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

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.
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• 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