Today's Number Talk
For a detailed description of the Number Talk procedure, please refer to the Number Talk Explanation. For this Number Talk, I am encouraging students to represent their thinking using an array model. For each task today, students shared their strategies with "someone new across the room." It was great to see students inspiring others to try new methods and it was equally as great to see students examining each other work for possible mistakes!
Task 1: 13 x 20
During the first task, some students decomposed both the 13 and the 20: 13 x 20 while others only decomposed the 13 to solve this problem. I loved watching students write out equations to represent their thinking!
Task 2: 26 x 40
Task 3: 260 x 4
For the final task, students quickly discovered that 26 x 40 = 260 x 4. Here, a student drew an array to represent 4(200 + 60): 260 x 4.
Throughout every number talk, I continually model student thinking on the board to inspire other students. This also requires students to use math words to explain their thinking instead of relying on a model to represent the math. As students solved each task, I wrote the answers on the board to encourage students to use prior tasks to solve the more complex tasks.
Goal & Introduction
For today's lesson, I created a Powerpoint Presentation: Lawn Service Presentation. I invited students to come up to the front carpet with their white boards. To begin, I introduced today's Goal: I can multiply a 2-digit number by a multiple of 10. I explained: For the past week, we've focused on solving single digit x multi-digit multiplication problems. Now, we are going to begin solving 2-digit x 2 digit problems! To begin with, we will be multiplying 2-digit numbers by multiples of 10.
Multiples of 10
First, let's review the multiples of 10. I then projected the next slide, Multiples of 10. Some students jumped right in, listing multiples while others looked a little confused. It didn't take them long to look at our math wall for help or to turn and talk with a partner. During this time, I walked around the classroom and observed students: Writing Multiples of 10. We discussed student findings and made a Class List of Multiples of 10.
We then moved on to the next slide, which was a picture of a Lawn. I asked students to turn and talk: What do you need to do to care for a lawn?
Lawn Care Services
In order to engage students in Math Practice 4 (Model with Mathematics), I wanted to provide them with a real-world problem, comparing lawn services. I showed the next slide, Lawn Care Service and explained: Dan and Pete both get paid to mow lawns. Pete always gets paid ten times as much as Dan. Turn and talk: Why would Pete get paid more? Students immediately pointed out to one another, "Pete's mowing package includes more," and "Dan mows the lawn quickly when Pete mows slowly."
Problem 1: Bar Diagram
I explained Problem 1: Let's say that Dan makes $3 per lawn. How much will each boy make after caring for 12 lawns? I wonder if we could make a bar diagram to show show how much more Pete makes than Dan. Students went right to work, creating bar diagrams on their white boards. here, I model a Bar Diagram on the board.
Problem 1: Calculations
Next, I asked students to turn and talk: What should we do next? After students had time to talk, I asked a volunteer to come up and explain her thoughts: Discussing What to Do Next. It was great to see students jumping in and solving this problem without hesitation. Next, we went over our calculations altogether: Solving Problem #1.
For the next problem, Problem 2, students worked even more independently. Most students found how much money Dan made by multiplying 5 x 36 and how much money Pete made by multiplying 36 x 50 (because 50 is 10 x as much as 5). Some students even used Decomposing! Students turned and shared their work when finished. We then discussed and I modeled the problem on the board.
With Problem 3, we followed the same process. Students multiplied 96 x 8 to find Dan's commission and 96 x 80 to find Pete's commission as Pete makes 10 times more than Dan. I loved hearing students make personal connections, "Wow, Pete is loaded!" or "I wouldn't mind being Pete!"
Picking math partners is always easy as I already have students placed in desk groups based upon behavior, abilities, and communication skills. Before students began working, I asked them to discuss how they would like to support each other today. I gave them many examples: Do you want to take turns talking out loud? Do you want to solve quietly and then check with each other? Or do you want to turn and talk anytime you get stuck? Students loved being able to develop a "game plan" with their partners!
Monitoring Student Understanding
Once students began working, I conferenced with every group. My goal was to support students by asking guiding questions. I also wanted to encourage students to construct viable arguments by using evidence to support their thinking (Math Practice 3).
All students were able to complete this page during this time. Here's a Completed Page.