Fifth Grade · Math · week 31

Numerical patterns to graphs

Generate two numerical patterns from given rules, form ordered pairs from corresponding terms, and graph them on a coordinate plane.

You can build a pattern by starting with a number and repeating a rule, like "start at 0, add 3 each time": 0, 3, 6, 9, 12. Two patterns built from related rules can be paired up as (x, y) points and graphed.

Graphing the pairs often reveals a relationship you can see at a glance, like one pattern always being a fixed multiple of the other.

📋 For the teacher
Teach it (10–15 min):
  • Build the two number patterns first as simple side-by-side lists before combining them into pairs -- do not skip straight to points.
  • Pair up the terms in order: the 1st number of pattern A with the 1st number of pattern B, and so on.
  • After plotting, ask "what do you notice?" and let them describe the relationship in their own words before naming it formally.
  • Try changing one rule slightly, like "add 3" instead of "add 2," and predict how the graph will change before checking.
Talk about it:
  • How do you turn two separate number patterns into ordered pairs?
  • What relationship did you notice between your two patterns?
  • What do you think would happen to the graph if you changed the second rule?

Mastery looks like: They can generate two related numerical patterns, form ordered pairs from them, plot the pairs, and describe the relationship.

Common stumbles: Pairing terms out of order; describing the relationship backward, mixing up which pattern is the multiple of the other.

See it visually

Interactive, spoken-aloud tools that show this idea in motion.

Coordinate PlanePlot points and explore the four quadrants.try →
Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
Records attendance + 15 min of Math for this learner.
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