Learn on PengiSaxon Math, Intermediate 4Chapter 1: Lessons 1–10, Investigation 1

Lesson 10: Even and Odd Numbers

In this Grade 4 lesson from Saxon Math Intermediate 4, students learn to identify even and odd numbers by examining a number's last digit and understand that even numbers can be divided into two equal groups while odd numbers cannot. Students practice classifying whole numbers including zero, and apply their understanding to construct three-digit even or odd numbers using given digits. The lesson also introduces generalizations about the sums of even and odd numbers.

Section 1

📘 Even and Odd Numbers

New Concept

The numbers we say when we start with 2 and then count up by twos are even numbers.

What’s next

Next, you’ll apply this rule to identify even and odd numbers and use this property to solve problems.

Section 2

even numbers

Property

The numbers we say when we start with 2 and then count up by twos are even numbers (2,4,6,8,2, 4, 6, 8, \ldots). An even number of objects can be separated into two equal groups.

Example

456456 is even because its last digit is 66. 1818 is even because it can be split into two equal groups of 99. The number 328328 ends in an even digit, 88, so it is an even number.

Explanation

Think of even numbers as perfect for sharing! If you have an even number of cookies, you can split them into two equal piles with none left over. The easiest trick is to check the last digit: if it’s a 0, 2, 4, 6, or 8, then the whole number is even, no matter how big it is.

Section 3

odd number

Property

If a whole number is not an even number, then it is an odd number (1,3,5,7,1, 3, 5, 7, \ldots). If you try to separate an odd number of objects into two equal groups, there will be one extra object.

463463 is odd because its last digit is 33. 9999 is odd because it ends in 99. Trying to split 55 dots into two groups leaves one dot leftover, proving 55 is odd.

Odd numbers are the quirky individualists of the number world! When you try to divide them into two equal groups, there’s always one item left out, like the odd one out. A number is odd if its very last digit is a 1, 3, 5, 7, or 9. That's the only clue you need!

Section 4

Sum of two odd numbers

Property

Will the sum of any two odd numbers be an odd number or an even number? The sum will always be an even number.

Example

3(odd)+5(odd)=8(even)3 (\text{odd}) + 5 (\text{odd}) = 8 (\text{even}). 7(odd)+11(odd)=18(even)7 (\text{odd}) + 11 (\text{odd}) = 18 (\text{even}). 201(odd)+99(odd)=300(even)201 (\text{odd}) + 99 (\text{odd}) = 300 (\text{even}).

Explanation

When you add two odd numbers, think of it as combining two groups that each have a 'leftover one.' These two lonely leftovers find each other and form a new pair! Because the leftovers pair up perfectly, the final sum is always a nice, neat even number. It's like teamwork making the dream work!

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 1: Lessons 1–10, Investigation 1

  1. Lesson 1

    Lesson 1: Review of Addition

  2. Lesson 2

    Lesson 2: Missing Addends

  3. Lesson 3

    Lesson 3: Sequences

  4. Lesson 4

    Lesson 4: Place Value, Activity Comparing Money Amounts

  5. Lesson 5

    Lesson 5: Ordinal Numbers, Months of the Year

  6. Lesson 6

    Lesson 6: Review of Subtraction

  7. Lesson 7

    Lesson 7: Writing Numbers Through 999

  8. Lesson 8

    Lesson 8: Adding Money

  9. Lesson 9

    Lesson 9: Adding with Regrouping

  10. Lesson 10Current

    Lesson 10: Even and Odd Numbers

  11. Lesson 11

    Lesson 11: Investigation 1 Number Lines, Activity Drawing Number Lines

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

📘 Even and Odd Numbers

New Concept

The numbers we say when we start with 2 and then count up by twos are even numbers.

What’s next

Next, you’ll apply this rule to identify even and odd numbers and use this property to solve problems.

Section 2

even numbers

Property

The numbers we say when we start with 2 and then count up by twos are even numbers (2,4,6,8,2, 4, 6, 8, \ldots). An even number of objects can be separated into two equal groups.

Example

456456 is even because its last digit is 66. 1818 is even because it can be split into two equal groups of 99. The number 328328 ends in an even digit, 88, so it is an even number.

Explanation

Think of even numbers as perfect for sharing! If you have an even number of cookies, you can split them into two equal piles with none left over. The easiest trick is to check the last digit: if it’s a 0, 2, 4, 6, or 8, then the whole number is even, no matter how big it is.

Section 3

odd number

Property

If a whole number is not an even number, then it is an odd number (1,3,5,7,1, 3, 5, 7, \ldots). If you try to separate an odd number of objects into two equal groups, there will be one extra object.

463463 is odd because its last digit is 33. 9999 is odd because it ends in 99. Trying to split 55 dots into two groups leaves one dot leftover, proving 55 is odd.

Odd numbers are the quirky individualists of the number world! When you try to divide them into two equal groups, there’s always one item left out, like the odd one out. A number is odd if its very last digit is a 1, 3, 5, 7, or 9. That's the only clue you need!

Section 4

Sum of two odd numbers

Property

Will the sum of any two odd numbers be an odd number or an even number? The sum will always be an even number.

Example

3(odd)+5(odd)=8(even)3 (\text{odd}) + 5 (\text{odd}) = 8 (\text{even}). 7(odd)+11(odd)=18(even)7 (\text{odd}) + 11 (\text{odd}) = 18 (\text{even}). 201(odd)+99(odd)=300(even)201 (\text{odd}) + 99 (\text{odd}) = 300 (\text{even}).

Explanation

When you add two odd numbers, think of it as combining two groups that each have a 'leftover one.' These two lonely leftovers find each other and form a new pair! Because the leftovers pair up perfectly, the final sum is always a nice, neat even number. It's like teamwork making the dream work!

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 1: Lessons 1–10, Investigation 1

  1. Lesson 1

    Lesson 1: Review of Addition

  2. Lesson 2

    Lesson 2: Missing Addends

  3. Lesson 3

    Lesson 3: Sequences

  4. Lesson 4

    Lesson 4: Place Value, Activity Comparing Money Amounts

  5. Lesson 5

    Lesson 5: Ordinal Numbers, Months of the Year

  6. Lesson 6

    Lesson 6: Review of Subtraction

  7. Lesson 7

    Lesson 7: Writing Numbers Through 999

  8. Lesson 8

    Lesson 8: Adding Money

  9. Lesson 9

    Lesson 9: Adding with Regrouping

  10. Lesson 10Current

    Lesson 10: Even and Odd Numbers

  11. Lesson 11

    Lesson 11: Investigation 1 Number Lines, Activity Drawing Number Lines