# 2.16 - Patterns

The student will

• identify, describe, create, extend, and transfer patterns found in objects, pictures, and numbers.

### BIG IDEAS

• So that I can use patterns to organize my world and make connections of things and events around us
• So that I can understand that patterns have a core section and can grow by equal or unequal segments

### UNDERSTANDING THE STANDARD

• Patterning is a fundamental cornerstone of mathematics, particularly algebra. The process of generalization leads to the foundation of algebraic reasoning.
• Opportunities to create, identify, describe, extend, and transfer patterns are essential to the primary school experience and lay the foundation for thinking algebraically.
• The part of the pattern that repeats is called the core.
• 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.
• In numeric patterns, students must determine the difference, called the common difference, between each succeeding number in order to determine what is added to each previous number to obtain the next number. Students do not need to use the term common difference at this level.
• Sample numeric patterns include:
• 6, 9, 12, 15, 18,...(growing pattern);
• 2, 4, 6, 8, 10,...(growing pattern); and
• 1, 3, 5, 1, 3, 5, 1, 3, 5… (repeating pattern).
In grade two, growing numeric patterns will only include increasing values.
• In patterns using objects or figures, students must often recognize transformations of a figure, particularly rotation or reflection. Rotation is the result of turning a figure, and reflection is the result of flipping a figure over a line.
• Examples of patterns using objects or figures include:
• Transferring a pattern is creating the pattern in a different form or representation.
• Examples of pattern transfers include:
• 10, 20, 30, 40 has the same structure as 14, 24, 34, 44;
•  has the same structure as ; and
• 1, 3, 5, 1, 3, 5, 1, 3, 5 has the same structure as ABCABC

### ESSENTIALS

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

• Identify a pattern as growing or repeating.
• Describe the core (the part of the sequence that repeats) of a given repeating pattern.
• Describe how a given growing pattern is changing.
• Create a growing or repeating pattern, using objects, pictures, or numbers.
• Extend a given pattern, using objects, pictures, or numbers.
• Transfer a given growing or repeating pattern from one form to another using objects, pictures, or numbers.

### KEY VOCABULARY

Updated: Aug 22, 2018