Big Idea:

Big Idea 1

Line segment relationships are determined by length and direction on the coordinate plane.

1 week

Evidence of Understanding

  • analyze distance in the coordinate plane and use distance to relate points and lines
    • calculate the distance between two points using the Pythagorean Theorem
    • generalize methods for determining the distance between two coordinate points
      • derive the distance formula using a right triangle and the Pythagorean Theorem
    • explain how the distance formula and Pythagorean Theorem can both be used to find length measurements of segments (or sides of a geometric figure)
    • partition a segment using any point on the segment and find the ratio of its parts
      • describe connections between the partition ratio, dilation, and scale factor
      • given a specified ratio, find the coordinates of a point that partitions a line segment
    • find the coordinates of a segment’s midpoint
      • prove the midpoint of a segment creates two congruent lengths
      • recognize that partitioning a segment with its midpoint bisects the segment in a 1:1 ratio
  • describe direction in the coordinate plane and use direction to relate points and lines
    • given two points, determine the direction of the line containing the two points
    • generalize methods for determining the direction between two coordinate points
      • generate and describe the slope formula using a right triangle
    • dilate a line segment or line and analyze connections between the pre-image and its image
      • make conjectures and use tools to prove parallel lines have the same slope
      • describe connections between parallel lines, dilation, and scale factor
    • rotate a line and analyze the relationship between the slope of the original line and its image
      • show if slopes of two lines have a product of negative one, then they are perpendicular
    • identify and justify if two lines are parallel or perpendicular
    • create equations that represent parallel lines or perpendicular lines
      • given the equation of a line and a specified transformation, determine the equation of its image or pre-image on the coordinate plane

Develop conceptual understanding:

distance formula, partition, midpoint, direction, slope formula, parallel, perpendicular

Supporting terms to communicate:

Pythagorean Theorem, ratio, bisect, dilation, scale factor, similarity, proportion, reciprocal, congruent, rotation

Core Resource

A core resource supports multiple days of instruction.

Instructional Routine: Sharing Skepticism

The primary goal of this instructional routine is to support students in constructing and critiquing mathematical arguments.