Mathematics · 2nd Grade · Algebraic Thinking: Patterns and Equations · Weeks 19-27

Identifying Even and Odd Numbers

Investigating the properties of numbers that can be divided into two equal groups or pairs.

• Common Core State Standards
• CCSS.Math.Content.2.OA.C.3

About This Topic

The symmetry of even and odd numbers introduces students to the concept of parity and divisibility. Students learn that an even number can be split into two equal groups or paired up perfectly with no 'leftovers.' An odd number, by contrast, always has one 'odd man out.' This topic is a precursor to division and multiplication, as it focuses on the structure of numbers rather than just their names.

This topic aligns with CCSS standards for determining whether a group of objects (up to 20) has an odd or even number of members and writing an equation to express an even number as a sum of two equal addends. It encourages students to look for patterns, such as the fact that even numbers always end in 0, 2, 4, 6, or 8. This topic comes alive when students can physically model the patterns using their own bodies or classroom manipulatives.

Key Questions

1. What makes a number 'even' when looking at it as a collection of pairs?
2. Why does adding two odd numbers always result in an even sum?
3. How can we use rectangular arrays to prove a number is even?

Learning Objectives

• Classify whole numbers up to 20 as either even or odd based on their properties.
• Explain why a number is even by demonstrating it can be divided into two equal groups or pairs.
• Represent even numbers as the sum of two equal addends using equations.
• Compare the sums of two odd numbers to identify the resulting parity.

Before You Start

Counting and Cardinality

Why: Students need to be able to count objects accurately to determine the total number in a set.

Addition Concepts

Why: Understanding how to add numbers is essential for representing even numbers as sums of equal addends and for exploring the sums of odd numbers.

Key Vocabulary

Even Number	A whole number that can be divided into two equal groups or pairs with no remainder. Even numbers end in 0, 2, 4, 6, or 8.
Odd Number	A whole number that cannot be divided into two equal groups or pairs without one left over. Odd numbers end in 1, 3, 5, 7, or 9.
Pair	A set of two identical or similar items that are used together or are considered as a unit. In this context, it refers to grouping numbers by twos.
Sum	The result when two or more numbers are added together. For example, the sum of 3 and 5 is 8.

Watch Out for These Misconceptions

Common Misconception

Thinking a number is odd because it is 'big.'

What to Teach Instead

Students sometimes associate 'odd' with 'difficult' or 'large.' Use hands-on modeling with very large even numbers (like 40) to show that as long as every piece has a partner, the number is even, regardless of size.

Common Misconception

Only looking at the first digit of a two-digit number to determine parity.

What to Teach Instead

A student might think 32 is odd because 3 is odd. Use peer discussion and physical grouping to prove that only the 'ones' digit determines if the whole group can be paired up.

Active Learning Ideas

Inquiry Circle: The Partner Parade

The teacher gives the class a number. Students must quickly find a partner. If everyone has a partner, they shout 'Even!' If one person is left without a partner, they shout 'Odd!' They then record the result on a class chart to find patterns.

15 min·Whole Class

Think-Pair-Share: The Sum Secret

Pairs are given two odd numbers to add together (e.g., 3 + 5). They use cubes to model the addition and then discuss why two numbers with 'leftovers' suddenly join to make a perfect 'even' set with no leftovers.

20 min·Pairs

Stations Rotation: Even/Odd Explorations

Students move through three stations: one for sorting handfuls of beads into pairs, one for building 'towers of two' with LEGOs, and one for coloring a hundreds chart to visualize the alternating pattern of parity.

40 min·Small Groups

Real-World Connections

• When setting the table, you can determine if you have an even or odd number of guests by checking if you have enough pairs of plates, cups, and silverware.
• In sports like basketball, players often try to score in pairs of points (2-point shots or 3-point shots), and the total score can be analyzed for its parity to understand game dynamics.

Assessment Ideas

Exit Ticket

Give students a card with a number from 1 to 20. Ask them to write 'Even' or 'Odd' on the card and draw a picture showing how they can group the number into pairs to prove their answer.

Quick Check

Write several numbers on the board (e.g., 12, 7, 18, 15). Ask students to hold up one finger for odd and two fingers for even. Then, ask: 'What do you notice about the last digit of all the even numbers?'

Discussion Prompt

Pose the question: 'If you add two odd numbers together, is the answer always even or always odd? How do you know?' Encourage students to use manipulatives or drawings to explain their reasoning.

Frequently Asked Questions

How can active learning help students understand even and odd numbers?

Active learning, like 'The Partner Parade,' makes the concept of parity a social and physical experience. When a student is the 'odd man out,' they never forget what an odd number represents. Physically pairing objects or classmates provides a concrete anchor for the abstract rule of 'ending in 0, 2, 4, 6, or 8.'

Why does adding two odd numbers make an even number?

Every odd number has one 'extra' piece that doesn't have a partner. When you add two odd numbers, those two 'extra' pieces find each other and form a new pair, making the total sum even.

What is the best way to introduce even and odd?

Start with the concept of 'fair shares' or 'partners.' Ask students if a certain number of cookies can be shared between two people with none left over. This connects the math to a real-world scenario they care about.

How does this topic prepare students for 3rd grade?

It is the foundation for multiplication (specifically the 2s table) and the concept of division. Understanding that even numbers are 'doubles' helps them grasp the relationship between addition and multiplication.