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

Lesson 3: Sequences

In this Grade 4 Saxon Math lesson from Chapter 1, students learn about counting sequences, including how to identify the rule of a sequence and find missing or next numbers by counting up or down by a given amount. The lesson also introduces digits, the numerals 0 through 9 used to write numbers, with practice identifying how many digits a number contains and what its last digit is. A problem-solving focus on making a table helps students organize combinations systematically.

Section 1

📘 Sequences

New Concept

A counting pattern is a sequence.

What’s next

Next, you’ll practice identifying the rule for a sequence and use it to find the next numbers in the pattern.

Section 2

Sequences

Property

A counting pattern is a sequence. A counting sequence may count up or count down, following a specific rule.

Examples

The sequence 10,20,30,...10, 20, 30, ... counts up by tens. The next number is 4040.
The sequence 21,18,15,...21, 18, 15, ... counts down by threes. The next number is 1212.

Explanation

Think of a sequence as a number puzzle! It is simply a list of numbers that follows a secret rule. Your job as a math detective is to find that rule so you can figure out what numbers come next in the pattern.

Section 3

Digits

Property

Digits are the ten numerals we use to write all numbers: 0,1,2,3,4,5,6,7,8,90, 1, 2, 3, 4, 5, 6, 7, 8, 9.

Examples

The number 64,00064,000 is built using five different digits.
In the number 52815281, the very last digit is 11.

Explanation

Digits are the basic building blocks for every number you can imagine, just like letters are for the alphabet! We can use them to count how many digits are in a huge number or find the very last one, which is super handy.

Section 4

Reading Math

Property

The three dots (......) written after a sequence mean that the pattern continues without end, even though the numbers are not written.

Examples

The sequence 2,4,6,8,...2, 4, 6, 8, ... continues by adding two forever.
The counting numbers 1,2,3,4,5,...1, 2, 3, 4, 5, ... go on without end.

Explanation

Those three little dots are a math shortcut called an ellipsis! It’s a cool way of saying 'and so on, forever' without having to write an infinite list of numbers. It signals that the pattern you see keeps repeating endlessly.

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 3Current

    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 10

    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

📘 Sequences

New Concept

A counting pattern is a sequence.

What’s next

Next, you’ll practice identifying the rule for a sequence and use it to find the next numbers in the pattern.

Section 2

Sequences

Property

A counting pattern is a sequence. A counting sequence may count up or count down, following a specific rule.

Examples

The sequence 10,20,30,...10, 20, 30, ... counts up by tens. The next number is 4040.
The sequence 21,18,15,...21, 18, 15, ... counts down by threes. The next number is 1212.

Explanation

Think of a sequence as a number puzzle! It is simply a list of numbers that follows a secret rule. Your job as a math detective is to find that rule so you can figure out what numbers come next in the pattern.

Section 3

Digits

Property

Digits are the ten numerals we use to write all numbers: 0,1,2,3,4,5,6,7,8,90, 1, 2, 3, 4, 5, 6, 7, 8, 9.

Examples

The number 64,00064,000 is built using five different digits.
In the number 52815281, the very last digit is 11.

Explanation

Digits are the basic building blocks for every number you can imagine, just like letters are for the alphabet! We can use them to count how many digits are in a huge number or find the very last one, which is super handy.

Section 4

Reading Math

Property

The three dots (......) written after a sequence mean that the pattern continues without end, even though the numbers are not written.

Examples

The sequence 2,4,6,8,...2, 4, 6, 8, ... continues by adding two forever.
The counting numbers 1,2,3,4,5,...1, 2, 3, 4, 5, ... go on without end.

Explanation

Those three little dots are a math shortcut called an ellipsis! It’s a cool way of saying 'and so on, forever' without having to write an infinite list of numbers. It signals that the pattern you see keeps repeating endlessly.

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 3Current

    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 10

    Lesson 10: Even and Odd Numbers

  11. Lesson 11

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