Number Sequencing and Patterns

Grade 2 Medium Counting Cardinality

Learning Objectives

  • Recognize and continue simple number patterns
  • Identify missing numbers in a sequence
  • Create original number patterns

Concept Explanation

Number sequencing involves recognizing the pattern or rule that determines how numbers follow each other. Patterns might involve adding, subtracting, or multiplying by a constant value. Being able to identify and continue patterns helps students develop logical thinking and prepares them for algebraic concepts later on.

Worked Examples

Example 1

Problem: What are the next two numbers in the sequence: 2, 4, 6, 8, …?
Solution: 10, 12
Explanation: Each number increases by 2, so after 8 comes 10, then 12.

Example 2

Problem: Fill in the missing number: 5, 10, ___, 20, 25
Solution: 15
Explanation: The pattern adds 5 each time, so the missing number is 10 + 5 = 15.

Example 3

Problem: What’s the pattern in this sequence: 1, 3, 9, 27, …?
Solution: Multiply by 3 each time
Explanation: 1 × 3 = 3, 3 × 3 = 9, 9 × 3 = 27, so the pattern is “multiply by 3.”

Common Errors

ErrorCorrectionReason
Focusing only on the difference between consecutive termsLook for multiple possible patternsSome sequences follow more complex rules than just addition.
Assuming all patterns are increasingCheck if numbers are decreasing or alternatingPatterns can go up, down, or alternate in various ways.
Overlooking the starting pointNote the first number in the sequenceThe starting point is crucial for understanding the pattern.

Practice Problems

  1. Problem: What comes next: 3, 6, 9, 12, …?
    Solution: 15
  2. Problem: Fill in the blank: 20, ___, 12, 8, 4
    Solution: 16
  3. Problem: What’s the pattern: 2, 4, 8, 16, …?
    Solution: Multiply by 2 each time
  4. Problem: Continue the sequence: 1, 4, 7, 10, …
    Solution: 13, 16
  5. Problem: What’s the missing number: 25, 20, ___, 10, 5
    Solution: 15

Real-World Application Example

Number patterns appear in many real-world contexts, from the arrangement of petals on a flower to the design of calendar months. Understanding patterns helps us predict what comes next, whether we’re looking at growth cycles in nature or planning regular payments like monthly bills.

Related Concepts