ALEX Classroom Resource

Students:

• Recognize, describe, and explain arithmetic patterns.
• Given a number pattern, find the next number or numbers in the pattern.
• Given a number pattern, find a characteristic of the next number or numbers in the pattern.
• Given an addition table or multiplication table, find the missing values in the table.
• Given an addition table or multiplication table, find a characteristic of a row or column of that table.

Students know:

• that mathematical ideas and concepts build on patterns and recognize and identify those patterns to make sense of math, and the ability to make generalizations is the foundation for algebraic reasoning.

Students are able to:

• Identify arithmetic patterns in number sequences, in the addition table, or multiplication table.
• Use logical reasoning and properties of numbers and operations to explain characteristics of arithmetic patterns.

Students understand that:

• Mathematical concepts build on patterns.
• When consecutive terms always differ by the same amount, an arithmetic pattern is formed.
• Visual patterns can be found in the multiplication table.

Learning Objectives:
M.3.9.1: Define arithmetic patterns: geometric or numeric.
M.3.9.2: Explain arithmetic patterns using properties of operations.
M.3.9.3: Recognize arithmetic patterns (including geometric patterns or patterns in the addition table or multiplication table).
M.3.9.4: Construct repeating and growing patterns with a variety of representations.
M.3.9.5: Demonstrate computational fluency, including quick recall, of addition and multiplication facts.
M.3.9.6: Duplicate an existing pattern.
M.3.9.7: Skip count.
M.3.9.8: Represent addition and multiplication with manipulatives.

Students:
When given a rule or pattern,

• Generate a number or shape pattern that follows a given rule.
• Identify a missing number or shape in the pattern.
• Identify a feature of the pattern.

Example: Given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence, and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers continue to alternate in this way.

Students know:

• Strategies for generating and recording number or shape patterns from a given rule.
• Strategies for identifying and communicating shape and number patterns.

Students are able to:

• Generate a number or shape pattern that follows a given a rule.
• Analyze a number or shape pattern that follows a given rule.

Students understand that:

• A pattern is generated from a given rule.
• The properties of a rule or pattern can be used to extend a pattern.
• Some features of a given pattern are not explicit in the pattern's rule.

Learning Objectives:
M.4.5.1: Identify arithmetic patterns, including patterns in the addition table or multiplication table; and explain them using properties of operations.
M.4.5.2: Recognize arithmetic patterns (including geometric patterns or patterns in the addition table or multiplication table).
M.4.5.3: Construct repeating and growing patterns with a variety of representations.
M.4.5.4: Continue an existing pattern.
M.4.5.5: Identify arithmetic patterns.
M.4.5.6: Demonstrate computational fluency, including quick recall, of addition multiplication facts.