 # Even and Odd Numbers

Videos to help Grade 6 students learn how to apply odd and even numbers to understand factors and multiples.

New York State Common Core Math Grade 6, Module 2, Lesson 16

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Opening Exercise

What is an even number?
List some examples of even numbers.
What is an odd number?
List some examples of odd numbers.
What happens when we add two even numbers? Will we always get an even number?

Exercises

1. Why is the sum of two even numbers even?
a. Think of the problem 12 + 14. Draw dots to represent each number.
b. Circle pairs of dots to determine if any of the dots are left over.
c. Will this be true every time two even numbers are added together? Why or why not?

2. Why is the sum of two odd numbers even?
a. Think of the problem 11 + 15. Draw dots to represent each number.
b. Circle pairs of dots to determine if any of the dots are left over.
c. Will this be true every time two odd numbers are added together? Why or why not?

3. Why is the sum of an even number and an odd number odd?
a. Think of the problem . Draw dots to represent each number.
b. Circle pairs of dots to determine if any of the dots are left over.
c. Will this be true every time an even number and an odd number are added together? Why or why not?
d. What if the first addend was odd and the second was even. Would the sum still be odd? Why or why not? For example, if we had 11 + 14, would the sum be odd?

Lesson Summary

Addition

Even + even = even
Odd + odd = even
Odd + even = odd

Multiplication

The product of two even numbers is even.
The product of two odd numbers is odd.
The product of an even number and an odd number is even.

Exit Ticket

Determine whether each sum or product will be even or odd. Explain your reasoning.
1. 56,426 + 17, 895
2. 317,362 × 129,324
3. 10,481 + 4,569
4. 32,457 × 12,781
5. Show or explain why 12 + 13 + 14 + 15 + 16 will result in an even sum.

Exercises 1 - 3
Exploratory Challenge
The product of two even numbers, the product of two odd numbers, or the product of an even number and an odd number. Encourage students to use previous knowledge about even and odd numbers, the connection between addition and multiplication, and visual methods (e.g., dots) in their proofs.

1. The product of two even numbers is even.
2. The product of two odd numbers is odd.
3. The product of an even number and an odd number is even. Problem Set
Without solving, tell whether each sum or product is even or odd. Explain your reasoning.
1. 346 + 721
2. 4,690 × 141
3. 1,462,891 × 745,629
4. 425,922 + 32,481,064
5. 32 + 45 + 67 + 91 + 34 + 56

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