I begin this lesson by asking 3 girls and 4 boys to stand in front of the class.
What do you know about the number of students in front of the room? After the students return to their seats, I have the class turn and talk about the things they noticed. If necessary, I help by guiding those students who aren't sure where to begin to look at the number of girls and number of boys.
Think about how many students there are in all. How do you know?
Now I'm moving students to think about this more abstractly by asking students to think about how they could represent the information about the parts of the whole group of students who stood in front of the room.
I begin by demonstrating the part/part/whole model, drawing 3 squares to represent the girls in one part and 4 squares in the other part to represent the boys. I ask the students to turn and talk, thinking about if there is a number sentence they could use to represent the part, part, and the whole group of girls and boys at the front of the room. I am asking them to think of quantities (boys, girls, altogether) and relationships between those quantities and make sense of this using a representation, or model (MP1 & MP4).
Part-whole instruction is drawing students' attention specifically to the parts and the relationship of the parts to the whole. Students need many of these experiences to develop the flexibility of understanding that allows them to understand that 10 can be composed as 5 + 5, but it can also be composed of 6 + 1. With this understanding, students will be able to manipulate numbers, with understanding, when adding and subtracting, and later when multiplying and dividing.
Using a Part/Part/Whole Mat, have the students build the part 6 cubes with one color and the part 3 cubes with another color. Have the students work in partners to place the cubes in the correct spot on the model. Have the students then write a number sentence to represent the model. Can they find the whole?
At this time, introduce the vocabulary for this lesson:
Addends and Sum name the numbers in an addition problem.
Explain to the students that the two parts in an addition number sentence are called the addends. The whole in an addition problem is called the sum. I don't expect my students to know these words, but I will now begin to use them, in context and with specificity so that the students bring them into their own vocabulary.
The next step needs to done thoughtfully. It may seem obvious to us as adults, but it is more abstract for 2nd graders. I have the students switch the two parts on their part/part/whole mat. Looking at the part/part/whole model, have them turn and talk to discuss what has changed and what has stayed the same. Students should recognize that the addends have changed order, but the amount in all has stayed the same.
I teach my students a chant to help them remember: “No matter the order the addends are in, the sum remains the same. Cha Cha!”
The students should build several more examples using their part/part/whole mat and their connecting cubes. Have them practice writing addition number sentences for each model they create on their part/part/whole mat. I want to ensure that my students can demonstrate and explain their understanding (2.NBT.B.9). As the students are working, I circulate around the classroom, stopping to ask questions about the numbers that the students are building. Some of the questions I may ask are: "What are your two addends? How did you know which addend to build first? What if your partner really wanted to build the other addend first, how would that change your sum?"
The materials for this lesson include dominos, which may not be a math manipulative that is already in your classroom. I love them! Give each student a pile of 8 dominoes and the domino addition worksheet. I have found domino sets that have up to 18 dots on each side. You can differentiate based on the need of your students with these as well as the basic dominoes. Those who need more of a challenge can receive dominoes with more dots.
The students should use the halves of the dominoes to help them create a part/part/whole model. Once they have drawn the model, students will then write the addition number sentence that represents the model.
When students finish their independent work doing domino addition, they work in partners to share a few of their domino number sentences. The purpose of the partner discussion is that they discuss the parts and whole of the model. The partner share is also a means to occupy earlier finishers. Ideally, all students should have time to share with a partner, because this prepares them for the class share. As you circulate during independent work, you'll have identified those students who are struggling, and can work with them individually or in a small group. This way they too will have time to discuss, and make sense, of their work. Then come together as a class and choose a few students share their understandings.