Elaborations on Level Four: Geometry and Measurement

Measurement

GM4-1: Use appropriate scales, devices, and metric units for length, area, volume and capacity, weight (mass), temperature, angle, and time.

This means students will work with the commonly used units of the metric system and measurement devices for:

• Length- kilometre, metre, centimetre, millimetre, using rulers and tape measures
• Area- square kilometre, hectare, square metre, square centimetre
• Volume/Capacity- Cubic kilometre, cubic metre, litre (cubic decimetre), cubic centimetre using jugs, measurement cylinders
• Weight- tonne, kilogram, gram, using scales
• Temperature- degrees Celsius using thermometers

They should also be able to work with standard units for angle and time, degrees, hours, minutes, seconds. In carrying out measurement tasks students should be able to estimate approximate measurements, use units and devices that are appropriate to the task, for example measuring a cup of water in cubic centimetres, read scales with accuracy, for example a ruler to the nearest millimetre or a protractor to the nearest degree, and use symbols to record their results, for example 45mg (45 milligrams) or 6km ² (6 square kilometres). Supporting teaching resources.

GM4-2: Convert between metric units, using whole numbers and commonly used decimals.

This means 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. Conversions are restricted to convertinhg between whole number or decimal measures involving tenths, for example 0.6ha = 6000m² or 675mm = 67.5cm. Supporting teaching resources.

GM4-3: Use side or edge lengths to find the perimeters and areas of rectangles, parallelograms, and triangles and the volumes of cuboids.

At Level Four students should apply their multiplicative strategies to find perimeters and areas of commonly used polygons and volumes of cuboids where the lengths of sides and edges are given as whole number measures. Calculations required are:

Rectangle: Area = base x height Perimeter = 2 x (base + height)	Parallelogram: Area = base x height Perimeter = 2 x (base + side length)	Triangle: Area = 1/2 (base x height) Perimeter = side + side + side

Cuboid: Volume = base x height x depth

Students should express the areas and volumes using symbols, for example 48cm³ (48 cubic centimetres).
Supporting teaching resources.

GM4-4: Interpret and use scales, timetables, and charts.

This means students will be literate in getting required information from the following:

1. Scales, such as thermometers, analogue (and digital) clocks, rulers, protractors, weight scales, capacity containers.
2. Timetables, such as those used in transport (12 or 24-hour time), tides, broadcast programming, telephone books (international calls), sports events.
3. Charts used to convey measurement information, such as weather reports, cooking recipes, Guiness Book of Records, statistics on living organisms.

At Level Four it is expected that students will use the information from scales, timetables and charts in the course of solving problems and select information that is relevant to solving the problem. Supporting teaching resources.

Click to download a PDF of second-tier material relating to Level 4 Measurement (150KB)

Shape

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

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.
   Supporting teaching resources.

GM4-6: Relate three-dimensional models to two-dimensional representations, and vice versa.  

This means students will focus on key characteristics of 3-dimensional models (shape and relationship of faces and surfaces, faces joining at edges and vertices) to create 2-dimensional drawings of those models. Drawings of objects can take the form of isometric projections, plan views or nets. Students should also be able to construct a model from given 2-dimensional drawings, for example build a model using interlocking cubes from the plan views below.

Students should be able to create nets for simple polyhedral and closed surfaces by visualising the “unwrapping” of those solids, for example the net for a cube. Supporting teaching resources.

Position and orientation

GM4-7: Communicate and interpret locations and directions, using compass directions, distances, and grid references.

This means students will apply their understanding of the measurement system, particularly of length and angle. This involves converting the scale on a map to actual measurements and describing direction given the orientation of North.

1. Give or interpret the location of a feature on a map using grid references (for example, AA 24), distances and direction from a landmark (for example, 160m South-East of the library), or coordinates (for example, Latitude 12^o South, 77^o East).
2. Follow instructions given by others using coordinates or grid references, compass directions and distances and by interpreting a scale map, for example travel from New Plymouth to Tauranga.
   Supporting teaching resources.

Transformation

GM4-8: Use the invariant properties of figures and objects under transformations (reflection, rotation, translation, or enlargement).

This means students will know invariant properties are those features of a figure that do not change as it is reflected, rotated, translated or enlarged.

Under rotation lengths, areas, angles do not change but orientation does.

Under reflection lengths, areas and angles do not change but orientation does.

Under translation lengths, areas, angles and orientation do not change.

Under positive enlargement angles and orientation do not change but lengths and areas do.

At Level Four students should be able to use the above invariant properties to create symmetrical patterns such as tessellations, logos and friezes, and to create enlarged copies of graphics. Supporting teaching resources.