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Level Five

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Relevant and up-to-date teaching resources are being moved to Tāhūrangi (tahurangi.education.govt.nz). 
When all identified resources have been successfully moved, this website will close. We expect this to be in June 2024. 
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For more information visit https://tahurangi.education.govt.nz/updates-to-nzmaths

S5-1: Plan and conduct surveys and experiments using the statistical enquiry cycle: determining appropriate variables and measures; considering sources of variation; gathering and cleaning data; using multiple displays, and re-categorising data to find patterns, variations, relationships, and trends in multivariate data sets; comparing sample distributions visually, using measures of centre, spread, and proportion; presenting a report of findings.

This means that students will use the statistical enquiry cycle to plan and conduct investigations. The cycle has five phases that relate to each other. Some enquiries follow these phases in sequence but often new considerations mean that a statistician must go back to previous phases and rethink. The phases are:

GM5-9: Define and use transformations and describe the invariant properties of figures and objects under these transformations.

This means that students will accurately describe the transformation a figure or object has undergone and describe the invariant properties. At Level Five this will include the angle and centre of rotation, the distance and direction of translation, the magnitude and centre of enlargement (including fractional changes for example 1 1/2), and the line of reflection. Students will also draw the results of transformations on objects. 

Students will be able to describe which properties of shapes change for each transformation:

GM5-7: Construct and describe simple loci.

This means that students will draw the graph of linear and simple quadratic equations. They will also be able to identify the linear equation for the graph of a given simple loci.

parabola and straight line.

 
They will also describe the common properties of points on a circle or ellipse and recognise the circle as a special case of the ellipse.

 

 

circle. 

GM5-6: Create accurate nets for simple polyhedra and connect three-dimensional solids with different two-dimensional representations.

This means that students will use appropriate equipment to create accurate nets for simple polyhedra. Polyhedra are 3 dimensional shapes bound by polygons, for example a cube is made from 6 squares, a tetrahedron is made from 4 equilateral triangles, an octahedron is made from 8 equilateral triangles.  The range of polyhedra should include the platonic solids, cuboids, right-angled prisms and pyramids.

GM5-3: Deduce and use formulae to find the perimeters and areas of polygons and the volumes of prisms.

Students should create formulae for perimeters and areas of polygons by attending to features of those polygons. For perimeters they should recognise when side lengths are equal and use multiplicative strategies rather than additive ones. For example to calculate the perimeter of a parallelogram the student should double the length of two adjacent sides, for a regular pentagon they should multiply the length of one side by five.

GM5-2: Convert between metric units, using decimals.

This means that students will apply their knowledge of decimal place value to convert between units for the same attribute, for example between units for weight. They should know the meaning of prefixes used in the metric system that act as “scalars” on base units, for example “kilo” means one thousand, “centi” means one hundredth.

Students are able to convert between units for the same attribute (for example volume, mass) with more than 1 decimal place, for example 0.125 kg = 125g, or 17.5 cm = 0.175.