Lesson objective: Understand that a whole number is either even or odd; an even number can be decomposed into two equal groups, while an odd number cannot.

Students use prior knowledge of decomposing whole numbers from Grade 1, Unit 6, 1.OA.C.6. This prior knowledge is extended to decomposing whole numbers into two groups in order to determine if a number is even or odd. A conceptual challenge students may encounter is understanding that a number is considered even when it can be decomposed into two equal groups, but it may or may not be even if it can be decomposed into more than two equal groups.

The concept is developed through work with dividing even and odd sets of items into two groups, which develops the understanding that a whole number is considered even when it can be divided into two equal groups.

This work helps students deepen their understanding of operations because when dividing an even whole number into two equal addends, the sum of the two addends will result in the starting whole number. This lesson helps set the stage for later work with writing an equation to represent even and odd numbers.

Students engage in Mathematical Practice 4 (Model with mathematics) as they apply what they know about decomposing numbers to a real-world context of sharing toys. Students will focus on decomposing whole numbers into two groups to determine if a given whole number is even or odd. Mathematical Practice 7 (Look for and make use of structure) is also featured in this lesson as students make generalizations about odd and even numbers. Possible generalizations that students may discover are all even numbers contain two equal addends, all odd numbers contain two equal addends plus one, and in a given set, if objects can be paired without any single objects leftover, the set contains an even number of objects.

**Key vocabulary:**

- decompose
- even
- odd

**Special materials needed:**

- connecting cubes or counters (something students can model the truck and car amounts with)