Standard 3: Recognize numerical patterns, including patterns that follow a given rule.

General Information
Number: MA.4.AR.3
Title: Recognize numerical patterns, including patterns that follow a given rule.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Grade: 4
Strand: Algebraic Reasoning

Related Benchmarks

This cluster includes the following benchmarks.

Related Access Points

This cluster includes the following access points.

Access Points

MA.4.AR.3.AP.1
Explore factor pairs for a whole number. Factors may not exceed single-digit whole numbers.
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 topic.

Educational Games

Arithmetic Workout:

This tutorial will help you to brush up on your multiplication, division and factoring skills with this exciting game. 

Type: Educational Game

Sigma Prime: A Prime Factorization Game:


This fun and engaging game will test your knowledge of whole numbers as prime or composite.  As you shoot the asteroids with a particular factor, the asteroids will break down by that chosen factor.  Keep shooting the correct factors to totally eliminate the asteroids.  But be careful, shooting the wrong factor has consequences!

Type: Educational Game

Formative Assessments

Find All the Factor Pairs:

Students are asked to find all the factor pairs for each of four given numbers.

Type: Formative Assessment

Factor Pairs:

Students are asked to find all the factor pairs of a given number and identify the number as a multiple of the factors.

Type: Formative Assessment

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

Prime or Composite:

Students are asked to determine whether each of four given numbers is prime or composite and justify their choices.

Type: Formative Assessment

Lesson Plans

Fantastic Factors:

In this lesson, students will start out using manipulatives to create arrays which will be used to find factor pairs. Students will use a T-Chart to determine the factor pairs of numbers. Students will then use their T-Charts to determine if a number is prime or composite.

Type: Lesson Plan

Hooray for arrays!:

Students will identify prime and composite numbers through arrays. The lesson begins with a fun situational story.

Type: Lesson Plan

Using Rectangles to Find Prime and Composite Numbers:

In this lesson, students will be using rectangles to find prime and composite numbers.  Students will draw different rectangles for the area of a given set of numbers.  They will determine the factor pairs for each number in the given set and use them to discover the meaning of prime and composite numbers.

Type: Lesson Plan

Numbers Grow Here:

The students will use prior knowledge of the area formula to design a garden with a  area. Students will compare gardens and note that rectangles with the same area could have different dimensions.

Type: Lesson Plan

Pattern Fun:

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

Type: Lesson Plan

Fun with Factors:

This is an introductory lesson addressing factors for number 1-20. Factoring will lead students to discover differences and similarities between prime and composite numbers. Students will also discuss five claims about factors, prime, and composite numbers and create support from examples and non-examples to determine whether these claims are valid or invalid.

Type: Lesson Plan

Fish Ahoy Fish:

Students will work in groups to assist a client in purchasing different fish for a fish pond. From a data table, they will need to decide which type of fish and how many fish to purchase according to the size of the each pond. After, they will need to revisit a revised data table to make different selection of fish and calculate costs for the purchase of the fish.

Type: Lesson Plan

Searching for the Primes:

Students will use a 100s chart to sort out the prime numbers under 100 using the Sieve of Eratosthenes method. 

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

Prime Factorization - From Fingerprints to Factorprints:

This activity provides an introduction to composite numbers and prime numbers through factorization.

Type: Lesson Plan

Area and Perimeter of Rectangles Investigations:

Students will determine the validity of the statement, "All rectangles with the same area will have the same perimeter" through two investigations.

Type: Lesson Plan

Original Student Tutorials

Wubble Double Trouble:

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

Type: Original Student Tutorial

Prime and Composite Backyard Dilemma :

Discover what makes prime and composite numbers unique thanks to an interesting backyard problem 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 Tasks

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

Identifying Multiples:

The goal of this task is to work on finding multiples of some whole numbers on a multiplication grid. After shading in the multiples of 2, 3, and 4 on the table, students will see a key difference.  The focus can be on identifying patterns or this can be an introduction or review of prime and composite numbers.

Type: Problem-Solving Task

Tutorial

Recognizing Prime and Composite Numbers:

This Khan Academy tutorial video reviews how to determine if a number is prime or composite.

Type: Tutorial

Student Resources

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

Original Student Tutorials

Wubble Double Trouble:

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

Type: Original Student Tutorial

Prime and Composite Backyard Dilemma :

Discover what makes prime and composite numbers unique thanks to an interesting backyard problem in this interactive tutorial.

Type: Original Student Tutorial

Educational Games

Arithmetic Workout:

This tutorial will help you to brush up on your multiplication, division and factoring skills with this exciting game. 

Type: Educational Game

Sigma Prime: A Prime Factorization Game:


This fun and engaging game will test your knowledge of whole numbers as prime or composite.  As you shoot the asteroids with a particular factor, the asteroids will break down by that chosen factor.  Keep shooting the correct factors to totally eliminate the asteroids.  But be careful, shooting the wrong factor has consequences!

Type: Educational Game

Problem-Solving Tasks

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

Identifying Multiples:

The goal of this task is to work on finding multiples of some whole numbers on a multiplication grid. After shading in the multiples of 2, 3, and 4 on the table, students will see a key difference.  The focus can be on identifying patterns or this can be an introduction or review of prime and composite numbers.

Type: Problem-Solving Task

Tutorial

Recognizing Prime and Composite Numbers:

This Khan Academy tutorial video reviews how to determine if a number is prime or composite.

Type: Tutorial

Parent Resources

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

Problem-Solving Tasks

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

Identifying Multiples:

The goal of this task is to work on finding multiples of some whole numbers on a multiplication grid. After shading in the multiples of 2, 3, and 4 on the table, students will see a key difference.  The focus can be on identifying patterns or this can be an introduction or review of prime and composite numbers.

Type: Problem-Solving Task