Standard algorithm addition

Here you will learn about what standard algorithm addition is and how to solve addition equations using the standard algorithm.

Students will first learn about standard algorithm addition as a part of number and operations in base ten in 4 th grade.

What is standard algorithm addition?

Standard algorithm addition (traditional algorithm) is a method of adding two or more numbers, typically taught in elementary school. The standard algorithm for math involves adding numbers that are aligned vertically, column by column.

For example,

To perform the standard algorithm, add the two addends, starting at the smallest place value.

For example,

begin adding at the ones place, regrouping as needed.

Then move to the tens place, adding and regrouping as needed.

And finally, add the hundreds place, regrouping as needed.

What is standard algorithm addition?

Common Core State Standards

How does this relate to 4 th grade math?

• Grade 4: Number and Operations in Base Ten (4.NBT.B.4)
  Fluently add and subtract multi-digit whole numbers using the standard algorithm.

How to use standard algorithm addition

In order to add using the standard algorithm:

1. Line up numbers vertically by place value.
2. Start adding with the smallest place value present, regrouping as needed.
3. Continue to add each place value, regrouping as needed.

Standard algorithm addition examples

Example 1: adding 2-digit numbers

Add the following numbers:

1. Line up numbers vertically by place value.

Line the numbers up by place value, making sure the ones and tens place are correctly aligned.

2Start adding with the smallest place value present, regrouping as needed.

The smallest place value is the ones place, so add 6+3=9. Place the 9 under the answer line in the ones place.

3Continue to add each place value, regrouping as needed.

The tens place is the last present place value, so add 2+3=5. Place the 5 under the answer line in the tens place.

Example 2: 3-digit addition

Add the following numbers:

Line up numbers vertically by place value.

Line the numbers up by place value, making sure the ones, tens and hundreds place are correctly aligned.

Start adding with the smallest place value present, regrouping as needed.

The smallest place value is the ones place, so add 9+6=15. Place the 5 under the answer line in the ones place and regroup the ten.

Continue to add each place value, regrouping as needed.

Next, add the digits in the tens place. Add 5+0+1=6. Place the 6 under the answer line in the tens place.

Add the digits in the hundreds place, 2+5=7. Place the 7 under the answer line in the hundreds place.

259+506=765

Example 3: 3-digit addition

Add the following numbers:

Line up numbers vertically by place value.

Line the numbers up by place value, making sure the ones, tens and hundreds place are correctly aligned.

Start adding with the smallest place value present, regrouping as needed.

The smallest place value is the ones place, so add 9+8=17. Place the 7 under the answer line in the ones place and regroup the ten.

Continue to add each place value, regrouping as needed.

Next, add the digits in the tens place. Add 5+0+1=6. Place the 6 under the answer line in the tens place.

Add the digits in the hundreds place, 3+7=10. Place a zero in the hundreds place, and regroup the one in the thousands place.

Add any remaining digits in the thousands place, 1+0=1. Place the 1 under the answer line in the thousands place.

308+759=1,067

Example 4: multi-digit addition

Add the following numbers:

Line up numbers vertically by place value.

Line the numbers up by place value, making sure all place values are correctly aligned.

Start adding with the smallest place value present, regrouping as needed.

The smallest place value is the ones place, so add 1+8=9. Place the 9 under the answer line in the ones place.

Continue to add each place value, regrouping as needed.

Next, add the digits in the tens place. Add 3+3=6. Place the 6 under the answer line in the tens place.

Next, add the digits in the hundreds place. Add 5+2=7. Place the 7 under the answer line in the hundreds place.

Add the digits in the thousands place. Add 4+6=10. Place the 0 under the answer line in the thousands place, and regroup the 1 to the ten thousands place.

Add any remaining digits in the ten thousands place, 1+0=1. Place the 1 under the answer line in the ten thousands place.

4,538+6,231=10,769

Example 5: multi-digit addition

Add the following numbers:

Line up numbers vertically by place value.

Line the numbers up by place value, making sure all place values are correctly aligned.

Start adding with the smallest place value present, regrouping as needed.

The smallest place value is the ones place, so add 5+3=8. Place the 8 under the answer line in the ones place.

Continue to add each place value, regrouping as needed.

Next, add the digits in the tens place. Add 2+7=9. Place the 9 under the answer line in the tens place.

Next, add the digits in the hundreds place. Add 4+3=7. Place the 7 under the answer line in the hundreds place.

Add the digits in the thousands place. Add 5+6=11. Place the 1 under the answer line in the thousands place, and regroup the 1 to the ten thousands place.

Add any remaining digits in the ten thousands place, 1+0=1. Place the 1 under the answer line in the ten thousands place.

6,425+5,373=11,789

Example 6: addition word problem

An apple farmer harvested 37,491 apples on Tuesday, 26,081 on Wednesday, and 30,077 on Thursday. How many apples did he harvest on Tuesday and Thursday?

Line up numbers vertically by place value.

The question asks for the total number of apples on Tuesday and Thursday, so you will add 37,491 and 30,077.

Line the numbers up by place value, making sure all place values are correctly aligned.

Start adding with the smallest place value present, regrouping as needed.

The smallest place value is the ones place, so add 1+7=8. Place the 8 under the answer line in the ones place.

Continue to add each place value, regrouping as needed.

Next, add the digits in the tens place. Add 9+7=16. Place the 6 under the answer line in the tens place and regroup the 1 to the hundreds place.

Next, add the digits in the hundreds place. Add 4+0+1=5. Place the 5 under the answer line in the hundreds place.

Add the digits in the thousands place. Add 7+0=7. Place the 7 under the answer line in the thousands place.

Add the remaining digits in the ten thousands place, 3+3=6. Place the 6 under the answer line in the ten thousands place.

37,491+30,077=67,568

The farmer harvests 67,568 apples on Tuesday and Thursday.

Teaching tips for standard algorithm addition

• Printable worksheets are an easy way to provide practice addition problems to students. Consider finding a way to make completing these worksheets more interactive, like placing different practice problems around the classroom to allow for students to move about and discuss the process.

• Use of visuals when first teaching addition, such as number lines and manipulatives, before introducing the standard algorithm.

• When introducing the standard addition algorithm, begin with smaller numbers, such as two-digit by single-digit numbers, before moving students on to larger numbers.

Easy mistakes to make

• Not aligning the digits by place value
  It is important that students align digits by their place value. Not doing so can result in errors in calculations. This tends to happen when the numbers students are adding have a different number of digits. For example,
  
  

• Forgetting to regroup or regrouping to the wrong place value
  When adding digits that add up to greater than 10, students will need to regroup to the next place value. Forgetting to add these digits when adding up the digits will result in incorrect answers.

Related addition and subtraction lessons

• Addition and subtraction
• Adding and subtracting integers
• Adding and subtracting rational numbers
• Adding and subtracting negative numbers

The next lessons are

• Multiplication and division
• Types of numbers
• Rounding numbers

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