Students will use their whiteboards today to solve 37 x 49. For this warm up, students are allowed to use any of the methods practiced in the previous lesson. Once most students have finished, I ask a few students to share their solutions under the document camera. One goal of this warm up is for students to see all three strategies for this one problem. As students are working, I wander around the room making mental note of which students are using the various strategies and ask them to share out. The strategies I expect students to use at this time area model for multiplication and/or two variations of expanded notation methods.
In the photo below, "A" is the are model method. "B" and "C" are both versions expanded notation. You can see in method "C", students move towards more mental calculations and write less numbers when calculating partial products.
Students watch this video of one the school's food service employees giving them a problem to solve.
I then assign students to work in partners. I assign students based on what I have observed to be their current multiplication ability. I group students into mixed ability partnerships. I want the students that are firm in their understanding to be put into a position in which they can model and help their partner who may not be quite at the level of student one. When I assign groups, students are mixed ability, but close in ability. I do not place a very high student with a very low student. This pairing wouldn't be beneficial for either of them in this activity. From my experience, a drastic difference in ability can make both partners produce less quality work.
One of my classroom goals is to help students become better at solving problems, and to think of solving problems as a common, even exciting and engaging process. By using school staff members in math videos, this is one way I infuse this idea about problem solving being common, a part of "real" life and exciting. Another goal is to recognize and discuss with students the problem solving strategies that they use in their work. By giving students a rich task, I am able to do that. While students work, I am able to move to different student groups to add support if needed and question them about their thinking. Applying these techniques allows students to build their understanding of mathematical concepts while increasing the level of their confidence and their perseverance which embodies CCSS Math Practice Standard 1.
This lesson section also focuses on Math Practice standard 2. To develop students’ capacity to "reason abstractly and quantitatively" I need to guide students in understanding the relationships between problem scenarios and mathematical representation, as well as how the symbols represent strategies for solution. Students must make sense of what the numbers in the problem mean and what operations they may or must use in order to find a solution to this problem. While this problem may seem easy for adults, it is not so for fourth grade students. Many students need a solid 20 to 30 minutes to wrestle with this problem and make sense of what to do.
Below, you can see a sample of one student's work.
This is a video of two students talking about the problem and what they are going to do to solve this problem. You can hear the background noise in this video. This is what my classroom sounds like during this activity. There is a lot of talking, thinking, and then more talking.
Note: My food service chef was very nervous to do this, but I think it's important to let all staff members in a building know they are part of students' education. I prepared the script ahead of time with her using the number she chose. That way, when students ask if "this" is true, I can answer yes. It also helps students understand the amount of food students consume on a daily, weekly, and monthly basis and how much work that requires. I think videos like this help build in understanding and respect of all school community members while practicing math. It's a win win for everyone!
For this wrap up, I lead a brief class discussion about how groups solved this problem. I want students to see the various ways that they could have arrived at an answer for how many chicken nuggets are cooked for an entire month. Some students used repeated addition. This is important for all students to see. The students that used repeated addition can benefit from seeing the multiplication strategies, as well as the students who used multiplication can benefit from seeing another way to solve this problem and gain flexibility in their thinking.