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.

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.

193+34=227

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.

36+23

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.

36+23=59

259+506

Line up numbers vertically by place value.

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

Continue to add each place value, regrouping as needed.

308+759

Line up numbers vertically by place value.

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

Continue to add each place value, regrouping as needed.

4,538+6,231

Line up numbers vertically by place value.

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

Continue to add each place value, regrouping as needed.

6,425+5,373

Line up numbers vertically by place value.

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

Continue to add each place value, regrouping as needed.

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.

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

Continue to add each place value, regrouping as needed.

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.

1. Solve: 77+62.

129

310

139

135

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

Start adding at the smallest place value, the ones place, and continue to add each place value, regrouping as needed.

77+62=139.

2. Solve: 405+378.

783

775

625

885

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

Start adding at the smallest place value, the ones place, and continue to add each place value, regrouping as needed.

405+378=783.

3. Solve: 914+597.

1,501

1,411

1,401

1,511

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

Start adding at the smallest place value, the ones place, and continue to add each place value, regrouping as needed.

914+597=1,511.

4. Solve: 1,103+2,716.

3,917

3,819

3,910

3,821

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

Start adding at the smallest place value, the ones place, and continue to add each place value, regrouping as needed.

1,103+2,716=3,819.

5. Solve: 9,062+7,859.

16,911

16,921

16,811

16,821

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

Start adding at the smallest place value, the ones place, and continue to add each place value, regrouping as needed.

9,062+7,859=16,921.

6. Kaleigh’s purchased a computer for \$1,976 and a new video game console for \$ 698. How much money did Kaleigh spend on the computer and video game console?

\$2,664 \$ 2,544

\$2,574 \$ 2,674

To find the total that Kaleigh spent, you should add \$1,976 and \$ 698 .

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

Start adding at the smallest place value, the ones place, and continue to add each place value, regrouping as needed.

1,976+698=2,674.

Kaleigh spent \\$ 2,674 on the computer and video game console.

Can the standard algorithm be used with any type of number?

Yes, the standard algorithm can be used for computations with any type of number, including whole numbers, decimals and fractions. The process remains the same, as long as you align the numbers properly.

Are there other addition strategies that can be used other than the standard algorithm?

Yes, there are other methods, including mental math strategies, partial sums, place value strategies and other visual methods.

Is there a difference between the addition algorithm and the subtraction algorithm?

While both addition and subtraction algorithms involve aligning numbers vertically and performing an operation on digits column by column, the addition algorithm is used for addition, and the subtraction algorithm is used for subtraction. The key difference lies in the specific operations performed at each step of the process.

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