Today's Number Talk
For a detailed description of the Number Talk procedure, please refer to the Number Talk Explanation.
Task 1: 2 x 15
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, students tried decomposing 15 in a variety of ways. Here, a student justifies how she found the solution to 2 x 15 = 2x5+2x5+2x5. By allowing student the opportunity to construct and share viable arguments, students will become more proficient with Math Practice 3.
Task 2: 15 x 4
When we moved on to 15 x 4. Students eagerly shared several strategies. Here a student proved: 15 x 4 = 15x2 + 15x. Another student explained how he Decomposed the 15 to solve 15 x4. I modeled his thinking on the board so other students could understand his thinking process. During each Number Talk, students always want to share on the board. Today, I decided to let many students show Multiple Strategies on Board. They loved this!
To begin, I we reviewed the word, capacity, by acting the meaning out: Meaning of Capacity.
To review the meaning of capacity, I demonstrated how to find the capacity of two different paper cylinders: Volume of Two Cylinders. I took a file folder and cut off the tabs. Then I cut the folder in 1/2, resulting in two identical rectangles. Next, I rolled one rectangle, joining the top and bottom edges with tape. Then I rolled the other rectangle, joining the right and left edges with tape. This resulted in two paper cylinders (one taller and one shorter with greater radius). I then asked students: If I fill both cylinders up with beans, what do you think will happen? Do you think one will hold more beans than the other? Or do you think both cylinders will have the same capacity? Turn & Talk! Many students thought the taller one would hold more whereas others thought both cylinders would hold the same since they both were created by the same size paper.
I placed the skinnier cylinder inside the wider cylinder. Then I placed both cylinders inside a plastic tub. If filled up the skinny cylinder. Then I lifted the skinny cylinder, allowing the beans to fill the wider cylinder. Students were astonished! The beans only filled up the wider cylinder just past the half way point! Students conferred with each other and concluded, "You can't always judge the capacity of a container based on height!"
I then explained today's goal: I can determine the number of milliliters in one liter. Today, I'm going to give you some information about a liter, but I'm not going to tell you how many milliliters are in one liter! I want you to discover this on your own! I then held up a water bottle and explained to students: This water bottle is 1/2 a liter. I then placed the water bottle on the white board and wrote "equals 1/2 a liter" so students could continually refer to the provided information: 1 Liter. Today, I want you to work with your group to find the number of milliliters in one liter. I'll give you a tub of tools to help you with your investigation. I passed out a plastic tub, graduated cylinders (varied sizes), a 2-gallon pitcher, a plastic cup, and a water bottle. I purposefully gave students too many tools as I wanted to see if students could use appropriate tools strategically (Math Practice 5).
Prior to investigating, I reminded students to be the type of partner others want to work with by being on task, helping out, and sometimes asking others, "Would you like to go first?" After going over group expectations, students went right to work.
During this time, I moved about the room to question students and encourage group conversations.
Here, Confusion about the Pitcher, a group begins filling up the pitcher using the graduated cylinder. They were so determined to find the total number of milliliters in the pitcher that they had lost track of the goal of the problem. This reminded me of students who sometimes add all the numbers in a word problem without fully understanding what the problem is asking and eliminating unnecessary information.
I then moved on and found another group figuring out How many Milliliters are in a Bottle?. I was happy to see this group working so well together and sharing responsibilities. I appreciated listening to them participate in mathematical discourse, which is an important part of constructing viable arguments and critique the reasoning of others (Math Practice 3).
Eventually, I made my way back to the first group who had moved on to finding the number of milliliters in the plastic cup: Confusion about the Cup. I'll have to admit, it was quite difficult to not correct the students! I just kept asking questions!
I walked off again and found this group Discovering 1000mL = 1 L! This was such a wonderful and memorable moment - much more memorable than my just writing this conversion on the board!
I went back to the first group a final time to check on their understanding, and they were Finally There!. It was so important to give them the time necessary to eliminate unneeded tools!
To bring closure to the lesson, I asked students to clean up and return the plastic tubs of tools to the back counter. We then discussed student findings. I purposefully called on one of my students who struggles to explain how he discovered the number of milliliters per liter.
I wanted to enforce this idea even more so I asked students to gather around the back table. I had taken centimeter grid paper and cut out a 3 x 3 grid to fold up into a little cubic box with one open side. I demonstrated how one milliliter is equal to one cubic centimeter by pouring one milliliter in the little box. I also created a 1000 cube by cutting out five 10 x 10 squares out of the centimeter grid paper and taping them together with shipping tape. In the following video, a student poured a liter (or 1000 milliliters) into the cube measuring 1000 centimeters cubed: 1000 cm3 = 1000 mL. Again, this further demonstrated the concept that 1000 mL = liters and provided one more way for students to construct knowledge instead of memorizing this conversion!