Cluster Standards

This cluster includes the following benchmarks.

Visit the specific benchmark webpage to find related instructional resources.

MAFS.3.OA.4.8 : Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
MAFS.3.OA.4.9 : Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

Cluster 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

Cluster Access Points

This cluster includes the following 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.

Cluster Resources

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

Original Student Tutorials

Stuffing School Supplies: Learn how Maritza uses multiplication to stuff school supplies into backpacks with this interactive tutorial.
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.
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.
- Part 1 - Party Patterns: Odds and Evens in Addition
- Part 2 - Party Patterns: Odds and Evens in Addition
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.
- Part 1 - Party Patterns: Evens and Odds in Addition
- Part 3 - Party Patterns: Evens and Odds in Addition
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
- Part 3: Party Patterns: Evens and Odds in Addition
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.

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.
Adding Odd Numbers: Students are asked to consider what type of number results when adding two odd numbers and when adding three odd numbers.
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.
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.
Multiplication of Even Numbers: Students are asked to determine if the total number of students in five classes will be even or odd.
Zoo Field Trip: Students solve a two-step word problem involving subtraction and division and then choose an equation that represents the word problem.
Party Beverages: Students solve a two-step problem requiring multiplication and addition and then write an equation to represent the problem.
Bake Sale: Students solve a two-step word problem involving addition and division and then write an equation to represent the problem.
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.

Lesson Plans

Getting the hang of two-step word problems: Students will solve two-step word problems involving any of the four operations and represent these problems using equations.
Chess Wish List: Students will think like chess club members to 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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx
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 attendees' reviews of the camps which should create interesting student discussions. They will use knowledge of operations to determine the difference in camp costs.

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.
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.
Water Park Fun Day: In this Model Eliciting Activity, MEA, students 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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx
The Power of Patterns: Students will work a real-world problem to discover similarities and differences between a pattern that extends by adding 2 to each term and a pattern that extends by doubling each term. The problem is set in the real-world context of twin brothers who choose between different pattern rules given by their grandma to save for buying a car.

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.
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.
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.
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.
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.

Tutorial

Total Seats in a Theater: Solve a two-step word problem by drawing a picture and creating an equation.