In today's lesson, the students learn to use objects to help with reasoning in order to solve a problem. The objects are represented in the word problems, and they give the students a visual to help understand the concept. This aligns with 4.OA.A3 because the students solve multistep word problems posed with whole numbers and having whole-number answers using the four operations. If the students can master this skill, it will help them with future lessons on reasoning through problems by drawing out models.
To get the students started, I ask them a question. "How can you find half of a number?" I give the students a few minutes to think about the question. I take a few student responses. One student says, "See which two numbers make up 18. If you find that out, you will know how much to take away." Another student wanted to add on to what the first student said. He added, "You divide by 2." I let the students know that we will use objects to help reason the answer. For example, what if you have a total of 18 pencils? Half of them are red, 3 of them are yellow, and the rest are blue. How many pencils are blue? Let's find out.
I call the students to the carpet as we prepare for a whole class discussion. The Use Objects and Reasoning power point is already up on the Smart board. I like for my students to be near so that I can have their full attention while I'm at the Smart board.
I begin by going over important vocabulary for this lesson. The students will have to know this term to understand the lesson.
Reasoning - The ability of the mind to think and understand things in a logical way.
I go back to the scenario that I posed earlier for the students about the pencils.
If you have a total of 18 pencils. Half of them are red, 3 of them are yellow, and the rest are blue. How many pencils are blue?
Let’s find out.
You know that there are a total of 18 pencils.
What is half of 18?
9 + 3 + ___ = 18
The solution is there are 6 blue pencils.
I give the students practice on this skill by letting them work together. I find that collaborative learning is vital to the success of students. Students learn from each other by justifying their answers and critiquing the reasoning of others (MP3).
For this activity, I put the students in groups of 3. I give each group a Group Activity Sheet Use Objects and Reasoning.docx. The students must decontextualize the problem and represent them symbolically (MP2). The students must work together to find the solution to the problems. They must model the problem by drawing out the objects (MP4). This is evident in the Student Work. You can see where the students drew out the problem with objects, as well as used calculations to solve the problem. They must communicate precisely to others within their groups (MP6). They must use clear definitions and terminology as they precisely discuss this problem (MP1).
The students are guided to the conceptual understanding through questioning by their classmates, as well as by me. The students communicate with each other and must agree upon the answer to the problem. Because the students must agree upon the answer, this will take discussion, critiquing, and justifying of answers by both students (MP3). As the groups discuss the problem, they must be precise in their communication within their groups using the appropriate math terminology for this skill (MP6). As I walk around, I am listening for the students to use "talk" that will lead to the answer. I am holding the students accountable for their own learning.
As they work, I monitor and assess their progression of understanding through questioning.
1. What information does the problem give you?
2. What did the problem ask you to find?
3. Does you model represent the information in the problem?
As I walked around the classroom, I heard the students communicate with each other about the assignment. From the Video, you can hear the classroom chatter and constant discussion among the students. Before Common Core, I thought that a quiet class working out of the book was the ideal class. Now, I am amazed at some of the conversation going on in the classroom between the students. As I walked around the room, I heard a lot of discussion. I heard the students trying to convince their partner that their answer was correct. I always tell my students that they must justify their answer by referring back to the problem. I heard a student say, "Oh, now I get what you're saying." This was great especially since the information she understood was correct.
To close the lesson, I have one or two students share their answers. This gives those students who still do not understand another opportunity to learn it. I like to use my document camera to show the students' work during this time. Some students do not understand what is being said, but understand clearly when the work is put up for them to see.
I feel that by closing each of my lessons by having students share their work is very important to the success of the lesson. Students need to see good work samples, as well as work that may have incorrect information. More than one student may have had the same misconception. During the closing of the lesson, all misconceptions that were spotted during the group activity will be addressed whole class.
There were a few students who struggled with solving the problem. From this sample of Incorrect Student Work, you can see that the pair did not understand the phrase"2 times as a many" to find the number of triangles for problem 1 on the Group Activity Sheet Use Objects and Reasoning. During the closing of the lesson, the meaning of "2 times as many" is addressed. This phrase has been discussed in class before, but still I see that there are some students who do not know how to apply it in context.