Angles

This unit goes past measuring with a protractor to working angles out by calculation. It opens with Vertical Angles and Angles on a Line, then builds Sum of Angles, Difference of Angles, Angles on a Straight Line, The Remaining Angle and Crossing Type out of addition and subtraction, using pairs of set squares.

Mixing up the 30-degree and 45-degree corners of the set squares, using 45 where 60 was intended, is the most frequent error. An answer off by 15 degrees identifies it. In Crossing Type, children misjudge whether the angle wanted is a vertical angle or the rest of a straight line, and subtract from 180 degrees one time too many.

Shapes had been sorted by side length and outline until now; a new number, the size of an angle, joins that picture here. The sense of a right angle picked up in Triangles and Quadrilaterals in grade 2 becomes the base for calculating vertical angles and angles on a line, and this reasoning grows in grade 5, in Congruent Figures and Angles, into totaling the interior angles of a triangle or a quadrilateral.