#### Math - 2018-19

# 4.15 - Patterns

**The student will **

**identify, describe, create,**and**extend**patterns found in objects, pictures, numbers, and tables.

*Adopted: 2016*

### BIG IDEAS

So that I can find patterns and relationships in numbers that help us to have a better understanding of numbers and math operation

So that I can find patterns within a set of data and use that information to help me understand the data

So that I can see Meteorologists look for patterns within the weather to help make better predictions each year

So that when we read books we look for patterns to help us understand the book. For example in the story

__The Three Bears__, Goldilocks looks for items that are considered too large, too small, and just rightSo that we can look for patterns in rhyming words in poetry and musice use patterns to help use understand multiplication, addition, subtraction, and division

- So that I can find symmetry in figures
- So that I can use patterns I notice to classify and remember facts in chunks instead of separately

### UNDERSTANDING THE STANDARD

- Patterns and
functions can be represented in many ways and described using words, tables,
graphs, and symbols.
- Patterning
activities should involve making connections between concrete materials and
numerical representations (e.g., number sequence, table, description). Numeric
patterns, at this level, will include both growing and repeating patterns
(limited to addition, subtraction, and multiplication of whole numbers and
addition and subtraction of fractions with like denominators of 12 or less).
- Students need experiences with growing patterns using concrete materials and calculators.
- Reproduction of a given pattern in a different representation, using symbols and objects, lays the foundation for writing the relationship symbolically or algebraically.
- Sample growing patterns that are, or can be, represented as numerical (arithmetic) growing patterns include:
- 2, 4, 8, 16, …;
- 8, 10, 13, 17, …;
- 1/4, 3/4, 1 1/4, 1 3/4…; and
- Students in
grade three had experiences working with input/output tables. At this level,
input/output tables should be analyzed for a pattern to determine an unknown
value or describe the rule that explains how to find the output when given the
input. Determining and applying rules builds the foundation for functional
thinking. Sample input/output tables that require determination of the rule or
missing terms can be found below:

Rule: ? | Rule: ? | Rule: ? | |||||

Input | Output | Input | Output | Input | Output | ||

4 | 11 | 145 | 130 | 2 | 8 | ||

5 | 12 | 100 | 85 | 4 | 16 | ||

6 | 13 | 75 | 60 | ? | 20 | ||

10 | 17 | 50 | ? | 8 | 32 |

### ESSENTIALS

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

- Identify and describe patterns, using words, objects, pictures, numbers, and tables.
- Create patterns using objects, pictures, numbers, and tables.
- Extend patterns, using objects, pictures, numbers, and tables.
- Solve practical problems that involve identifying, describing, and extending single-operation input and output rules, limited to addition, subtraction, and multiplication of whole numbers and addition and subtraction of fractions with like denominators of 12 or less.
- Identify
the rule in a single-operation numerical pattern found in a list or table,
limited to addition, subtraction, and multiplication of whole numbers.

### KEY VOCABULARY

*Updated: Mar 06, 2019*