# 5.18 - Patterns

The student will

• identify, describe, create, express, and extend number patterns found in objects, pictures, numbers, and tables.

### BIG IDEAS

• So that I can look for patterns within a set of data and use that information to help me understand the data
• So that a Meteorologist can look for patterns within the weather to help make better predictions each year
• So that I can use patterns to help me understand multiplication, addition, subtraction, and division

### UNDERSTANDING THE STANDARD

• Mathematical relationships exist in patterns. There are an infinite number of patterns.
• Patterns and functions can be represented in many ways and described using words, tables, and symbols.
• Students need experiences exploring growing patterns using concrete materials and calculators.  Calculators are valuable tools for generating and analyzing patterns.  The emphasis is not on computation but on identifying and describing patterns.
• Patterns at this level may include: addition, subtraction, or multiplication of whole numbers; addition or subtraction of fractions (with denominators 12 or less); and decimals expressed in tenths or hundredths).  Several sample numerical patterns are included below:
• 1, 2, 4, 7, 11, 16, ...;
• 2, 4, 8, 16, 32, ...;
• 32, 30, 28, 26, 24...;
• 0.15, 0.35, 0.55, 0.75...; and
• 1/4 , 3/4 , 1 1/4  , 1 3/4
• Students in grades three and four had experiences working with input/output tables to determine the rule or a missing value.  Generalizing patterns to identify rules 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: ? Input Output Input Output 4 8 8.9 9.4 5 ? 6.6 7.1 6 12 ? 3.5 ? 20 0.5 1.0

• A numerical expression is a representation of a quantity.  It is made up of numbers, variables, and/or computational symbols.  It does not have an equal symbol (e.g., 15 × 12).
• A verbal expression involving one operation can be represented by a variable expression that describes the relationship. Numbers are used when they are known; variables are used when the numbers are unknown.  The example in the table below defines the relationship between the input number and output number as x + 3. Students at this level are not expected to write a variable expression to describe patterns.  They might describe the pattern below as + 3 or given any number, add three.

 x y 6 9 7 10 11 14 15 18

• An algebraic expression is a variable or a combination of variables, numbers, and/or operation symbols and represents a mathematical relationship.

### ESSENTIALS

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

• Identify, create, describe, and extend patterns using concrete materials, number lines, tables, or pictures.
• Describe and express the relationship found in patterns, using words, tables, and symbols.
• Solve practical problems that involve identifying, describing, and extending single-operation input and output rules (limited to addition, subtraction and multiplication of whole numbers; addition and subtraction of fractions, with denominators of 12 or less; and addition and subtraction of decimals expressed in tenths or hundredths).
• Identify the rule in a single-operation numerical pattern found in a list or table (limited to addition, subtraction and multiplication of whole numbers; addition and subtraction of fractions, with denominators of 12 or less; and addition and subtraction of decimals expressed in tenths or hundredths).

### KEY VOCABULARY

Updated: May 29, 2019