Level 1 Shape

Achievement Objectives Learning Outcomes Unit title
  • sort, compare and classify 2D and 3D objects such as triangle, square, oblong, circle, oval, pentagon, hexagon, diamond, box, cylinder, and sphere
  • describe shape attributes in their own language
Shape Makers
  • use the language ‘side’ and ‘corner’ in describing shapes
  • classify 2D shapes according to how many sides they have
  • identify 2D shapes by name
Shape Explorers
  • classify the shapes into categories
  • discuss differences and likenesses of the shapes
  • explore, experiment and talk about the form and function of the shapes in their own language
  • follow a sequence of directions
New Kids on the Block
  • name 2-dimensional shapes: triangle, square, oblong (non-square rectangle), circle, oval, pentagon, hexagon and diamond
  • describe shape attributes in their own language
Arty Shapes

Level 2 Shape

Achievement Objectives Learning Outcomes Unit title
  • explore and describe faces, edges, and corners of 2D and 3D objects
  • make, name and describe polygons and other plane shapes
Foil Fun
  • 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

Level 3 Shape

Achievement Objectives Learning Outcomes Unit title
  • construct models of polyhedra using everyday materials
  • use the terms faces, edges and vertices to describe models of polyhedra

Shapes With Sticks

Polyhedra (3D shapes)

  • investigate properties of symmetry in shapes
  • investigate spatial features of shapes
  • use both English and Te Reo Māori to describe different polygonal shapes
Te Whānau Taparau
  • 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 Licences

Level 4 Shape

Achievement Objectives Learning Outcomes Unit title
  • explain why a shape tessellates
  • find the size of the interior and exterior angles in regular polygons
  • use the properties of interior angles in regular polygons to justify the existence of only five platonic solids
Space Tiling with Captain Planet
  • 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
  • construct models of polyhedra using construction materials, like geoshapes or polydrons.
  • use the terms faces, edges and vertices to describe models of polyhedral and look for relationships between these features.
  • anticipate the features of the solid created when a Platonic solid is truncated.
  • anticipate if an arrangement of regular polygons around a vertex will create a bounded polyhedron.
  • create nets for regular and semi-regular polyhedra using knowledge of the faces and symmetry.
Solid understanding
  • construct triangles with specified dimensions using two different techniques
  • design and construct nets for three-dimensional objects
  • name basic three-dimensional objects, especially those made with equilateral triangles
Building with triangles 

Level 5 Shape

Achievement Objectives Learning Outcomes Unit title
  • make an instrument to measure turning in a range of situations
  • measure the angle
  • investigate angles of polgons
  • find counter-examples to incorrect conjectures
Angles, Parallel lines and Polygons
  • apply Pythagoras' theorem
  • use their knowledge of the sum of interior angles of a polygon
  • construct angles based on halving and combining 90° and other straightforward angles
  • apply knowledge of length and area
How High? and Other Problems
  • construct perpendicular bisectors of lines
  • construct bisectors of angles
  • use these skills to construct equilateral triangles and squares with a given side length, parallel lines, parallelograms and trapeziums, and regular polygons with a small number of sides
  • use construction techniques, given defined parameters, to produce nets and to illustrate loci
Ruler and Compass Constructions

Level 6 Shape

Achievement Objectives Learning Outcomes Unit title
  • devise an algebraic rule to identify tilted squares that can fit on geoboards of different sizes
  • devise an algebraic rule to identify the size of the smallest square geoboard on which tilted squares can fit
  • devise and use an algebraic rule for Pythagoras’ theorem
  • devise algebraic rules to find Pythagorean triples
Tilted squares and triangles

In this part of geometry, the main goal for students to achieve by the end of primary school is a solid practical knowledge of the common two- and three-dimensional shapes and their basic properties. In Levels 1 and 2 the emphasis is on identifying and describing objects. In Level 3 this gradually changes to drawing and constructing.

Relating back to the van Hiele Stages, you can expect students to come to school at Stage 0. They will have generally have some basic acquaintance with shapes but probably not much more.

Levels One and Two: The world of students is naturally one of three-dimensional shapes. They play with boxes, move carts, and fill buckets. So it may be best to start their geometrical work in the three-dimensional area rather than a two-dimensional one.

Children first learn to recognise whole shapes. As they may have had little experience with geometry and geometrical language, they should be given every opportunity to play with objects and talk about their properties. Here are some activities that will stimulate playing and talking. Some of these can be used with both three-dimensional and two-dimensional objects.

  • sort materials – initially allow the students to use their own criteria but be prepared to add some ideas of your own;
  • build buildings – use blocks, Lego, any material that is handy. You might like to suggest that they build the tallest or the widest building they can, or a solid building or one with holes;
  • pack boxes – put blocks or tennis balls away in boxes to fit in as many as possible;
  • make models – use plasticine or whatever is around to build pirates’ cannonballs, dice and ice cream cones;
  • feel a shape – put a shape in a feely bag and get the students to identify it. You might also ask one student to ‘feel’ the shape and describe what they feel to the class so that the class can guess what the object is.

Moving from three-dimensional shapes to two-dimensional ones might be done by:

  • painting the different faces of a solid different colours. This could be extended to paint similar faces the same colour;
  • after painting a shoe box as above, make cuts down its sides of a shoe box and lay it out flat. Match the shapes on the ground to the painted faces;
  • make copies of the faces of a polyhedron on cards. The students have to match the cards to the faces.

In two-dimensions, students should explore the basic shapes (triangle, square, oblong, hexagon, circle). This can be done by:

  • feel a shape – as with three-dimensional objects;
  • cutting given shapes – what shapes can you make by making one cut through any basic shape;
  • joining triangles – cut an oblong in half. In how many ways can the two pieces be joined to make a four-sided figure? Name these figures;
  • making patterns – start of with circle, square, circle, square, circle. What comes next? Get them to repeat the pattern. This might be done on strips of paper and the end result coloured in.

Levels Three and Four: Many of the things that we have mentioned above can be used again at these Levels either with or without some variations. Below we give further activities, some of which can be used with both two- and three-dimensional objects.

  • given four objects pick which one is different;
  • given some objects pick in what ways they are the same;
  • play ‘I Spy’: one student picks an object in the classroom and the students have to guess it by using the language of geometry;
  • find how many shapes can be made with three cubes, or four squares, and so on;
  • make nets with basic shapes such as circles and rectangles. Which of these make solids?
  • try to find something new about an old shape or object.

Levels Five and Six: Students at this level are able to construct angles and shapes using instruments. They explore the properties of shapes using Pythagoras' theorem and trigonometry.
Activities could include:

  • constructing shapes with compasses and rulers
  • finding the angles of shapes and side lengths using instruments and applying formula.