Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
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 two- column 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 two- column table and as ordered pairs on a coordinate plane (MA.5.GR.4.2).
Common Misconceptions or Errors
- Students may make computational errors when calculating the output for a given rule and input.
- Students may confuse input and output values when recording the values in a two- column table.
Strategies to Support Tiered Instruction
- Instruction includes opportunities to record each step when calculating the output for a given rule and input.
- For example, for the rule 8 + 3x students record the steps to calculate the output using an input of 5 and the order of operations.
- Instruction includes using highlighters when recording inputs and outputs in a two- column table. Students highlight the “inputs” label in the table and all corresponding inputs using one color. Then, students highlight the “outputs” label in the table and all corresponding outputs using a different color.
Instructional Task 1 (MTR.5.1)
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.
- Part B: Extend your table to show the outputs for x = 10, 11 and 12.
Instructional Item 1
What is the missing value in the two-column table below?
Rule: 40 − 3x
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.