Level 1 Shape
Achievement Objectives  Learning Outcomes  Unit title 
GM12 

Shape Makers 
GM12 

Shape Explorers 
GM12 

New Kids on the Block 
GM12 

Arty Shapes 
Level 2 Shape
Achievement Objectives  Learning Outcomes  Unit title 
GM24 

Foil Fun 
GM24 GM27 

Fold and Cut 
Level 3 Shape
Achievement Objectives  Learning Outcomes  Unit title 
GM33 


GM33 

Te Whānau Taparau 
GM34 GM36 

Logo Licences 
Level 4 Shape
Achievement Objectives  Learning Outcomes  Unit title 
GM45 

Space Tiling with Captain Planet 
GM45 

Quadrilaterals 
GM45 GM46 

Solid understanding 
GM46 GM41 

Building with triangles 
Level 5 Shape
Achievement Objectives  Learning Outcomes  Unit title 
GM55 

Angles, Parallel lines and Polygons 
GM55 GM53 

How High? and Other Problems 
GM55 GM56 GM57 

Ruler and Compass Constructions 
Level 6 Shape
Achievement Objectives  Learning Outcomes  Unit title 
GM66 NA67 

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 threedimensional 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 threedimensional shapes. They play with boxes, move carts, and fill buckets. So it may be best to start their geometrical work in the threedimensional area rather than a twodimensional 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 threedimensional and twodimensional 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 threedimensional shapes to twodimensional 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 twodimensions, students should explore the basic shapes (triangle, square, oblong, hexagon, circle). This can be done by:
 feel a shape – as with threedimensional 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 foursided 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 threedimensional 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.