Math - 2018-19

1.14 - Patterns

The student will 

  • identify, describe, extend, create, and transfer growing and repeating patterns.

Adopted: 2016

BIG IDEAS

  • So that I can recognize patterns and predict what might occur in future
  • So that I can connect unrelated things/events through patterns to organize my thinking
  • So that I can Recognize the difference between repeating and growing patterns
  • So that if I am making my mother a bracelet or necklace I need to be able to tell what bead or shell comes next in the bracelet pattern

UNDERSTANDING THE STANDARD

  • Opportunities to identify, describe, extend, create, and transfer patterns are essential to the primary school experience and lay the foundation for thinking algebraically.
  • Patterning should include:
    • creating a given pattern, using objects, sounds, movements and pictures;
    • recording a pattern with pictures or symbols;
    • transferring a pattern into a different form or different representation (e.g., blue–blue–red–green to an AABC repeating pattern); and
    • analyzing patterns in practical situations (e.g., calendar, seasons, days of the week).
  • In a repeating pattern the part of the pattern that repeats is the core. 
  • At this level students should have experiences extending patterns when given a complete repetition of a core (e.g., ABACABACABAC) as well as when the final repetition of the core is incomplete (e.g., AABBAABBAA …; Red, Blue, Green, Red, Blue, Green, Red, Blue....).
  • Examples of  repeating patterns include:
    • AABCAABC;
    • ABACABAC;
    • ABBCABBC;
    • AABCAABC; and
    • ABACDABACD.
  • Growing patterns involve a progression from step to step which make them more difficult for students than repeating patterns.  Students must determine what comes next and also begin the process of generalization, which leads to the foundation of algebraic reasoning. Students need experiences identifying what changes and what stays the same in a growing pattern. Growing patterns may be represented in various ways, including dot patterns, staircases, pictures, etc.
  • Examples of growing patterns include:
    •  
    • 5, 10, 15, 20…
  • Transferring a pattern is creating the pattern in a different form or representation.
  • Examples of pattern transfers include:
    • 1, 2, 3, 4... has the same structure as 10, 11, 12, 13…;
    • ABABAB… has the same structure as red, blue, red, blue, red, blue; and
    • Snap, clap, jump, clap, snap, clap, jump, clap has the same structure as ABCBABCB.

ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

  • Identify the pattern in a given rhythmic, color, geometric figure, or numerical sequence.
  • Describe the pattern in a given rhythmic, color, geometric figure, or numerical sequence in terms of the core (the part of the sequence that repeats).
  • Extend a repeating or growing pattern, using manipulatives, geometric figures, numbers, or calculators.
  • Create a repeating or growing pattern, using manipulatives, geometric figures, numbers, or calculators (e.g., the growing patterns 2, 3, 2, 4, 2, 5, 2, 6, 2, ¼).
  • Transfer a pattern from one form to another. 


KEY VOCABULARY

Updated: Aug 22, 2018