Today's Number Talk
For a detailed description of the Number Talk procedure, please refer to the Number Talk Explanation.
Task 1: 2 x 18
For today's Number Talk, I asked team leaders to pass out the Number Line Model to help students show their thinking later on. For the first task, 2 x 18, students showed their work using multiple strategies, including Halving 18 and Doubling 4.
Task 2: 18 x 4
During the next task, we discussed 18 x 4. I loved hearing the various strategies students used. One student one student explained how you can either Decompose the 18 or the 4. Either way, you'll get the same answer. This student showed how she experimented with Decomposing 18 to find 18 x 4.
Note: This lesson was inspired by the Georgia CCGPS 4th Grade Measurement Unit, p. 86.
Prior to today's lesson, I projected and traced a picture of a water balloon package on the whiteboard. I also added: Balloon Capacity: 300 mL. I wanted to provided students with a high-interest problem that provided them with the opportunity to model with mathematics (Math Practice 4).
To begin the lesson, I introduced the goal as well as the water balloon problem: Goal & Problem. I explained: We have learned a lot about milliliters and liters. Today is the day that you get to use this information to solve real-world problems about water balloons! Turn & Talk: Tell someone next to you about an experience you have had with water balloons! I encouraged students to tell stories about water balloons as the more students enjoy math, the more they will learn!
I continued: Let's say you bought this package of water balloons. Tell me what you notice! "That the capacity of a balloon is 300 milliliters." How many balloons could you fill with 1 liter of water? Turn & Talk! Students excitedly pointed to the graduated cylinders from yesterday and naturally applied previous knowledge. Most students explained to another student, "Three balloons because 300 + 300 is 600 and if you add another 300, it would be 900 milliliters. And there are only 1000 milliliters per liter."
Before asking students to solve this problem in their student journals, I wanted to take this time to model problem solving methods. So I asked students to come up closer to the board and sit on the floor and in surrounding chairs/desks. Prior to the lesson, I created this Blank Anchor Chart to help facilitate this conversation. I explained: Fourth graders, whenever I solve a word problem, I always try to use more than one strategy. This way, if I get the answer twice, I'll know that I'm right. Also, it's important to know how to use multiple strategies just in case one strategy doesn't work with a certain type of problem. I began slowly modeling how to solve the first water balloon problem, "How many water balloons would you be able to fill with one liter of water?" by drawing a picture... then by using a number line... and then a t-chart. Students took notes in their journals as well: Problem Solving Strategies in Student Journal. Here's what the complete chart looked like when we were finished: Complete Anchor Chart.
Students were ready to begin practicing on their own! I explained: When problem solving today, I would like to see students using multiple problem solving strategies! I passed out a sheet of Water Balloon Problems to each group. I modeled how to format each problem using a Student Journal Template on the board. Then, I asked students to begin by solving, How many balloons would you be able to fill with two liters?
During this time, I circulated the room to conference with students. My goal during independent work time is to strengthen mathematical understandings through questioning, modeling, explicit teaching, and by providing immediate feedback. Inevitably, there's always a student or two who say, "I don't know what to do!" To encourage perseverance (Math Practice 1), I would respond: I know you can do this! I wonder if you could begin with one of the math strategies we just went over!?
As I moved about the room, it was interesting for me to see which strategies students felt most comfortable using. Here, a student chose to Draw a Picture. Other students used the T-Chart method. Many students tried using a Number Line to show their thinking. A few students tried Working Backwards by subtracting 300 milliliters from 2 liters (2000 milliliters). Overall, most students were successful with finding the the number of water balloons in 2 liters. However, once students moved on to 4 liters, they thought that they could just double the number of balloons that could be filled with 2 liters. This is where students began to struggle! Knowing that our math time was about to end, I realized that I would want to approach these water balloon problems differently tomorrow!
To bring closure to this lesson, I asked students to Turn & Talk: What problem solving strategies did you use today? How did it help you to solve problems using multiple strategies? I walked about the classroom and heard a variety of responses:
"I used the number line strategy!" "I used the t-chart strategy."
"This helped me make sure I got the right answer."