Multi-Digit Whole Number Addition

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Children begin adding and subtracting in kindergarten and gradually build their understanding through the first three grades. In the fourth grade, they’re already starting to employ the standard addition algorithm to accurately and quickly add multi-digit whole numbers.

If you’re a teacher, you may be wondering how to best guide your students toward mastery of multi-digit whole number addition. To help you out, we’ve compiled a list of tips in this article. Read on to find out more.

What Is Multi-Digit Whole Number Addition?

For starters, explain to students what multi-digit whole number addition means. You can simply say something like:

“Along with subtraction, multiplication, and division, addition is one of the four basic arithmetic operations. Multi-digit whole number addition simply means adding two (or more) numbers that contain several digits and are whole (i.e. they’re not decimals, fractions, or negative integers). For instance, 4,874 + 7,329.”

How to Teach Multi-Digit Whole Number Addition

Review Place Value

After having mastered the concept of place value, 4th graders should start using it to fluently add multi-digit whole numbers using the standard addition algorithm.

Even though place value is something they’ve already learned, it’s always wise to check up on their place value understanding and address potential gaps.

Bell-work Activity

You can review place value through a small exercise, such as this playful bell-work activity (Members Only). Print out sheets for each student and hand them out. Each sheet contains a multi-digit number with instructions to follow.

For example, if the multi-digit number is 649,281, you can ask children to draw a heart around the digit in the ten thousand place, a circle around the digit in the ones place, etc.

Number Word Form, Expanded Form, and Notation

Check children’s place value understanding by briefly reviewing the word form, expanded form, and expanded notation of multi-digit numbers. For instance, write a multi-digit number on the whiteboard, such as 5,315. Children should then explain that:

Its word form is five thousand, three hundred fifteen
Its expanded form is 5,000 + 300 + 10 + 5
Its expanded notation is (5×1,000)+(3×100)+(1×10)+(5×1)

Place Value Chart

Finally, brush up on students’ place value knowledge with the help of a place value chart. Create a place value chart on the whiteboard and ask children to put a given multi-digit number in the chart.

For example, ask them to put the number 53,487 in the place value chart. The five should go in the ten thousands place, the 3 in the thousands place, the 4 in the hundreds place, the 8 in the tens place, and the 7 in the ones place. In other words:

Hundred thousands	Ten thousands	Thousands	Hundreds	Tens	Ones
5	3	4	8	7

Practice this with a few more multi-digit numbers until you’re sure everyone is comfortable with place value charts. It’s important to highlight that each number can only have one digit per place value column.

Standard Addition Algorithm

Then, use the place value chart to introduce multi-digit whole number addition. You can give a math problem to your students concerning multi-digit whole number addition with the separate numbers, for instance, 3,419 + 1,322, and ask them to place both of the numbers in the place value chart. In other words:

Hundred thousands	Ten thousands	Thousands	Hundreds	Tens	Ones
3	4	1	9
1	3	2	2

Then, remove the place value chart and show students how the math problem can be presented vertically with each digit under a digit with the same place value. Each place value should be aligned directly above and below each other:

3,419

+1,322
_________
4,741

Explain to students that this is the standard addition algorithm and this is what they should use for adding multi-digit whole numbers. Now explain that, in math, we always start adding from the right to the left place value, starting with the ones place value.

Point out that by adding the 9 and the 2, we end up with 11, which we can’t write as eleven, but only as one (remind students that each number can only have one digit per one place value column). That means that we’ll “carry” our extra one in the next place value – the tens place value, that is, 1+2 = 3; 3+1=4.

Multi-Digit Whole Number Addition Activity

Use a fun activity to practice adding multi-digit whole numbers. Print out page 1 from this Assignment Worksheet (Members Only) and make sure you have 2 copies per student. Bring a sufficient number of dice, depending on how many students you have in the class, as you’ll need two dice per group.

This activity can also work if you’re a homeschooling parent, You can easily adjust it by having your other child or even yourself join in as the second player.

Now launch the activity!

Divide students into pairs of two.
Tell them that you’re going to play a small game to hone their knowledge of multi-digit whole number addition.
Hand out the worksheet copies to them, as well as the dice.
Explain the instructions for the game: each player rolls the dice and writes down the numbers they get in the boxes in their worksheet (one digit per box). Then they roll the dice a few more times until they’ve filled all eight boxes on their worksheet.
Then, the other player repeats this process and fills in each of their eight boxes with numbers.
The two players add the two four-digit numbers they have on their sheet. The player with the largest number wins this round.
In the next round, encourage children to further use their understanding of place value, by telling them to put the numbers in the boxes strategically, so that they end up with the biggest answer in the end.
The students repeat the process of rolling the dice and filling out the boxes by using the second set of worksheets for this round.
The player that has the biggest answer wins this round.

Race to the Sum Game

You can include this game in your classroom to make multi-digit whole number addition both fun and competitive! The prep work might be a bit demanding as you’ll need to acquire a few things in advance, but it really pays off in the end!

Prepare for this game by getting magnetic mini-whiteboards for students, round magnets, and round sticker labels. The number of mini-whiteboards, round magnets, and sticker labels will depend on the number of students in your class. Just make sure there’s one mini-whiteboard per student.

The sticker labels should come in different colors to make the game more visually appealing. The round stickers are placed on the magnets so make sure they’re the same size or use scissors to adjust them.

Write a single-digit number on the round sticker of each magnet (0-9). It’s okay if each number repeats three or four times. Finally, get several timers.

Start playing!

Divide students into pairs of two.
Hand out the mini-whiteboards to each student, and place the magnets on the table. Make sure that the magnets are face down, that is, that children can’t see the numbers on them.
Place a timer on each table, that is, one per pair.
Explain the rules of the game to students, as well as the objective of the game.
Each student should randomly pick 15 magnets from the pile of magnets and use them to create a correct multi-digit addition equation.
After children have picked 15 numbers, they set the timer for two or three minutes (you can adjust the time if more time is needed) and start playing.
It is necessary that they create an addition equation that consists of two four-digit numbers that are being added, though the sum can of course contain more digits.
Explain to children that it’s okay if they don’t use up all the number magnets they selected – as long as they managed to create a correct equation with two four-digit numbers.
For instance, if a student selects three 3s, one 5, three 6s, one 4, two 2s, one 8, and one 9, they can create the following addition equation: 3,564 + 2,832 = 6,396.
After the time is up, they share their equations and check their results.
Then, they count how many points they received in that round. Each player gets two points for creating a correct addition equation and one bonus point for using up all of their number magnets (alternatively, one bonus point is given to the player that managed to use up more magnets).
Play as many rounds as time allows. In the end, the player that ends up with the most points in each pair wins the game.

Before You Leave…

This article outlines a few useful tips for how to teach multi-digit whole number addition to students in the 4th grade. If you liked these tips and you’re interested in more math resources for children of all ages, sign up today at MathTeacherCoach or check out our blog – you’ll find plenty of materials that will make your teaching easier than ever!

This article is based on:

Unit 2 – Multi-Digit Whole Number Addition and Subtraction