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



This document was generated on CPALMS - www.cpalms.org


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
Code Description
MA.4.AR.3.1: Determine factor pairs for a whole number from 0 to 144. Determine whether a whole number from 0 to 144 is prime, composite or neither.
Clarifications:
Clarification 1: Instruction includes the connection to the relationship between multiplication and division and patterns with divisibility rules.

Clarification 2: The numbers 0 and 1 are neither prime nor composite.

MA.4.AR.3.2: Generate, describe and extend a numerical pattern that follows a given rule.
Clarifications:
Clarification 1: Instruction includes patterns within a mathematical or real-world context.


Related Access Points

This cluster includes the following access points.

Access Points

Access Point Number Access Point Title
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.

Original Student Tutorials

Name Description
Wubble Double Trouble:

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

Prime and Composite Backyard Dilemma :

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

Educational Games

Name Description
Arithmetic Workout:

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

Formative Assessments

Name Description
Find All the Factor Pairs:

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

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.

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.

Dot Patterns:

Students examine triangular numbers through a given dot pattern.

Baseball Cards:

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

Generating Two Patterns:

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

Prime or Composite:

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

Lesson Plans

Name Description
Divisibility Rules and Factors:

The students will determine divisibility rules by looking for a pattern in multiples of a number. They will then utilize divisibility rules to find factors thereby strengthening this ability. The students will practice their factoring skills through the Four in a Row game. This lesson could be an introduction to divisibility rules but not findng factors.

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.

Hooray for arrays!:

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

Abundant Numbers:

This lesson provides practice in learning factors of numbers. Students will play a factor game then participate in a thought-provoking task. It is helpful if students know what a prime number is, but it is not essential.

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.

Factor That!:

This is a foundation lesson in which the students will visually see the relationship between factors and products. As a result of this hands-on lesson and guided discussion, they will learn to identify the factors of a given number.

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.

Factor Word Challenges:

Students will apply multiplication, division and factor knowledge to word problems.

Pattern Fun:

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

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.

Searching for the Primes:

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

Looking for Patterns in a Sequence of Fractions:

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

Prime Factorization - From Fingerprints to Factorprints:

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

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.

Perspectives Video: Teaching Idea

Name Description
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.

Problem-Solving Tasks

Name Description
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.

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.

Tutorial

Name Description
Recognizing Prime and Composite Numbers:

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



Student Resources

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

Original Student Tutorials

Title Description
Wubble Double Trouble:

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

Prime and Composite Backyard Dilemma :

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

Educational Games

Title Description
Arithmetic Workout:

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

Problem-Solving Tasks

Title Description
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.

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.

Tutorial

Title Description
Recognizing Prime and Composite Numbers:

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



Parent Resources

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

Problem-Solving Tasks

Title Description
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.

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.