Graphing Patterns on Coordinate Plane (Khan Academy)

Overview

• Video by Sal Khan on understanding numerical patterns.
• Focus on generating a second pattern from a given one by applying a specific rule.
• Graph pairs of corresponding terms from both patterns on a coordinate plane.

Key Concepts

Generating Pattern B

• Rule: Multiply each term of Pattern A by 3 and add 1.
• Example Calculations:
  • Pattern A term 0: Multiply by 3 (0) + 1 = 1
  • Pattern A term 1: Multiply by 3 (3) + 1 = 4
  • Pattern A term 2: Multiply by 3 (6) + 1 = 7
  • Pattern A term 3: Multiply by 3 (9) + 1 = 10
  • Pattern A term 4: Multiply by 3 (12) + 1 = 13

Graphing the Patterns

• Axes:
  • Horizontal Axis: Pattern A
  • Vertical Axis: Pattern B
• Points to Plot:
  • (0, 1)
  • (1, 4)
  • (2, 7)
  • (3, 10)
  • (4, 13)

Observations

• Pattern A increases by 1 each time.
• Pattern B increases by 3 for each increment in Pattern A due to the rule (multiply by 3).
• Pattern B starts at 1 because the operation adds 1 to the multiplied result.

Additional Information

• CCSS.Math Standard: 5.OA.B.3
• Video Resource: Part of Khan Academy's 5th grade curriculum on algebraic thinking and number patterns.

Importance of Coordinate Planes

• Used in various applications like air traffic control, map projections, and geographic locations.
• Essential for understanding relationships between numerical patterns visually.

Tips for Students

• When dealing with pattern problems, always start by understanding the rule and how it transforms the original pattern.
• Practice plotting points on a coordinate plane to get comfortable with visualizing patterns.
• Regular review and practice can help reinforce learning and improve problem-solving skills.