MA.2.AR.3.1

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Represent an even number using two equal groups or two equal addends. Represent an odd number using two equal groups with one left over or two equal addends plus 1.

Examples

Example: The number 8 is even because it can be represented as two equal groups of 4 or as the expression 4+4.

Example: The number 9 is odd because it can be represented as two equal groups with one left over or as the expression 4+4+1.

Clarifications

Clarification 1: Instruction focuses on the connection of recognizing even and odd numbers using skip counting, arrays and patterns in the ones place.

Clarification 2: Addends are limited to whole numbers less than or equal to 12.

General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 2
Strand: Algebraic Reasoning
Standard: Develop an understanding of multiplication.
Date Adopted or Revised: 03/20
Status: State Board Approved

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

 

Terms from the K-12 Glossary

  • NA

 

Vertical Alignment

Previous Benchmarks

 

Next Benchmarks

 

Purpose and Instructional Strategies

The purpose of this benchmark is to introduce the concept of even and odd numbers by building on students' understanding of equal groups and equal addends while continuing to build their automaticity with basic facts. This work lays the foundation for understanding multiples of 2 (MTR.5.1). 
  • Instruction includes the use of arrays to show equal groups in rows and columns.
  • Instruction includes the use of manipulatives, drawings, models, or equations to show a number as even or odd. 
  • Instruction includes numbers no larger than 25. 
  • Instruction includes building the foundation for patterns in grade 3.

 

Common Misconceptions or Errors

  • Students may think a number is odd if the doubles addition fact involves odd numbers.

 

Strategies to Support Tiered Instruction

  • Instruction includes opportunities to draw models of double facts or use two-color counters to explore the sums produced. Focus should be on sums always being even. 
    • For example, students draw a model for 4 + 4 and 9 + 9 by drawing a column of circles to represent each number. Students then pair the circle in each row to see there are no circles left without a match even when odd addends are used. Enough examples should be completed for students to see the pattern in the sums and realize the sums will always be even.
 a column of circles to represent each number
  • Instruction includes opportunities to build models of numbers using two-color counters to determine if a number is even or odd. 
    • For example, using 15 two-color counters, students pair the counters together to determine if each counter will have a partner or if one counter will be left without a partner. Students will determine if the number is even or odd by developing the understanding that an even number can be split into two equal groups.
number counters

 

Instructional Tasks

Instructional Task 1 (MTR.5.1) 

Present students with a variety of numbers between 0 and 25. Ask students to determine if the given number is even or odd by visually representing groups and creating an expression to determine if the total number of counters is even or odd. Student discussion should center around students being able to make generalizations about odd and even numbers.

 

Instructional Items

Instructional Item 1 

The counters below represent the number 10. Use groups and an expression to justify if the number 10 is even or odd. 

counter of 10

Instructional Item 2 

Tim says 15 is odd because there is a 5 in the ones place. Use an array to show that he is correct. 

 

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.

Related Courses

This benchmark is part of these courses.
5012040: Grade Two Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current))
7712030: Access Mathematics Grade 2 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5012005: Foundational Skills in Mathematics K-2 (Specifically in versions: 2019 - 2022, 2022 - 2024, 2024 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.2.AR.3.AP.1: Explore the concept of odd and even by pairing objects to represent an even number using two equal groups or represent an odd number by using two equal groups with one left over. Group of objects may not exceed 20.

Related Resources

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

Formative Assessments

Showing a Collection as Odd or Even:

Students are asked to determine if each of two collections has an odd or even number of objects, and to explain how they made their decisions.

Type: Formative Assessment

How Do You Know if a Number is Even or Odd?:

Students are asked to determine if a given number is even or odd.

Type: Formative Assessment

Is it Even or Odd?:

Students are asked to determine if a given number is even or odd.

Type: Formative Assessment

Even Numbers as the Sum of Two Equal Addends:

Students are asked to write even numbers within 20 as the sum of two equal addends.

Type: Formative Assessment

Lesson Plans

Is It Odd or Even?:

This lesson will introduce students to the concept of odd and even numbers. The lesson will show that objects that can be grouped by 2's (in pairs) represent even numbers and objects that cannot be grouped in pairs (have 1 left over) represent odd numbers. The lesson will also address two-digit numbers (up to 20) to show that the place value of the number in the ones place determines whether a two-digit number is odd or even.

Type: Lesson Plan

"Even" and "Odd" Go on a Picnic:

In this lesson, the class will be guided through representing even numbers using two equal groups and odd numbers as two equal groups with one left over. Students will explore various strategies for representing numbers that are even or odd based on whether they can be divided into two equal teams for a kickball game or whether everyone will have a buddy to pair up with on the picnic. Students will explore writing addition expressions to represent even numbers as two equal addends and odd numbers as two equal addends plus 1.

Type: Lesson Plan

Odds and Evens Dodgeball:

Students will create groups of objects to determine if a number is even or odd.

Type: Lesson Plan

Odds and Evens:

This resource helps students identify numbers as odd or even using a variety of methods including creating pairs, skip counting by two’s, using number lines, and arrays. It also leads them to understand that all even numbers can be written as a sum of equal addends and odds can be written as the sum of equal addends plus one.

This resource can be conducted as one lesson or can be spread over multiple mini sessions if needed as noted within this resource as Lesson 1 and Lesson 2.

Type: Lesson Plan

Original Student Tutorial

Beach Buddies: Even or Odd? :

Come explore even and odd numbers of objects and learn to determine if a group of objects has an even or odd number in this beach-themed, interactive tutorial.

Type: Original Student Tutorial

Perspectives Video: Teaching Ideas

The Van de Walle Dot Matrix: A tool to support concepts from counting to multiplying polynomials:

Unlock an effective teaching tool that can help students all the way from basic counting principles to multiplying polynomials.

Dot Matrix sheet is available for dowload here.

Type: Perspectives Video: Teaching Idea

Equations on the Math Balance:

Unlock an effective teaching strategy for teaching inequalities and equations with the math balance in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

Problem-Solving Task

Red and Blue Tiles:

This task is specifically written so that students have opportunities to use different strategies to determine whether a set has an even or odd number of objects.

Type: Problem-Solving Task

MFAS Formative Assessments

Even Numbers as the Sum of Two Equal Addends:

Students are asked to write even numbers within 20 as the sum of two equal addends.

How Do You Know if a Number is Even or Odd?:

Students are asked to determine if a given number is even or odd.

Is it Even or Odd?:

Students are asked to determine if a given number is even or odd.

Showing a Collection as Odd or Even:

Students are asked to determine if each of two collections has an odd or even number of objects, and to explain how they made their decisions.

Original Student Tutorials Mathematics - Grades K-5

Beach Buddies: Even or Odd? :

Come explore even and odd numbers of objects and learn to determine if a group of objects has an even or odd number in this beach-themed, interactive tutorial.

Student Resources

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

Original Student Tutorial

Beach Buddies: Even or Odd? :

Come explore even and odd numbers of objects and learn to determine if a group of objects has an even or odd number in this beach-themed, interactive tutorial.

Type: Original Student Tutorial

Problem-Solving Task

Red and Blue Tiles:

This task is specifically written so that students have opportunities to use different strategies to determine whether a set has an even or odd number of objects.

Type: Problem-Solving Task

Parent Resources

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

Problem-Solving Task

Red and Blue Tiles:

This task is specifically written so that students have opportunities to use different strategies to determine whether a set has an even or odd number of objects.

Type: Problem-Solving Task