Addition - Expanded Form

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Students will be able to demonstrate understanding of regrouping by using expanded number forms in addition problems.

Big Idea

Expanded form can help clear up confusion about regrouping.


7 minutes

This lesson relies on an understanding of expanded form so I go through this Expanded Form Mini Review with students.  If students do not understand how to write numbers in expanded form, stop and reteach it.  Do not proceed with this lesson.

Note: Some students may want to leave out the zeros that are place holders.  


807 = 800 + 7

For this lesson, they need to use the zeros as place holders:  807 = 800 + 0 + 7

Mini Lesson

15 minutes

It's important that they learn the correct procedure so the first examples we work through these simple guided examples together that have 2-digit numbers.  There are usually a few students who are struggling in general that might show confusion at this point and I look carefully to see if anyone else has lost there way and make note.  Then I move them to working through several guided examples of expanded form subtraction with 3-digit numbers.  I again provide them with a page which has the first step already completed.  This allows me to monitor them for conceptual understanding (does their regrouping make sense or is it random) instead of worrying about whether or not the error lies in the copying.  In this brief practice session, I look again for any addition students who are experiencing difficulty.

After we work through at least three examples of 3-digit subtraction, most of them return to their seats to work through examples on their own.  I will keep the students who are experiencing difficulty with me at the carpet.

Active Engagement

25 minutes

Students choose which problems they want to work on from the expanded form subtraction - independent practice equations I project on the board.  These can also be written on a whiteboard or passed out.  I did create these problems to specifically assess different skills (regrouping in the ones place only, the tens place only, not regrouping if unnecessary) but other problems could easily be substituted.

I monitor for appropriateness of choices but if a student places themself in a level of greater difficulty than I would have chosen for them, I confer with them more immediately and frequently than I might have otherwise, but I do not automatically "bump them down".  I admire and support students when they choose something difficult out of a genuine desire to learn and if they are willing to work through their difficulties, I see no issue with giving them extra support at a "higher" level rather than bumping them down to a lower level (for example, a student who's really struggling might be self-sufficient at the 2-digit level).

Wrap up

10 minutes

I place students into teams of three or four and ask them to work out a short demonstration in which they teach this procedure to a student or class that's unfamiliar with it.  If they want, one of the children in their group can act out the role of the student.