• MA.5.AR.3 Algebraic Reasoning

    Analyze patterns and relationships between inputs and outputs



    Given a rule for a numerical pattern, use a two-column table to record the inputs and outputs. Example: The expression 6 + 2𝑥, where 𝑥 represents any whole number, can be represented in a two-column table as shown below. 


    Benchmark Clarifications:
    Clarification 1: Instruction builds a foundation for proportional and linear relationships in later grades.
    Clarification 2: Rules are limited to one or two operations using whole numbers. 

    Purpose and Instructional Strategies
    The purpose of this benchmark is to relate patterns to a two-column table for students to record inputs and outputs. It is related to MA.5.AR.3.1 where students determine rules from given patterns. This is the first grade in which students record inputs and outputs two-column tables, and this work helps build the foundation for proportional relationships (MA.6.AR.3.3) in middle school and functional relationships starting in Grade 8.

     Instruction of this benchmark should be paired with MA.5.AR.3.1. Organizing patterns into input and output tables lays the foundation for students to explore proportional and linear relationships in later grades (MTR.5.1).

     During instruction, teachers can relate the idea of “inputs” and “outputs” on a twocolumn table to a machine. The input is the term number, and the output is the corresponding term’s value. Students are to find what the machine does to determine the output.

     Instruction should make connections between representing the information in a twocolumn table and as ordered pairs on a coordinate plane (MA.5.GR.4.2).

    Common Misconceptions or Errors
     A common mistake that students make is to determine a rule based on the change in only the first two terms (in a pattern or on a two-column table). During instruction, teachers should emphasize that a rule must work for the change in any two terms in a pattern.

    Instructional Tasks
    Instructional Task 1
    The Math Machine makes two-column tables when the user tells it a rule. Jacob tells the Math Machine to create a table using the rule “10 + 2𝑥.” Unfortunately, the machine is malfunctioning and only some of the table is correct.
    Part A: Identify which values are incorrect and complete the table correctly.


    Instructional Items
    Instructional Item 1
    What is the missing value in the two-column table below? Rule: 40 − 3𝑥 


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