##
* *Reflection: Developing a Conceptual Understanding
Put It All Together - Section 2: Develop the Concept

During this lesson I quickly learned that students had spent too much time working with the Part/Part/Whole model with subtraction. When they got to the problems of comparison, they knew to subtract (something they hadn't known before. Yay, progress!) but they continued to use the part/part/whole model instead of thinking about how they could use cubes or draw a comparison model.

I found that it was necessary to spend a bit more time with determining the difference between separating problems and comparison problems and why you can't use the part/part/whole model.

*Developing a Conceptual Understanding: Putting It All Together Reflection*

# Put It All Together

Lesson 7 of 7

## Objective: Students will be able to determine the correct mathematical operation for a word problem, write the number sentence, and solve the problem.

#### Activator and Materials

*10 min*

I begin this lesson by having the students turn and talk about the following question:

*“When you are working on a word problem, how do you know whether you should add or subtract?” *

Once the students have had ample time to turn and talk, I bring them back together to share their ideas. Sometimes they need some mental prompts, today I prompt them to think about things like key words and the big idea *“Does it make sense?”*

Key words are charted, and displayed in the classroom. My expectation is that students check these charts independently, but when and if needed, I can prompt them to do so without interrupting using a physical cue such as nodding toward the chart, or pointing.

At this point of the year, the key words are mostly those learned in 1st grade:

- all together
- together
- in all
- add
- difference
- take away
- left
- fewer than
- subtract

In my classroom we spend a great amount of time, in all curriculum areas, thinking about the big question, *“Does it make sense?”* Often when we work on word problems, I “accidentally” choose the wrong operation. As result, students follow me more closely, now that they know they have a chance to "correct" the teacher's work! When they wonder if it is the incorrect operation (and perhaps I did pick the correct one, but they are confused), we are ready to have a discussion about whether or not a choice makes sense.

#### Resources

*expand content*

#### Develop the Concept

*25 min*

I have the students use their individual whiteboards or they could use a Part/Part/Whole Mat and connecting cubes, to follow along with the Putting It All Together Power Point. I model at least the first word problem but if I think students need more, I'll go on to do the next problem with the students. It is important that I engage the students in participating in the modeling. I do this by choral reading the problem, asking the students to think (often they do this with a partner) and then choose the word problem type (Joining, Separating, or Comparison) and then the operation (addition or subtraction).

Here's what it looks like. First we sing. We do a lot of singing in my classroom. For this lesson students are using the Are You Adding or Subtracting Song. It is a terrific warm up for our work, and it can also be used at any point throughout the day (e.g., during transitions) so that students learn it by memory.

To begin the first problem, after we've read it together I have the students turn and talk to a neighbor to share the type of word problem it is, what information they know, and which operation they would use to solve that problem. Based on their decision, if the word problem is a joining or separating word problem they should draw a part/part/whole model on their whiteboard and fill in the information that they know. Then they should write the corresponding number sentence and solve.

Today’s lesson is challenging. It demands that students look for, and make use of, the structure of the relationship between addition and subtraction (MP7). Students will be reasoning through the configuration of part/part/whole in both addition and subtraction problems, such as 7 + 2 = 9 can be thought of as 9 – 7 = 2, but could also be thought of as 9 – 2 = 7.

*expand content*

#### Practice the Concept

*20 min*

As students work independently to solve the problems in the rest of the PowerPoint, I am circulating and checking in with them. You may need to create a small group to support some students as they solve each problem, then circulate.

It is important that students are encouraged and supported in working independently. Sometimes they struggle, but I hold off on helping unless they are stuck. In order to learn, students need to develop their own mathematical reasoning. If necessary, I'll ask questions to get them pointed in the right direction:

What does subtraction mean to you?

What does addition mean to you?

What happens if ________?

What is the relationship of the quantities? How many parts? How many wholes?

What does this number represent? The whole? A part?

As students finish, they are challenged to create their own word problem in their math notebook, and give it problem to a friend (who has also finished) to have them solve.

*expand content*

#### Summarizer

*10 min*

When the students come back together as a class to discuss their work, it is an important opportunity for them to use their mathematical vocabulary in context. So to begin, I encourage students to turn and talk about the relationship between the parts and the whole, and how they create addition and subtraction problems, and how those problems differ from comparison word problems.

I remind them of our math vocabulary wall, where the words that they should be using today are available to check. Some of the words I expect to hear today are *whole, part, add, subtract, fact family, join, separate, compare, as well as the phrases "same as", "different than*".

After students have had time to practice their thinking, partners explain the word problems they created with the class and show how they solved it on the board.

*expand content*

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- LESSON 1: The Recipe for a Great Word Problem
- LESSON 2: Domino Addition: Understanding the Part/Part/Whole Relationship
- LESSON 3: Addition in the Real World
- LESSON 4: Much Much More Than Take Away
- LESSON 5: I've Got More Than You
- LESSON 6: We Are All a Happy Fact Family
- LESSON 7: Put It All Together