ALEX Classroom Resource

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.

Students:
Use two related rules to

• Generate numerical patterns and record as ordered pairs.
• Graph ordered pairs consisting of corresponding terms.
• Identify and explain relationships between corresponding terms.

Example: Given the rule "add 1 starting at 0", and "add 2 starting at 0," explain the terms in one sequence as 1/2 the corresponding terms in the other sequence, or the terms in one sequence are twice the corresponding terms in the other sequence.

Students know:

• Strategies to identify numerical patterns and recognize the relationship between the terms in the pattern.
• Reasoning strategies to generate a numerical pattern which follow a given rule.

Students are able to:

• Generate two numerical patterns using two given rules.
• Complete an input/output table for data.
• Identify relationship between terms in an input/output table.
• Form ordered pairs from an input/output table.
• Graph ordered pairs on a coordinate plane.

Students understand that:

• relationships between two numerical patterns can be represented by ordered pairs and graphed in the first quadrant of the coordinate plane.

Learning Objectives:
M.5.2.1: Construct repeating and growing patterns with a variety of representations.
M.5.2.2: Continue an existing pattern.
M.5.2.3: Identify arithmetic patterns (including patterns in the addition table or multiplication table).