Student Actions

Teacher Actions

• Develop a deep and flexible conceptual understanding of lines, parts of lines (point, segment, ray), and groups of lines (angles, parallel, perpendicular) by modeling examples with manipulatives, identifying examples in varied contexts (pictorial and real-world), and drawing them.

• Develop mathematical reasoning by analyzing pairs of lines and extending them as needed to determine if they are parallel or may intersect at some point, and if intersecting, whether they intersect to form right angles (perpendicular lines), acute angles or obtuse angles.

• Implement tasks that promote reasoning and problem solving by asking students to identify lines, parts of lines, or combinations of lines in a variety of formats (architectural, manipulative, electronic, hand-drawn, etc.).

• Use and connect a variety of mathematical representations of lines and angles.

• Elicit and use evidence of student thinking about lines and angles to assess progress toward mastery of the objective.

Key Understandings

Misconceptions

• Lines that will never cross, no matter how far they are extended, are parallel lines.  If a pair of lines will cross at any point, they are not parallel.

• Lines that are not parallel are identified as intersecting lines; those which intersect to form right angles are identified as perpendicular.

• The intersection of lines, line segments, or rays forms angles, which may be classified as acute, right, or obtuse.

• Lines, parts of lines, and combinations of lines may be found in both mathematical and real-world contexts. 

• If an angle appears to be a right angle, they may classify it as such without checking against a benchmark, such as the corner of a sheet of paper.

• Placing a right angle symbol (the box in the vertex) in an angle is what makes it a right angle.

• The size of an angle is determined by the length of the sides, or rays.