Overview
This module introduces points, lines, line segments, rays, and angles, as well as the relationships between them. Students construct, recognize and define these geometric objects before using this new knowledge to classify figures and solve problems. In these problems, where the unknown angle is represented by a letter, students explore both measuring the unknown angle with a protractor and reasoning through the solving of an equation.
Topic A begins with students drawing points, lines, line segments, and rays, as well as identifying these in various contexts and within familiar figures. They create right angles through a paper-folding activity, identify right angles in their environment, and see that one angle can be greater (obtuse) or less (acute) than a right angle. Next, students use their understanding of angles to explore relationships between pairs of lines as they define, draw, and recognize intersecting, perpendicular, and parallel lines.
Topic A begins with students drawing points, lines, line segments, and rays, as well as identifying these in various contexts and within familiar figures. They create right angles through a paper-folding activity, identify right angles in their environment, and see that one angle can be greater (obtuse) or less (acute) than a right angle. Next, students use their understanding of angles to explore relationships between pairs of lines as they define, draw, and recognize intersecting, perpendicular, and parallel lines.
In Topic B, students explore the definition of degree measure, beginning with a circular protractor. Through exploration, students realize that, although the size of a circle may change, and angle spans an arc, representing a constant fraction of the circumference. Armed with with their understanding of the degree as a unit of measure, students use various types of protractors to measure angles to the nearest degree and sketch angles of a give measure.
Topic C begins by decomposing 360 degrees using patter blocks, allowing students to see that a group of angles meeting at a point with no spaces or overlaps add up to 360 degrees.
Topic C begins by decomposing 360 degrees using patter blocks, allowing students to see that a group of angles meeting at a point with no spaces or overlaps add up to 360 degrees.
Topic D introduces the precise definition of a triangle, and then classify triangles based on angle measure and side length. For isosceles triangles, a line of symmetry is identified, and a folding activity demonstrates that base angles are equal. Folding an equilateral triangle highlights multiple lines of symmetry and establishes that an interior angles are equal. Finally, students explore the definitions of familiar quadrilateral and classify them based on their attributes, including angle measure and parallel and perpendicular lines.