MA.4.AR.3.2

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Generate, describe and extend a numerical pattern that follows a given rule.

Examples

Generate a pattern of four numbers that follows the rule of adding 14 starting at 5.

Clarifications

Clarification 1: Instruction includes patterns within a mathematical or real-world context.
General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 4
Strand: Algebraic Reasoning
Standard: Recognize numerical patterns, including patterns that follow a given rule.
Date Adopted or Revised: 08/20
Status: State Board Approved

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

Terms from the K-12 Glossary

  • Expression

Vertical Alignment

Previous Benchmarks

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Purpose and Instructional Strategies

The purpose of this benchmark is to build understanding of numerical patterns. Students should generate numerical patterns that follow a given rule with one step. This concept builds on identifying, creating and extending numerical patterns (MA.3.AR.3.3). 
  • As students use numerical patterns, they will reinforce facts and develop fluency with operations (MTR.5.1). 
  • A pattern is a sequence that repeats the same rule over and over. Patterns and rules are related. A rule dictates what that pattern will look like. 
  • Students need multiple opportunities creating and extending number patterns. 
  • Students investigate different patterns to find rules, identify features in the patterns and justify the reason for those features. 
  • Students should look for relationships in the patterns they create and be able to describe and generalize.

Common Misconceptions or Errors

  • Students often make mistakes due to lack of fluency with the four operations which hinders them from being able to extend the pattern according to the rule.

Strategies to Support Tiered Instruction

  • Instruction includes students drawing quick pictures of the numbers represented or using two-color counters or square tiles to model their patterns to aid students in seeing how the rule affects the terms and to make accurate calculations. 
    • For example, shown is the pattern beginning with 4 and the rule is “add 7.”
two-color counters

Instructional Tasks

Instructional Task 1 (MTR.5.1) 

The first term of a pattern is an odd number. The rule is add 13. Will the 4th term be odd or even? Based on the pattern described, will the 4th term always be odd or even? Explain your reasoning.

Instructional Task 2 (MTR.5.1) 

Part A. Find the areas of the squares shown in which the side lengths start at 1 and increase by 1 each time: (1 × 1) (2 × 2) (3 × 3) (4 × 4), etc. 
Extend the pattern up to 10 terms. 

Part B. Find the perimeters of the squares shown in which the side lengths start at 1 and increase by 1 each time: (1 × 1) (2 × 2) (3 × 3) (4 × 4), etc.
Extend the pattern up to 10 terms.

Instructional Items

Instructional Item 1 

The first term in a pattern is 6. The pattern follows the rule “add 4.” 
Which of the numbers below is a term in the pattern? 
  • A. 1 
  • B. 8 
  • C. 14 
  • D. 16
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.

Related Courses

This benchmark is part of these courses.
5012060: Mathematics - Grade Four (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7712050: Access Mathematics Grade 4 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5012055: Grade 3 Accelerated Mathematics (Specifically in versions: 2019 - 2022, 2022 and beyond (current))
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022, 2022 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.4.AR.3.AP.2: Generate a numerical pattern when given a starting term and a one-step addition rule (e.g., starting at the number 5 use the rule add 5 and generate the pattern).

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Formative Assessments

Multiply By Four:

Students are asked to generate a sequence of numbers based on a given rule and then to identify features of the pattern that are not explicit.

Type: Formative Assessment

Dot Patterns:

Students examine triangular numbers through a given dot pattern.

Type: Formative Assessment

Baseball Cards:

Students generate a number pattern based on a given rule and explain the pattern found.

Type: Formative Assessment

Generating Two Patterns:

Students are given two rules and are asked to generate patterns.

Type: Formative Assessment

Lesson Plans

Pattern Fun:

In this lesson, students will use manipulatives to build, extend, and describe increasing patterns from a rule.

Type: Lesson Plan

Looking for Patterns in a Sequence of Fractions:

Students generate and describe a numerical pattern using the multiplication and subtraction of fractions.

Type: Lesson Plan

Original Student Tutorial

Wubble Double Trouble:

Join Pete as he explores patterns within patterns with feisty Wubbles and Dipples in this interactive tutorial.

Type: Original Student Tutorial

Perspectives Video: Teaching Idea

Classroom Storytime: Creating Mathematical Models:

Watch as the Wubbles double to show you how a mathematical pattern can be made.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Teaching Idea

Problem-Solving Task

Double Plus One:

The purpose of this task is to help students gain a better understanding of patterns. This task is meant to be used in an instructional setting.

Type: Problem-Solving Task

MFAS Formative Assessments

Baseball Cards:

Students generate a number pattern based on a given rule and explain the pattern found.

Dot Patterns:

Students examine triangular numbers through a given dot pattern.

Generating Two Patterns:

Students are given two rules and are asked to generate patterns.

Multiply By Four:

Students are asked to generate a sequence of numbers based on a given rule and then to identify features of the pattern that are not explicit.

Original Student Tutorials Mathematics - Grades K-5

Wubble Double Trouble:

Join Pete as he explores patterns within patterns with feisty Wubbles and Dipples in this interactive tutorial.

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Original Student Tutorial

Wubble Double Trouble:

Join Pete as he explores patterns within patterns with feisty Wubbles and Dipples in this interactive tutorial.

Type: Original Student Tutorial

Problem-Solving Task

Double Plus One:

The purpose of this task is to help students gain a better understanding of patterns. This task is meant to be used in an instructional setting.

Type: Problem-Solving Task

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.

Problem-Solving Task

Double Plus One:

The purpose of this task is to help students gain a better understanding of patterns. This task is meant to be used in an instructional setting.

Type: Problem-Solving Task