##
* *Reflection: Student Grouping
Subtraction - Expanded Form - Section 2: Mini Lesson

**I work with the students who are on or above level prior to my re-teaching group** because it is the best use of student time overall. The re-teaching group demonstrated that they have not mastered their basic facts (2nd grade) so it is acceptable, at this time in the year, to have them work own 20 minutes of basic fact practice. Basic fact practice is a task that works very as homework, because everyone understands what to do, but now that they have had 1/2 a year in 3rd grade to continue to practice these facts, they should really have them mastered. Thus it's okay, on this occasion, to give them 20 minutes of what may appear to be busy work. I watch them to see who is still counting on their fingers and what other strategies they might be employing (filling out certain facts on the sheet first, looking for inverse problems, counting on by a certain number).

That said, I am clear with the students about what group they are in, and how they got there. (I made the decision based on the evidence of how the completed 2 digit subtraction problems when they did the temperature table (A Week of Winter) when they had a substitute). If they did not demonstrate successful 2 digit addition on the temperature table but still wish to sit at the carpet for the 3 digit group, they may do so. In real life we have to earn our way into groups, and if we don't meet the bar, sometimes we don't get a second chance. Fortunately, I'm in control of the mini real-world in my classroom. If they are motivated enough to want to try something that is either out of their level OR that they were unmotivated about the last time, I want to encourage that increased involvement, not shut them down. Making groups exclusive is not only punitive; it can also affect how they feel about math. I did poorly on a beginning of the year test in 5^{th}grade and I spent the rest of the year watching the “high” group over the partition because I’d already completed my assignment. We don’t do that anymore, but I think it’s good to be careful even on a day to day level. I also have to be honest with myself about the fact that sometimes I’m annoyed with the children who rushed through an assignment and that’s why they didn’t do well, but I have to be very aware of how that gets expressed.

*Avoid Rigid Grouping*

*Student Grouping: Avoid Rigid Grouping*

# Subtraction - Expanded Form

Lesson 3 of 8

## Objective: Students will demonstrate understanding of regrouping by using expanded number forms in subtraction problems.

*57 minutes*

#### Opener

*7 min*

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.

Example:

807 = 800 + 7

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

#### Resources

*expand content*

#### Mini Lesson

*15 min*

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 3 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.

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#### Active Engagement

*25 min*

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 ona whiteboard or passed out. I did create these problems to specifically test out 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 I student places themselves 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).

*expand content*

#### Wrap up

*10 min*

I place students into teams of 3 or 4 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.

*expand content*

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- UNIT 1: 1st Week: Getting to Know Each Other Through Graphs
- UNIT 2: Addition and Subtraction
- UNIT 3: Multiplication
- UNIT 4: Introduction to Basic Division
- UNIT 5: Division in Context
- UNIT 6: Time
- UNIT 7: Rounding
- UNIT 8: Place Value Practice
- UNIT 9: Fractions
- UNIT 10: Math and Me: Nutrition, Health and More
- UNIT 11: Geometry in Architecture
- UNIT 12: Time Cycle 2
- UNIT 13: Patterns in Math
- UNIT 14: Area and Perimeter
- UNIT 15: Solving Mult-Step Word Problems Using the Four Operations
- UNIT 16: Musical Fractions
- UNIT 17: Volcanoes (Data Collection, Graphs, Addition & Subtraction)

- LESSON 1: Addition - Expanded Form
- LESSON 2: Switching to Subtraction
- LESSON 3: Subtraction - Expanded Form
- LESSON 4: Equal & Opposite Change Model of Addition
- LESSON 5: Everyone Try It! (Equal & Opposite Change)
- LESSON 6: Subtraction - The Equal Change Algorithm- It's Fun!
- LESSON 7: Subtraction - Equal Change- Stations (1)
- LESSON 8: Subtraction - Equal Change - Stations (2)