. A PDF of the student activity is included.

make and describe a tessellation pattern

describe a tessellation pattern using interior angles