Today's Number Talk
For a detailed description of the Number Talk procedure, please refer to the Number Talk Explanation.
Task 1: 2 x 14
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 14, some students took two jumps of ten and then added in two jumps of four: 2 x 10 + 2 x 4. Other students solved: 2x5 + 2x5 + 2x2 + 2x2. When student were done with one strategy, they moved on until they had Multiple Strategies represented.
Task 2: 2 x 28
Note: This lesson was inspired by the Georgia CCGPS 4th Grade Measurement Unit, p. 53.
I began the lesson by introducing the goal of the lesson: I can estimate and measure capacity. I created an anchor chart to explain the difference between Capacity and Volume: Capacity vs. Volume. In a lesson later on, I'll further define volume, for now, I wanted to focus on capacity. During this time, students took notes in their Student Journals. I explained: Volume refers to the amount of units in an object, so when you find the volume of a plastic pitcher, you would find the amount of plastic in the pitcher. Capacity refers to the amount of units the pitcher will hold. Today, we will be focusing on capacity. At this point, I taught students the Meaning of Capacity and we took time to act out the new vocabulary word.
Next, I showed students how to measure capacity using a graduated cylinder. I explained: Graduated cylinders come in different sizes, so you always want to pay close attention to the scale. I drew an example on my anchor chart. This scale, counts by 10 milliliters (mL). I then explained the importance of setting the graduated cylinder on a level surface whenever you want to measure the number of units. I also pointed out the meniscus, or curved surface of the liquid in the graduated cylinder, and how to measure at the bottom of the meniscus.
Next, I held up several labeled Containers and asked students: Which container do you think has the greatest capacity? How about the lowest capacity? I drew the following diagram on the board and asked students to do the same in their journals: Estimated Capacity of Containers, Least to Greatest. Students then placed letters on the line accordingly. Students immediately began constructing arguments, "I think container B will hold the most because..." and critiquing the reasoning of others, "I respectfully disagree because..." (Math Practice 3).
I drew a data collection chart on the board and asked students to do the same: Student Data in Journal. In the first of the three columns, I wrote Container, the second column, Estimated Capacity, and the third column, Actual Capacity.
Next, I reviewed the expectations for group work (everyone is on task, taking turns, and under control). I handed out the following materials to each group of students: a tub (to catch drips), a small graduated cylinder, and a large graduated cylinder. I asked team leaders to choose a container to measure first. Students quickly began investigating.
I purposefully didn't model how to determine the capacity of each container as I wanted students to make sense of the this real-world problem and persevere (Math Practice 1). Some students filled the tub up with water to begin with and then realized that they would need to fill up the graduated cylinders instead. This was a great learning experience and also a great reminder of how problem solving can extend beyond a word problem.
At first students had to begin by Learning to use a Graduated Cylinder. One scale counted upward while the other scale counted downward. One student brilliantly pointed out, "One scale is for measuring the amount of water you pour out!"
Other students struggled with Subtracting from 500 mL to get the Answer. This was just like solving a multi-step problem: 1. How many milliliters are in the graduated cylinder? 2. How many milliliters will the cylinder hold? 3. How many milliliters were poured out?
I was pleased to see that students were often able to estimate the capacity of containers more accurately as the investigation went on. This means that they were beginning to understand the relative size of a milliliter!
Even though all groups hadn't measured the exact capacity of each container, we were running out of time! So I counted down from ten and asked students to clean up their work areas during this time. Once cleaned up, we completed the Estimated vs. Actual Capacities chart on the board using the data from each group's investigations. Students completed the charts in their journals as well.
Next, we went back to the capacity line up and listed the containers in order from lowest capacity to highest capacity: Actual Capacity of Containers. To help students visualize the results of their investigation, I lined up the Containers from Least to Greatest. This was on of the most powerful parts of the lesson as students were able to draw conclusions about the capacity of the containers based upon their collected evidence (supporting Math Practice 3).