In this Grade 4 Saxon Math lesson (Intermediate 4, Chapter 2, Lesson 17), students learn how to add columns of multiple numbers with regrouping when the ones column sums to 20 or more, carrying two or more tens into the tens column. The lesson covers multi-addend addition with two- and three-digit numbers, including how to properly align digits by place value before adding. Practice problems reinforce regrouping across the ones, tens, and hundreds places in real-world contexts.
Section 1
📘 Adding Columns of Numbers with Regrouping
When the sum of the digits in the ones column is 20 or more, we move a group of two or more tens to the tens column.
Next, you'll apply this regrouping skill to add columns of numbers and solve problems involving money.
Section 2
Regrouping Sums of 20 or More
When the sum of the digits in the ones column is 20 or more, we move a group of two or more tens to the tens column.
In , the ones column sum is . Write down the 2 and carry the 3 tens.
In , the ones column sum is . Write down the 7 and carry the 2 tens.
Adding , the ones sum is . Write the 1 and carry the 2 tens.
Imagine your ones column adds up to 32! That's not just one ten to carry, it's three whole tens and two leftover ones. So, you write down the 2 in the ones place and carry the entire group of 3 over to the tens column. This rule keeps your place values perfectly organized, no matter how big the sum gets.
Section 3
Lining Up by Place Value
To add whole numbers, you must line up the numbers vertically so that the rightmost digits are in the same column. This ensures you are adding ones to ones, tens to tens, and so on.
To solve , you must align the 7, 8, and 6 in the ones column.
To solve , you must align the 8, 6, and 5 in the ones column before adding.
Why start adding from the right? Because that's where the ones live! Adding them first tells you if you need to create a new ten to carry over. If you started from the left, you would have to constantly erase and fix your work every time you regrouped from the column to the right. Working right-to-left keeps your addition clean and accurate!
Section 4
Represent
Expanded form is a way of writing a number to show the value of each digit. It is shown as a sum of each digit multiplied by its matching place value. For example, 813 is written as .
Number 813 is written as and in words as 'eight hundred thirteen.'
Number 407 is written as and in words as 'four hundred seven.'
Adding in dollars, , can be seen as .
Think of expanded form as showing a number's secret recipe! The number 813 isn't just a random sequence; it's a combination of 8 hundreds, 1 ten, and 3 ones all mixed together. Expanded form breaks the number down into its core ingredients, showing you what each digit is truly worth based on its place value in the final number.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter
Expand to review the lesson summary and core properties.
Section 1
📘 Adding Columns of Numbers with Regrouping
When the sum of the digits in the ones column is 20 or more, we move a group of two or more tens to the tens column.
Next, you'll apply this regrouping skill to add columns of numbers and solve problems involving money.
Section 2
Regrouping Sums of 20 or More
When the sum of the digits in the ones column is 20 or more, we move a group of two or more tens to the tens column.
In , the ones column sum is . Write down the 2 and carry the 3 tens.
In , the ones column sum is . Write down the 7 and carry the 2 tens.
Adding , the ones sum is . Write the 1 and carry the 2 tens.
Imagine your ones column adds up to 32! That's not just one ten to carry, it's three whole tens and two leftover ones. So, you write down the 2 in the ones place and carry the entire group of 3 over to the tens column. This rule keeps your place values perfectly organized, no matter how big the sum gets.
Section 3
Lining Up by Place Value
To add whole numbers, you must line up the numbers vertically so that the rightmost digits are in the same column. This ensures you are adding ones to ones, tens to tens, and so on.
To solve , you must align the 7, 8, and 6 in the ones column.
To solve , you must align the 8, 6, and 5 in the ones column before adding.
Why start adding from the right? Because that's where the ones live! Adding them first tells you if you need to create a new ten to carry over. If you started from the left, you would have to constantly erase and fix your work every time you regrouped from the column to the right. Working right-to-left keeps your addition clean and accurate!
Section 4
Represent
Expanded form is a way of writing a number to show the value of each digit. It is shown as a sum of each digit multiplied by its matching place value. For example, 813 is written as .
Number 813 is written as and in words as 'eight hundred thirteen.'
Number 407 is written as and in words as 'four hundred seven.'
Adding in dollars, , can be seen as .
Think of expanded form as showing a number's secret recipe! The number 813 isn't just a random sequence; it's a combination of 8 hundreds, 1 ten, and 3 ones all mixed together. Expanded form breaks the number down into its core ingredients, showing you what each digit is truly worth based on its place value in the final number.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter