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Angle Units of Work

Angle is the measure of turn. An understanding of angle begins with students exploring turning left and right, clockwise and anticlockwise. Students move on to measure angles and construct angles and shapes using protractors.

Level 1 Angle

Achievement ObjectivesLearning OutcomesUnit title
GM1-1
GM1-3
  • show a quarter turn and a half turn in a number of situations
  • see that two quarter turns equals one half turn
  • recognise the ‘corner’ of a shape that is equivalent to a quarter turn

Turns

Level 2 Angle

Achievement ObjectivesLearning OutcomesUnit title

GM2-1

  • understand clockwise and anticlockwise directions
  • understand that quarter half turns may be begun from any direction and not just from lines parallel to the classroom walls or other fixed lines

Clockwise

  • estimate and measure angles using other angles

Angles

Level 3 Angle

Achievement ObjectivesLearning OutcomesUnit title

GM3-1

  • measure angles using degrees

Measuring Angles

  • identify and construct right, acute and obtuse angles
  • begin to appreciate the degree, unit of measurement of angle
  • know the degree value of angles that are simple fractions of a whole turn
  • know that the angle at a point is 360o

Simple Angles

Level 4 Angle

Achievement ObjectivesLearning OutcomesUnit title
GM4-1
GM4-6
  • construct triangles with specified dimensions using two different techniques
  • design and construct nets for three-dimensional objects
  • name basic three-dimensional objects, especially those made with equilateral triangles

Building with Triangles

GM4-1
GM4-5
  • investigate the relationship between the diagonals and lengths of a rectangle
  • investigate the relationship between the angle of the diagonal and length of rectangles sides
  • use rulers, compasses and protractors accurately

Quadrilaterals

Identifying the attribute

Early experiences with angle involve students developing an understanding of angle as an amount of turning. They develop the ideas of ‘how much’ turn by turning quarter, half and full turns. Students turn themselves and objects in the directions of left and right, and clockwise and anticlockwise.

Comparing and ordering

Comparing different angles is the next step in developing an understanding of angle. Students can compare quarter and half turns, and how many quarter turns make a half or full turn. The corners of two dimensional shapes can be seen as angles, for example right angle corners are quarter turns. Students can make direct comparsions between the angle sizes in the corners of shapes.

Non-standard units

The unit for measuring an angle is an angle. It does not need to be measured using degrees. It is easier for students to develop the sense of measuring an angle using a wedge rather than a protractor. A paper wedge protractor can be made by folding a circle in halves four times until 16 wedges (or sectors) have been formed. If the paper is see through then the paper can be places over a corner of a polygon or an angle ray. The number of wedges can be counted.

 

Standard units

Degrees or radians can be used as a measure of an angle. Being able to use degrees enables us to locate our position on Earth (longitudinal or latitude) and navigate using bearings. It also allows us to distinguish between triangles (by comparing their angles) and describe other polygons more accurately. A protractor is used to measure angles. It can be confusing for students to use as a single degree is too small to use as a single unit or to visualize and not every degree is marked on a protractor. Also as with a ruler the measuring line is not at the edge of the instrument. The horizontal line to mark the Oo / 180o line is above the horizontal edge of the protractor and the numbering of degrees on many protractors goes both clockwise and anticlockwise. Students will need explicit instructions to use the protractor accurately.

Applying and interpreting

When students are able to measure angles accurately and have a sense of the size of angles they can construct angles and shapes and investigate the geometry of shapes. There is a close link between the Measurement substrand focus on angles and the Shape substrand focus on the properties of polygons.