RIC-20153 ACM Measurement and Geometry (Yr 3) Geometric reasoning

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Sub-strand: Geometric reasoning—GR – 1 Identify angles as measures of turn and compare angle sizes in everyday situations (ACMMG064) RELATED TERMS TEACHER INFORMATION Angle • Two lines with a common end point called a vertex, or the extent of rotation about a point. Right angle 90° • Exactly 90°. Acute angle • An angle less than 90°. Obtuse angle • Greater than 90° but less than 180°. Straight angle • Exactly 180°. One rotation • A full turn to end up at the start (360°). Degree • A unit of measure of an angle, based on there being 360° in a circle. • Students need to be aware that degrees are also used to measure temperature, but this is not the same as the measure for angle. What this means • Right angles (those of approximately 90°) are ones that students should recognise. • Knowledge that an acute angle is less than 90°. • Knowledge that an obtuse angle is between 90° and 180°. • Knowledge that a full turn is the same as 360° and that half a turn is 180°. • Students are developing an awareness and understanding of the movement that relates to how angles are formed and to the measurement of angles. • The use of a protractor is not encouraged at this stage. Teaching points • Angles are classified by their size in their relationship to the right angle (90°). (Refer to related terms.) • Right angles are used extensively in most buildings. For example, where walls meet the floor and the ceiling, the corners of rooms and most of the angles in the construction of cupboards. Books and paper mostly have 90° angles. • Many doors open to 180°, though if near a corner, they may only open to about 90°. • Make links to the unit on time (UUM – 2) looking at the hands on an analogue clock as they turn in a clockwise direction. • Also make links to the unit on location and transformation (L&T – 1) where quarter and half turns are used, along with ideas about the four cardinal compass points (north, south, east and west) and left/right and clockwise/anticlockwise. • Students can get an intuitive idea of the size of angles when making comparisons. For example, that the size of the angles on the hexagon piece of pattern blocks are greater than a right angle (90°) and also much bigger than the size of the angles on the triangular block, which are less than a right angle. At this stage, they do not need to measure the angles on the two pieces. ©R.I.C. Publications Low Resolution Images Display Copy • Show right angles in different orientations. This should help avoid a common misconception that we can have right angles and ‘left angles’. Student vocabulary right angle acute angle obtuse angle straight angle degrees rotation arms (of an angle) • It is important to make angles with different arm lengths so students realise that the length of the arms does not affect the size of an angle. • National tests often include a question on angles, where students identify the largest or smallest angles from a set of angles that have different arm lengths. 72 Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3) R.I.C. Publications ® www.ricpublications.com.au
Sub-strand: Geometric reasoning—GR – 1 Identify angles as measures of turn and compare angle sizes in everyday situations (ACMMG064) TEACHER INFORMATION What to look for • Students know the properties of a right angle (90°) and can represent them without the use of a protractor. (Note: Protractors are not encouraged at this year level). • Students are aware that a straight angle is 180° (which is two right angles) and a full rotation is 360° (which is four right angles). • Students confused by the length of the arms of an angle, thinking that an angle with short arms is less than an angle of lesser degrees but with longer arms. Students with this misconception would judge that the first angle below is wider than the second because of the length of the arms. In fact, the second angle is larger. ©R.I.C. Publications Low Resolution Images Display Copy Proficiency strand(s): Understanding Fluency Problem solving Reasoning Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3) R.I.C. Publications ® www.ricpublications.com.au 73
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RIC-20153 ACM Measurement and Geometry (Yr 3) Geometric reasoning

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