Cluster 4: Solve problems involving the four operations, and identify and explain patterns in arithmetic. (Major Cluster)Archived

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Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

General Information
Number: MAFS.3.OA.4
Title: Solve problems involving the four operations, and identify and explain patterns in arithmetic. (Major Cluster)
Type: Cluster
Subject: Mathematics - Archived
Grade: 3
Domain-Subdomain: Operations and Algebraic Thinking

Related Standards

This cluster includes the following benchmarks.

Related Access Points

This cluster includes the following access points.

Access Points

MAFS.3.OA.4.AP.8a
Solve and check one-step word problems using the four operations within 100.
MAFS.3.OA.4.AP.9a
Identify and describe the rule for a numerical pattern where numbers increase by 2, 5 or 10.
MAFS.3.OA.4.AP.9b
Select or name the three next terms in a numeral pattern where numbers increase by 2, 5, or 10.
MAFS.3.OA.4.AP.9c

Identify multiplication patterns in a real-world setting.

Related Resources

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

Educational Game

Number Facts Bingo:

This Flash applet generates number fact questions for the game of Bingo. Each of the six levels focuses on a different range of number facts (addition, subtraction, and multiplication), which are displayed one at a time in a variety of question formats. The applet is intended for use in a class/group setting with a projector or interactive whiteboard. Downloadable cards for each level are available from the menu page. At any time in a game the "number facts so far" feature will reveal all the questions presented in the current round to facilitate review or verification of a winning board.

Type: Educational Game

Formative Assessments

Decomposing Into Equal Addends:

Students are presented with an equation and asked to find a pattern within the equation and to determine if the equation is true or not.

Type: Formative Assessment

Adding Odd Numbers:

Students are asked to consider what type of number results when adding two odd numbers and when adding three odd numbers.

Type: Formative Assessment

Adding Odds and Evens:

Students are asked to consider the parity of the sums of two even numbers, two odd numbers, and an even and an odd.

Type: Formative Assessment

Patterns Within the Multiplication Table:

Students are asked to find the missing numbers in a column of a multiplication table by using a pattern found within the table.

Type: Formative Assessment

Multiplication of Even Numbers:

Students are asked to determine if the total number of students in five classes will be even or odd.

Type: Formative Assessment

Zoo Field Trip:

Students solve a two-step word problem involving subtraction and division and then choose an equation that represents the word problem.

Type: Formative Assessment

Party Beverages:

Students solve a two-step problem requiring multiplication and addition and then write an equation to represent the problem.

Type: Formative Assessment

Bake Sale:

Students solve a two-step word problem involving addition and division and then write an equation to represent the problem.

Type: Formative Assessment

Books at the Book Fair:

Students solve a two-step word problem involving multiplication and subtraction and then write an equation to represent the problem.

Type: Formative Assessment

Lesson Plans

Multiplying Numbers: Fall Festival Extravaganza:

Students will organize and analyze data to create equations with variables. Students will use their understanding of equations to solve two-step word problems using data collected from the Morgan Woods Fall Festival Supply Sheet. Students will then communicate their understanding of the data through a written budget proposal sheet.

Type: Lesson Plan

Getting the hang of two-step word problems:

Students will solve two-step word problems involving subtraction and division and represent these problems using equations with a letter standing for the unknown quantity.

Type: Lesson Plan

Chess Wish List:

The 3rd grade chess club members will make two wish lists on how to spend $75 on chess related materials. Then they have to make two new wish lists on how to spend $750 on chess related materials.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

Science Space Camp:

This MEA asks the students to compare information provided on various Science Space Camps to be attended by a student during the summer. They will take into account past attendee's reviews of the camps which should create interesting student discussions.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

Tricky Rice Math Patterns MEA:

This is a 3rd grade MEA that requires students to use mathematical patterns to solve the problem, along with the analysis of data. After reading One Grain of Rice by Demi, students will look for ways to help Rani's relative find a new pattern so she can secure a large supply of rice to feed the people of her province in India. The twist is likely to cause controversy, so prepare for some strong debates.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

Water Park Fun Day:

This third grade MEA asks students to work as a team to figure out which activities they would like to do at the water park with a given amount of tickets and time. Students will make informed decisions about which activities and food and beverage items on which to spend their allotted tickets.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

The Power of Patterns:

Students will work a real world problem to discover similarities and differences between the patterns of adding 2 to a number and doubling a number. The problem is set in the real world context of twin brothers who choose different patterning strategies given by their grandma to save for buying a car.

Type: Lesson Plan

Original Student Tutorials

The Mystery of the Multiples:

Learn how to determine whether a whole number is a multiple of another whole number by using multiplication facts and skip-counting. You will be able to help Detective Barker in solving this mystery of which multiples belong to which whole numbers.

Type: Original Student Tutorial

Party Patterns: Odds and Evens in Addition - Part 3:

Determine if the sum of three odd or three even numbers will be odd or even as Lilly prepares for a math celebration in this interactive tutorial.

This is part 3 in a 3-part series. Click below to explore the other tutorials in the series. 

Type: Original Student Tutorial

Party Patterns: Evens and Odds in Addition – Part 2:

Explore addition patterns to find if the sum of an odd and an even number will be odd or even in this interactive tutorial.

This is part 2 in a 3-part series. Click below to explore the other tutorials in the series. 

Type: Original Student Tutorial

Party Patterns: Evens and Odds in Addition – Part 1:

Determine whether the sum of two odd numbers is odd or even and whether the sum of two even numbers is odd or even by helping Lilly prepare for a math celebration in this interactive tutorial.

This is part 1 in a 3-part series. Click below to explore the other tutorials in the series. 

  • Part 2: Party Patterns: Evens and Odds in Addition (COMING SOON)
  • Part 3: Party Patterns: Evens and Odds in Addition (COMING SOON)

Type: Original Student Tutorial

Protect the Turtles: Solve Two-Step Word Problems:

Solve some two-step word problems and write equations about sea turtles and how pollution created by people is impacting their survival in this interactive tutorial.  

Type: Original Student Tutorial

Problem-Solving Tasks

The Stamp Collection:

For students who are unfamiliar with this language the task provides a preparation for the later understanding that a fraction of a quantity is that fraction times the quantity.

Type: Problem-Solving Task

Symmetry of the addition table:

The goal of this task is to help students understand the commutative property of addition by examining the addition facts for single digit numbers. This is important as it gives students a chance, at a young age, to do more than memorize these arithmetic facts which they will use throughout their education.

Type: Problem-Solving Task

Making a ten:

This task asks students to study more carefully the make-a-ten strategy that they should already know and use intuitively. In this strategy, knowledge of which sums make a ten, together with some of the properties of addition and subtraction, are used to evaluate sums which are larger than 10. This task is intended for instruction purposes as it takes time to identify the patterns involved and understand the steps in the procedures.

Type: Problem-Solving Task

Addition Patterns:

The purpose of this task is to study some patterns in a small addition table. Each pattern identified persists for a larger table and if more time is available for this activity students should be encouraged to explore these patterns in larger tables.

Type: Problem-Solving Task

Patterns in the multiplication table:

The goal is to look for structure and identify patterns and then try to find the mathematical explanation for this. This problem examines the ''checkerboard'' pattern of even and odd numbers in a single digit multiplication table. The even numbers in the table are examined in depth using a grade appropriate notion of even, namely the possibility of reaching the number counting by 2's or expressing the number as a whole number of pairs.

Type: Problem-Solving Task

Student Center Activity

Edcite: Mathematics Grade 3:

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

Tutorial

Total Seats in a Theater:

Solve a two-step word problem by drawing a picture and creating an equation.

Type: Tutorial

Student Resources

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

Original Student Tutorials

The Mystery of the Multiples:

Learn how to determine whether a whole number is a multiple of another whole number by using multiplication facts and skip-counting. You will be able to help Detective Barker in solving this mystery of which multiples belong to which whole numbers.

Type: Original Student Tutorial

Party Patterns: Odds and Evens in Addition - Part 3:

Determine if the sum of three odd or three even numbers will be odd or even as Lilly prepares for a math celebration in this interactive tutorial.

This is part 3 in a 3-part series. Click below to explore the other tutorials in the series. 

Type: Original Student Tutorial

Party Patterns: Evens and Odds in Addition – Part 2:

Explore addition patterns to find if the sum of an odd and an even number will be odd or even in this interactive tutorial.

This is part 2 in a 3-part series. Click below to explore the other tutorials in the series. 

Type: Original Student Tutorial

Party Patterns: Evens and Odds in Addition – Part 1:

Determine whether the sum of two odd numbers is odd or even and whether the sum of two even numbers is odd or even by helping Lilly prepare for a math celebration in this interactive tutorial.

This is part 1 in a 3-part series. Click below to explore the other tutorials in the series. 

  • Part 2: Party Patterns: Evens and Odds in Addition (COMING SOON)
  • Part 3: Party Patterns: Evens and Odds in Addition (COMING SOON)

Type: Original Student Tutorial

Protect the Turtles: Solve Two-Step Word Problems:

Solve some two-step word problems and write equations about sea turtles and how pollution created by people is impacting their survival in this interactive tutorial.  

Type: Original Student Tutorial

Problem-Solving Tasks

The Stamp Collection:

For students who are unfamiliar with this language the task provides a preparation for the later understanding that a fraction of a quantity is that fraction times the quantity.

Type: Problem-Solving Task

Symmetry of the addition table:

The goal of this task is to help students understand the commutative property of addition by examining the addition facts for single digit numbers. This is important as it gives students a chance, at a young age, to do more than memorize these arithmetic facts which they will use throughout their education.

Type: Problem-Solving Task

Making a ten:

This task asks students to study more carefully the make-a-ten strategy that they should already know and use intuitively. In this strategy, knowledge of which sums make a ten, together with some of the properties of addition and subtraction, are used to evaluate sums which are larger than 10. This task is intended for instruction purposes as it takes time to identify the patterns involved and understand the steps in the procedures.

Type: Problem-Solving Task

Addition Patterns:

The purpose of this task is to study some patterns in a small addition table. Each pattern identified persists for a larger table and if more time is available for this activity students should be encouraged to explore these patterns in larger tables.

Type: Problem-Solving Task

Patterns in the multiplication table:

The goal is to look for structure and identify patterns and then try to find the mathematical explanation for this. This problem examines the ''checkerboard'' pattern of even and odd numbers in a single digit multiplication table. The even numbers in the table are examined in depth using a grade appropriate notion of even, namely the possibility of reaching the number counting by 2's or expressing the number as a whole number of pairs.

Type: Problem-Solving Task

Student Center Activity

Edcite: Mathematics Grade 3:

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

Tutorial

Total Seats in a Theater:

Solve a two-step word problem by drawing a picture and creating an equation.

Type: Tutorial

Parent Resources

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

Problem-Solving Tasks

The Stamp Collection:

For students who are unfamiliar with this language the task provides a preparation for the later understanding that a fraction of a quantity is that fraction times the quantity.

Type: Problem-Solving Task

Symmetry of the addition table:

The goal of this task is to help students understand the commutative property of addition by examining the addition facts for single digit numbers. This is important as it gives students a chance, at a young age, to do more than memorize these arithmetic facts which they will use throughout their education.

Type: Problem-Solving Task

Making a ten:

This task asks students to study more carefully the make-a-ten strategy that they should already know and use intuitively. In this strategy, knowledge of which sums make a ten, together with some of the properties of addition and subtraction, are used to evaluate sums which are larger than 10. This task is intended for instruction purposes as it takes time to identify the patterns involved and understand the steps in the procedures.

Type: Problem-Solving Task

Addition Patterns:

The purpose of this task is to study some patterns in a small addition table. Each pattern identified persists for a larger table and if more time is available for this activity students should be encouraged to explore these patterns in larger tables.

Type: Problem-Solving Task

Patterns in the multiplication table:

The goal is to look for structure and identify patterns and then try to find the mathematical explanation for this. This problem examines the ''checkerboard'' pattern of even and odd numbers in a single digit multiplication table. The even numbers in the table are examined in depth using a grade appropriate notion of even, namely the possibility of reaching the number counting by 2's or expressing the number as a whole number of pairs.

Type: Problem-Solving Task