# 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.
General Information
Subject Area: Mathematics
Domain-Subdomain: Operations and Algebraic Thinking
Cluster: Level 3: Strategic Thinking & Complex Reasoning
Cluster: Solve problems involving the four operations, and identify and explain patterns in arithmetic. (Major Cluster) -

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.

Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes
Test Item Specifications

• Assessment Limits :
Adding and subtracting is limited to whole numbers within 1,000. All values in items may not exceed whole number multiplication facts of 10 x 10 or the related division facts.
• Calculator :

No

• Context :

No context

Sample Test Items (1)
• Test Item #: Sample Item 1
• Question:

A multiplication table is shown.  Which statement correctly describes how to find the multiples of 6 in the multiplication table?

• Difficulty: N/A
• Type: MC: Multiple Choice

## Related Courses

This benchmark is part of these courses.
5012050: Grade Three Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
7712040: Access Mathematics Grade 3 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022 (current), 2022 and beyond)
5012055: Grade 3 Accelerated Mathematics (Specifically in versions: 2019 - 2022 (current), 2022 and beyond)
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022 (current), 2022 and beyond)

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
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 benchmark.

## Assessments

Sample 3 - Third Grade Math State Interim Assessment:

This is a State Interim Assessment for third grade.

Type: Assessment

Sample 1 - Third Grade Math State Interim Assessment:

This is a State Interim Assessment for third grade.

Type: Assessment

## 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

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

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

Type: Formative Assessment

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

## Lesson Plans

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.

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

## Lesson Study Resource Kit

Operations and Algebraic Thinking Lesson Study Resource Kit – Third Grade:

This lesson study resource kit can be used to guide and support teams of third grade teachers as they engage in lesson study focused on the academic standards in the Operations and Algebraic Thinking domain.

Type: Lesson Study Resource Kit

## Original Student Tutorials

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

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.

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.

## Student Center Activity

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

## STEM Lessons - Model Eliciting Activity

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.

## MFAS Formative Assessments

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

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

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.

Multiplication of Even Numbers:

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

## Original Student Tutorials Mathematics - Grades K-5

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)

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.

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.

## Student Resources

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

## Original Student Tutorials

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

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.

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.

## Student Center Activity

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

## Parent Resources

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

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.