#### Math - 2019-20

# 5.18 - Patterns

**The
student will**

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

*Adopted: 2016*

### 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*