# Even and Odd Numbers + Adding Equal Groups of Objects

Understanding even and odd numbers and how to add equal groups of objects are second grade, Common Core math skills: 2.OA.3 and 2.OA.4. Below we show two videos that demonstrate each of these standards. Then, we provide a breakdown of the specific steps in the videos to help you teach your class.

Prior Learnings

Your students should be experienced in solving all types of addition and subtraction problems. Before, “addition” was separate from subtraction and the problems were limited to one-step problems and numbers within 20 (1.OA.1).

Future Learnings

After learning these math skills, your students will be able to apply strategies to both one and two-step problems that involve the “four operations (addition, subtraction, multiplication, division).” Additionally, your students will learn how to represent an unknown using a letter (3.OA.8).

Common Core Standard: 2.OA.3 - Determine whether a group of objects (up to 20) has an odd or even number of members

Students who understand this principle can:

1. Recognize that objects in sets of equal numbers will pair up evenly, none left over.
2. Use various strategies to determine if a group of objects is even or odd.
3. Understand that all even numbers can be formed by adding 2 equal addends.
4. Count groups of objects by 2s up to the number 20.

Video 1: Counting Shoes - Even and Odd

The video begins by explaining that some numbers are called odd numbers and others are called even numbers. During the quest, the video teaches students how to identify even and odd numbers.

There are a few ways to determine if numbers are odd or even. The video explains that students can match pairs to determine this. If one is left over, then the number is odd. If not, the number is even.

1. The video uses shoes to demonstrate the concept.
a. There are 6 shoes; each shoe has a pair.
b. 6 is an even number.
2. A second set of shoes are shown.
a. There are 7 shoes; almost all the shoes have pairs.
b. Since 1 shoe is left alone, 7 is an odd number.

Video 2: Dividing Objects into Even and Odd Groups

Boddle combines standards 2.OA.3 and 2.OA.4 since they are very similar and related concepts. Learning the difference between even and odd numbers begins and ends at 0:00-2:30.

First, the video explains the difference between equal and odd numbers: “A number is even when you can divide it into 2 equal whole numbers.”

1. 6 paint brushes are even because they can be divided into 2 groups of 3.

However, a number is odd when it cannot be divided into 2 equal whole numbers.

1. 7 radios cannot be split into two even groups.
a. If you pair them up, then one is always left over.
b. So, 7 is an odd number.

The video then provides more groups of objects for students to practice identifying whether numbers are even or odd.

1. 4 red mailboxes are even because 4 can be split into 2 equal groups of 2.
2. 11 folders are odd because 11 cannot be divided into groups with equal numbers.
3. 16 diamond rings are even because 16 can be split into 2 equal groups of 8.
4. 9 cards are odd because 9 cannot be divided into groups with equal numbers.

The second half of the video discusses Common Core standard 2.OA.4.

Common Core Standard: 2.OA.4 - Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns

Students who understand this principle can:

1. Write an equation, from an array, with equal, repeated addends.
2. Understand that arrays can be written as addition problems with repeating addends.
3. Find the number of objects in rectangular arrays by solving repeated addition problems.

Video 1: Counting Groups of Goldfish

The video demonstrates an activity you can do with your students to help them understand and visualize how to count by equal groups: repeated addition.

On a paper, 3 goldfish are placed into each of the 4 circles--3 counters in each of the 4 groups. The speaker asks how to find the total number of counters without counting each one individually.

1. There are 3 goldfish in each group.
2. The number 3 is written below the groups.
a. 3 + 3 + 3 + 3 = ?
3. Once the “number sentence” is filled in, it reads, “4 groups of 3 equals __.”
4. The first two three are added (3 + 3 = 6), then the other 3s are added one by one.
a. (3 + 3 = 6); (6 + 3 = 9); (9 + 3 = 12).
5. So, 4 groups of 3 equals 12 .

The speaker then asks viewers to think about how the number sentence is related to the model. She explains that since each group was equal, she could count by 3s instead of 1s.

Video 2: Counting Equal Groups of Objects

Boddle combines standards 2.OA.3 and 2.OA.4 since they are very similar and related concepts. Standard 2.OA.4 begins at minute mark 2:30 and goes to the end.

Boddle starts by explaining how to find out how many objects are in a group by writing an addition sentence. Students can write an addition sentence based on how the following objects are grouped.

1. The first example is of capsules.
a. There are 4 groups with 2 capsules each.
b. Adding the 2s together equals 8 capsules.
c. Or, 2 + 2 + 2 + 2 = 8.
2. The second example is of telephones.
a. There are 3 groups with 5 telephones each.
b. Adding the 5s together equals 15 telephones.
c. Or, 5 + 5 + 5 = 15.
3. The third example is of microscopes.
a. There are 6 groups of 4 microscopes each.
b. Adding the 4s together equals 24 microscopes.
c. Or, 4 + 4 + 4 + 4 + 4 + 4 = 24.

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