Let’s integrate some Measurement and Geometry!

Measurement and Geometry are inextricably related. When students measure, they are measuring two-dimensional shapes and three-dimensional objects. The properties of the shapes and objects dictate how they are measured.

Metric Measurement and multiplicative Place Value are inextricable related, because metric measurement is based on multiplicative place value! (See the diagram below.)

Students begin investigating Geometry in Kindergarten / Prep / Reception as they name squares, rectangles, circles and triangles, describe lines as either straight or curved on two-dimensional shapes, and surfaces as either flat or curved on three-dimensional objects (MG 1, 6, 7), They begin investigating Measurement as they describe length as length, height and distance, compare lengths, volumes and capacities, areas and masses (MG 2, 4, 8, 10, 11 12). Students begin investigating position as they describe position and give and follow directions (MG 3, 5, 9).

Students begin investigating Geometry in Year 1 as they describe lines on shapes, identifying straight lines as sides and name shapes by their number of sides (MG 13). They describe surfaces on objects, identifying flat surfaces with sides are faces (MG 17). They begin investigating Measurement as they use multiple, and then a single informal unit to measure length, multiple units to measure area then identify the square is the best shape (MG 14, 16). They use multiple units to measure volume and capacity then identify the cube is best. Students identify that to measure the volume and capacity of objects with curved surfaces, we need liquid units. They measure volume and capacity using informal liquid units, by filling and by displacement (MG 18). Students measure mass using an equal arm balance (MG 19). Students investigate giving directions to a person facing the same way, and the opposite way (MG 15).

Students begin investigating Geometry in Year 2 as they investigate vertices, straight, curved, and parallel lines on two-dimensional shapes, flat and curved surfaces, straight, curved and parallel lines, vertices on three-dimensional objects, identifying that surfaces on three-dimensional objects are two-dimensional shapes (MG 20, 24, 25). They begin investigating Measurement as they construct tape measures in informal units and in centimetres, and measure in centimetres and metres (MG 30). They measure area in informal square units, in an array, and volume and capacity in layers of an array, and in informal liquid units and by displacement (MG 23, 26). Students measure mass using multiple units on an equal arm balance (MG 28). Students investigate simple maps and describe one-step slides, flips, full, half, quarter turns (MG 22, 27). 

Students begin investigating Geometry in Year 3 as they investigate triangles and quadrilaterals, angles and prisms, pyramids, cylinders, cones and spheres (MG 29, 31, 32, 34). They begin investigating Metric Measurement as they explain that the metric system is based on multiplicative place value. They investigate metres, divide by 10 to get a decimetre, divide by 10 to get a centimetre, and divide by 10 to get a millimetre. They measure length in millimetres, then in combinations of centimetres and millimetres, and in centimetres, then in combinations of metres and centimetres (MG 30). Students investigate area, by turning the length units of measurement into squares to make square metres and square centimetres (MG 33). Students then investigate volume and capacity, by turning the area units of measurement into cubes to make cubic centimetres. Students investigate volume and capacity of objects with curved surfaces and lines, identifying that a liquid unit is needed. They investigate litres, divide by 10 to get decilitres, divide by 10 to get centilitres, and divide by 10 to get a millilitre (MG 35). Students then investigate mass, investigating grams, multiply by 10 to get a decagram, multiply by 10 to get a hectogram, and multiply by 10 to get a kilogram (MG 36). Students investigate simple alpha-numeric maps to describe position (MG 37).   

Students begin investigating Geometry in Year 4 as they investigate reflecting, translating, rotating, combining and splitting shapes, identifying symmetry and tessellation, right, acute and obtuse angles with angle testers, and vertices, edges and faces on prisms, pyramids, lines and surfaces on cylinders and cones, and drawing from different perspectives and views (MG 38, 40, 41, 44). They continue investigating Metric Measurement explaining that the metric system is based on multiplicative place value, extending to decimals to tenths and hundredths. They measure length in millimetres, then in combinations of centimetres and millimetres, then in centimetres and a fraction of a centimetre, then in centimetres and a decimal fraction of a centimetre, and in centimetres, then in combinations of metres and centimetres, then in metres and a fraction of a metre, then in metres and a decimal fraction of a metre  (MG 39). Students investigate area, measuring in square metres and square centimetres using grids (MG 42). Students then investigate volume and capacity, measuring in millilitres using scale, converting to litres and a fraction of a litre, including using displacement (MG 45). Students then investigate mass, measuring in grams using scale, converting to kilograms and a fraction of a kilogram (MG 47). Students investigate key, compass, grid references and scale to locate features and work out distances (MG 43).

Students begin investigating Geometry in Year 5 as they investigate angles with protractor, and use their understanding to investigate side and angle properties of, and enlarging, two-dimensional shapes (MG 48, 49). They investigate rotational symmetry, and the transforming effects of reflections, translations, rotations (MG 50). Students investigate face and base properties, and cross-sections of prisms and pyramids, and draw them from different perspectives and views, and construct nets (MG 56). They continue investigating Metric Measurement, converting between millimetre-centimetre, centimetre-metre, millimetre-metre and kilometre-metre using multiplicative place value (MG 51). Students extend their investigation of area to measure in hectares and square kilometres (MG 52). Students extend their investigation of volume and capacity to measure in cubic metres (MG 55). Students extend their investigation of mass, to include tonnes, and investigate gross and net mass (MG 57). Students investigate legend / key, compass, scale and alpha-numeric grid to locate features and work out distances (MG 53).

Students begin investigating Geometry in Year 6 as they investigate diagonals on two-dimensional shapes, and the effects of combinations of translations, reflections and degrees of rotation (MG 58, 60). They investigate parts of a circle (MG 65), the Cartesian plane coordinate system using 4 quadrants to describe location and to construct shapes (MG 62), and angles on straight line or at a point, adjacent angles that form right angle, a straight angle or angle of revolution, and vertically opposite angles, and use their understanding to find unknown angles (MG 66). Students investigate skeletal models of prisms and pyramids, and draw them from different views (MG 63). They continue investigating Metric Measurement, Convert centimetres millimetres, metres centimetres, kilometres metres, using fractions and multiplicative place value (MG 59). Students investigate area and perimeter, to construct shapes with the same area and different perimeters, and different areas and the same perimeter (MG 61). Students investigate the relationship between cubic and liquid units – the millilitre and the cubic centimetre, and convert between millilitres and cubic centimetres, millilitres litres, litres kilolitres, kilolitres megalitres, using fractions and multiplicative place value (MG 64). Students investigate the relationship between liquid units and mass – a litre of water and a kilogram. They convert between milligrams, grams, kilograms, tonnes, using fractions and multiplicative place value (MG 67).

MG and PV