### Examples

The expression 6+2x, where x represents any whole number, can be represented in a two-column table as shown below.

Input (X) | 0 | 1 | 2 | 3 |

Output | 6 | 8 | 10 | 12 |

### 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.

**Subject Area:**Mathematics (B.E.S.T.)

**Grade:**5

**Strand:**Algebraic Reasoning

**Date Adopted or Revised:**08/20

**Status:**State Board Approved

## Benchmark Instructional Guide

### Connecting Benchmarks/Horizontal Alignment

### Terms from the K-12 Glossary

- NA

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### 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 and MA.7.AR.4) 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 + 3
*x*students record the steps to calculate the output using an input of 5 and the order of operations.

- For example, for the rule 8 + 3

- 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 Tasks

*Instructional Task 1* (MTR.5.1)

*x*.” 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 Items

*Instructional Item 1 *

*x*

**The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.*

## Related Courses

## Related Access Points

## Related Resources

## Formative Assessments

## Lesson Plans

## Tutorial

## MFAS Formative Assessments

Students are asked to fill in missing values in a table of numerical patterns and describe relationships between corresponding terms.

Students are asked to complete one of two number patterns, write ordered pairs composed of corresponding terms, graph the ordered pairs, and identify a relationship between corresponding terms of the patterns.

## Student Resources

## Tutorial

In this Khan Academy tutorial video a table is used to track a growing sequence of design.

Type: Tutorial