##
* *Reflection: Problem-based Approaches
Adding Three-Digit Numbers with Regrouping - Section 1: Problem of the Day

Prior to this lesson few of my students had seen three digit addition problems that require regrouping. Despite this, I chose to let them puzzle with a problem of the day instead of simply giving them a strategy and having them mimic my strategy. When I presented this problem I saw students respond in a variety of different ways:

1) Students drew hundreds, tens, and ones or used hundreds, tens, and ones blocks to represent the problem.

2) Students drew an open number line.

3) Students used cubes bundled in groups of tens to solve.

4) Students used invented algorithms (i.e: 100 + 30 + 200 + 29 or 30 + 30 + 100 + 199=)

5) Some students dove right into regrouping and solved the problem using the same kind of regrouping strategies that we had discussed when we learned about adding two digit numbers together.

Allowing students to solve this problem in creative ways allowed students to problem solve and begin to develop a conceptual understanding of how to solve these more advanced problems. Further, it allowed students with various levels of mathematical confidence/understanding to access this problem and understand what they were doing (i.e: my students who struggle more used cubes bundled into groups of tens to solve instead of being "forced" to learn the trick of regrouping , a concept that they might not understand right now.) Allowing students to use a strategy that works for them allows them to accurately solve these kinds of problems and attend to precision (MP6).

*Problem of the day*

*Problem-based Approaches: Problem of the day*

# Adding Three-Digit Numbers with Regrouping

Lesson 3 of 13

## Objective: SWBAT add three-digit numbers that require regrouping.

#### Problem of the Day

*5 min*

I write a problem of the day on the board:

**135+ 229= **

Have students work on their white boards or in their notebooks to solve the problem. I provide students with hundreds, tens, and ones blocks as well as cube manipulatives to use if they want.

Some students may solve this problem by using hundreds, tens, and ones. Others may solve the problem using an open number line or by using an invented algorithm (i.e: 100 + 30 + 200 + 29). Others may use column addition and regroup. Any strategy that yields an accurate answer is appropriate.

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#### Introduction to New Material

*10 min*

**Turn and talk: What did you do to solve this problem?**

After giving students a few minutes to work, I ask two or three students to share the strategies that they used.

Students should be able to discuss how they regrouped and made a new ten. Some students may have drawn hundreds, tens, and ones. If the lowest students are struggling, have one student model how they drew hundreds, tens, and ones to solve this problem.

**I give students another problem of the day: 134+ 182=**

Have students work on their white boards to solve this problem.

**Turn and Talk: What did you do to solve this problem? **

It is important in this discussion for students to understand that they regrouped to make another hundred. If necessary this can be illustrated by drawing tens and ones or by using cubes or place value blocks to model.

NOTE: In the first problem of the day, students are required to regroup in the tens place. In the second problem of the day, students are required to regroup into the hundreds place. This is a new skill for some students--however if students use hundreds, tens, and ones, they will see that regrouping into the hundreds is a similar skill to regrouping into the tens place.

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#### Guided Practice

*10 min*

I divide students into heterogenous groups of two or three. I give each group one white board (or ask them to come up to the board). I write a three-digit number sentence on each board. One member of the team will use the marker to solve the problem while the others will "coach" that teammate.

After one teammate has gone, leave time for feedback and rotate through the rest of the children in each group so that everyone has a chance to be "coached' by their teammates.

Before starting, I talk briefly about good ways to coach like giving friendly tips, saying "I liked the way that you...", "Make sure that you..." or "Next time you should..." If students do not have a lot of practice coaching each other it is important to give them sentence stems so that their coaching is meaningful. Before starting this activity you can model what good coaching looks like by having a student coach you using the sentence stems or by having a student coach another student in front of the class. Student coaching can be a powerful way to increase achievement and improve accuracy but students need practice to be effective coaches. (MP6)

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#### Independent Practice

*10 min*

Independent practice is differentiated based on proficiency with this concept (for this skill, err on the side of putting students in lower groups so that they can get enough practice and conceptually understand what regrouping into the hundreds place means).

While students work, I will circulate, starting with group A, then moving to group B, and finally group C.

**Group A: In need of intervention**

Students will work on a worksheet that requires regrouping from the ones to the tens (numbers 100-200). This group will be encouraged to draw hundreds, tens, and ones or use cubes bundled into groups of ten so that they get practice understanding the process of regrouping.

**Group B: **

Students will work on a worksheet that requires regrouping from the ones to the tens OR the tens to the hundreds (numbers 100-400). This group will be encouraged to draw hundreds, tens, and ones OR to regroup.

**Group C: **

Students will work on a worksheet with numbers 100-800 that requires regrouping from the ones to the tens OR the tens to the hundreds (no regrouping into the thousands). This group will be encouraged to regroup or draw hundreds, tens, and ones.

#### Resources

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#### Closing

*10 min*

I bring the students back to the rug.

*Today we learned how to regroup with numbers in the hundreds. I would like for one of you to model how you solved a problem.*

I pick a problem off the worksheet and ask student to model his/her strategy and thinking.

*Tomorrow, we will work on word problems that use numbers in the hundreds! *

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- LESSON 1: What is One Hundred More? What is One Hundred Less?
- LESSON 2: Adding Three-Digit Numbers Without Regrouping
- LESSON 3: Adding Three-Digit Numbers with Regrouping
- LESSON 4: Adding Four Three-Digit Numbers
- LESSON 5: Our Strategies for Result Unknown Problems
- LESSON 6: Two-Step Word Problems (Result Unknown)
- LESSON 7: Solving Result Unknown Problems with Three-digit Numbers.
- LESSON 8: Introduction to Change Unknown Problems
- LESSON 9: How do I solve a change unknown word problem?
- LESSON 10: Acting out Change Unknown Problems
- LESSON 11: Change Unknown Word Problems
- LESSON 12: Change Unknown Word Problems with Number Lines
- LESSON 13: Subtracting Across Zeros