Mathematics K–6 · Years 5–6
Angles on a straight line and at a point
Measurement and space
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The idea
Angles are measured in degrees with a protractor, the angles on a straight line add to 180 degrees and the angles around a point add to 360 degrees.
What you need
- a 180 degree protractor and a ruler per child
- paper triangles of different shapes, cut ready
- a sheet with two lines crossing at one point
- a pair of card strips joined with a split pin
How to do it
- Measure each angle of two paper triangles with the protractor, record each to the nearest degree and name it acute, right or obtuse.
- Construct angles of 65 degrees and 115 degrees with the protractor and ruler. Place them together on a line and check they make a straight angle.
- On the crossing-lines sheet, measure every angle around the point and add them. Measure the two angles opposite each other at a crossing and compare.
- Set the card strips to any angle, measure it, and calculate the angle needed to complete a straight line and a full turn. Check the straight-line partner directly with the protractor. The full-turn partner is more than 180 degrees and is off the scale, so check it by extending one arm to a straight line, measuring the angle left beside it and adding 180.
- Find an unknown angle on a diagram from the known ones, then measure it to confirm.
What you should see
Each triangle angle is read to the nearest degree, with a degree or two of reading error, and is named by its size: less than 90 degrees acute, 90 degrees right, between 90 and 180 degrees obtuse. 65 and 115 make 180. The angles around a point sum to 360, and vertically opposite angles at a crossing measure the same (for example 40 and 40 with 140 and 140). If the card strips show 74 degrees, the straight-line partner is 106, which the 180 degree protractor reads directly, and the full-turn partner is 286, which is off that scale: extending one arm to a straight line leaves 106 degrees to measure beside it, and 180 plus 106 is 286.
What changes
This activity lists no variables to change, measure and keep the same.
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- The size of an angle depends on the length of its arms.
- The angles around a point add to 180 degrees.
Safety card
Hazards
- split pins
- ruler edges
Controls
- an adult fits and flattens split pins
Note
No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package is not needed; ordinary classroom supervision under the school's usual risk management.
Curriculum references
The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.
Sources
The pages the author read to write this activity.