🔢 MathGrade 3Lesson 5
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Identify Patterns in Sequences

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Learning Objectives

  • 1Identify the rule in a number sequence (counting by 2s, 5s, 10s, 25s, or 100s)
  • 2Find the missing number in a growing or shrinking number sequence
  • 3Create or extend a number sequence using a given rule
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Mini Lesson

A number sequence is a list of numbers that follows a pattern or rule. Each number is called a term. The rule tells you how to get from one term to the next — usually by adding or subtracting the same amount each time.

Growing Sequences (Adding)

  • Count by 2s: 2, 4, 6, 8, 10 — rule: +2
  • Count by 5s: 5, 10, 15, 20, 25 — rule: +5
  • Count by 10s: 10, 20, 30, 40 — rule: +10
  • Count by 25s: 25, 50, 75, 100 — rule: +25
  • Count by 100s: 100, 200, 300, 400 — rule: +100

Shrinking Sequences (Subtracting)

  • Count back by 5s: 50, 45, 40, 35 — rule: -5
  • Count back by 10s: 100, 90, 80, 70 — rule: -10
  • Count back by 100s: 1,000, 900, 800 — rule: -100
  • To find the rule, subtract any term from the next: e.g. 20 - 10 = 10, so rule is +10.

Finding a Missing Term

  • Find the rule first: look at two consecutive terms and subtract the smaller from the larger.
  • Then apply the rule: add (or subtract) once from the term before the blank.
  • Check: does the term after the blank fit the same rule?
Counting patternsThree rows showing counting patterns. Row 1 counts by 5s: 5, 10, 15, 20, 25. Row 2 counts by 100s: 100, 200, 300, 400. Row 3 counts back by 5s: 50, 45, 40, 35.Counting Patterns510152025+5100200300400+10050454035-5Each row adds or subtracts the same amount.That amount is called the rule.
Find the rule — missing number in a sequenceTwo incomplete sequences with a question mark for the missing term. Sequence 1: 10, 20, ?, 40 with rule +10. Sequence 2: 300, 250, ?, 150 with rule -50.Find the Rule1020?4030Rule: +10 each time300250?150200Rule: -50 each timeFind the rule, then apply it to fill the blank.
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To find the rule: pick any two consecutive terms and subtract. The result is the rule.

Vocabulary
Pattern
A set of numbers or shapes that follow a rulee.g. 2, 4, 6, 8 is a pattern of even numbers.
Sequence
A list of items in a special ordere.g. 5, 10, 15, 20 is a number sequence.
Rule
How a pattern changes from one term to the nexte.g. The rule is: add 3.
Term
One number or item in a sequencee.g. The third term in 4, 8, 12 is 12.
Skip count
To count by a number greater than 1e.g. Skip count by 5: 5, 10, 15, 20.
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