Adding 3 Digits to 3 Digits Using Expanded Form

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Students will be able to write and add numbers in expanded notation.

Big Idea

Decomposing a large number into its expanded form is helpful in strengthening one's mental math ability. This lesson is designed to give the students practice in using this important strategy.


10 minutes

To begin the lesson, explain to the students that there is a strategy for adding large numbers that uses expanded notation.  This strategy can help them improve their mental math ability and is a great way to keep their work organized. 

Then, place an addition problem on the board. Mine is:

Ms. Marcus had 167 papers to check and Mr. Peters had 295 papers to check.  How many papers did they need to check over the weekend?

Walk through the steps appropriate for your class.  For mine, I ask them to talk with their partner about what we are looking for, what type of problem this is, and what their strategy would be.

Then, I explain that I like to group things together and the expanded notation (form) strategy really helps me stay organized.  I put my thinking on the board. 

167 = 100 + 60 + 7

295 = 200 + 90 + 5

300 + 150 + 12

450 + 12


I ask them to discuss why this makes sense or if there is anything that is confusing. You may want to place the digits in Place Value houses in order to help the students visualize the expanded notation strategy.

We then work through 2 or 3 examples as a class, with the students working on their white boards while I circulate to look at their work and ask probing questions, such as:

Why did you expand - take apart - the number this way? 

What are you expanding - separating - in this number?

Active Enagagement

30 minutes

In order to practice, I give the students several addition problems and ask them to use their white boards to solve using the expanded notation method.  As they work with their partners, I listen for vocabulary terms, the types of questions they ask each other, and how they explain their thinking. 

As each student finishes one card, they share their strategy with their partner and then drew another problem from the deck.  These cards came from a set of problems on the K-5 Math Teaching Resources website, and are attached in the resource section here. 

This student asks for some help with the ones place.  We talk through what each number means, and end up mentally adding the tens and then the remaining ones. 

For the same problem, this child works through it a little differently and formally wrote the addition of all of the tens and then the ones. 


10 minutes

As an exit ticket, I have the students complete one of the cards from the deck on an index card and share their solution with two people in the room. The students will initial each other's card and then the cards will be turned in to me. 

Tomorrow we will journal about this strategy and discuss how it is helpful in different mathematical situations.