Points and Lines All Around

10 min

Narrative

This Warm-up prompts students to carefully analyze and compare quadrilaterals and their sides. When students make comparisons, they have a reason to use geometric language precisely (MP6). The activity also enables the teacher to hear the terminology students use to talk about the characteristics of two-dimensional figures. The knowledge and ideas that students show here also may be insightful to teachers in the next lesson, when students learn about angles.

Launch

  • Groups of 2
  • Display the image.
  • “Pick 3 quadrilaterals that go together. Be ready to share why they go together.”
  • 1 minute: quiet think time
Teacher Instructions
  • “Discuss your thinking with your partner.”
  • 2–3 minutes: partner discussion
  • Record responses.

Student Task

Which 3 go together?

4 different 4 sided figures, labeled A, B, C, D.
4 different 4 sided figures, labeled A, B, C, D. A, one pair of vertical parallel line segments. Bottom side connects with the parallel line segments to form 2 right angles. B, 1 pair of horizontal parallel lines. C, 1 pair of parallel line segments that are slanted diagonally. D, two pairs of parallel line segments, opposite segments have same length.

Sample Response

Sample responses:

A, B, and C go together because:

  • They have exactly one pair of parallel lines.
  • They are trapezoids.
  • Their parallel sides have different lengths.

A, B, and D go together because:

  • They have a horizontal segment across the bottom.

A, C, and D go together because:

  • Their longest side is parallel to another side.

B, C, and D go together because:

  • They have a horizontal segment across the top.
  • They have 2 “pointy” corners and 2 “wide” corners.

Synthesis

  • “How might we know if the sides of a figure are parallel?” (We could extend the lines or measure to see if the two sides are always the same distance apart.)
  • “All four quadrilaterals have at least one pair of parallel sides. Do all quadrilaterals have at least one pair of parallel sides?” (No) “Can you draw one with no pairs of parallel sides?”
Standards
Addressing
  • 4.G.1·Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
  • 4.G.A.1·Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
Building Toward
  • 4.G.2·Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. (Two-dimensional shapes should include special triangles, e.g., equilateral, isosceles, scalene, and special quadrilaterals, e.g., rhombus, square, rectangle, parallelogram, trapezoid.)
  • 4.G.A.2·Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

15 min

20 min