To begin, we reviewed the last lesson, How Big is a Liter? I held up the 1/2 liter water bottle again and asked students to Turn & Talk: How many ounces are in one liter? How do you know? After coming back together, one student explains his discovery: Explaining Discovery.
I introduced today's goal and asked students to write the goal at the top of a new page in their math journals: I can record measurement equivalents (mL to L) in a two-column table. I revealed the conversion chart (numbers enclosed in yellow boxes were the given values): Conversion Anchor Chart. One column was labeled "Number of Milliliters" and the next column was labeled "Number of Liters." I gave student time to copy this chart down in their journals. As students finished, I asked: How many liters is equal to 1,000 milliliters? Students responded, "1 Liter!" I wrote "1 L." in the adjacent column and commented, "I wonder how many liters 2,000 milliliters is equal to!" to get students thinking about the next conversion task.
Then I asked students to try completing the chart on their own. I wanted to give students time to grapple with these complex conversions. During this time I walked around the classroom and provided extra support for struggling students. I would often grab the graduated cylinders to help the students model the conversion. For one student, who was struggling with finding the conversion for 1.5 L, I used the Money Model to Teach Decimal Numbers.
Most students were able to find that 2 liters = 2,000 mL because "you just add on three more zeros." I wanted to make sure students could represent their thinking with models so I would often ask: How do you know? Can you show me? Can you prove it to me?
Here, Discovering 250 mL = 1:4 L, a couple of girls stayed in at recess to show me how they figured out the number of milliliters in 1/4 Liter. Later on, I'll ask them to share their discovery with the class!
At this point, most students had correctly found the whole number conversions. The area in which students struggled the most was with fractional parts of a liter. Even though I have not taught my fractions and decimals unit yet, I included these concepts for two reasons: The 4th grade standard, CCSS.Math.Content.4.MD.A.2, states that students should be able to solve word problems involving measurement units including problems involving simple fractions or decimals. In addition, by weaving fraction and decimal concepts into units throughout the year, students will become more proficient in this areas, will be able to see the interconnectedness of math, and will be able to see a variety of ways in which fractions and decimals can be applied.
After giving students plenty of time to complete the conversions chart on their own, I pulled students back together by saying: Claaaaassssss! Students responded, "Yes?!" I continued: I am incredibly impressed with your willingness to persevere, when these conversion tasks became more and more challenging. I particularly loved watching you use the appropriate tools to prove the equivalency between two measurements! I wanted to celebrate and encourage students who were demonstrating both Math Practice 1 (Make sense of problems and persevere in solving them) and Math Practice 5 (Use appropriate tools strategically).
I explained: Now what I would like to do is come back together and complete this conversion chart. As you complete this chart, I'm looking for high-level mathematical explanations! I want you to prove how you know each answer to be true! This is because high-level mathematicians always provide evidence to support their argument (Math Practice 3: Construct viable arguments). Every opportunity I have to support the development of a math practice, I do!
I prompted student participation: I wonder how many liters are equivalent to 2,000 milliliters?! One student beautifully summarized what she knew about one liter and used this information to determine 2 L = 2000 mL. Then, I asked the rest of the class: Who can show me using the tools in front of you? After a student modeled how 2 liters is equal to 2000 milliliters, we moved to modeling 3 L = 3000 mL. I loved watching this student use appropriate tools strategically!
Next, we discussed 8 L = 8000 mL. This student began by explaining, "You just add on three zeros." I pushed his thinking a bit by asking him to demonstrate his understanding using a graduated cylinder. I was proud to see him provide a deeper level explanation.
After a student explained that 15 liters = 15,000 milliliters, I guided him to discover the operation taken to get from the 15 to the 15,000. I asked: What operation did you use to the 15 to get to 15,000? Did you add? multiply? divide? subtract? He responded, "I multiplied by 1000" and documented this on our chart. To encourage this higher level thinking, I then asked if he could explain the reverse operation used when figuring the number of liters: Multiplying by 1000. We then connected this new understanding to the next task: Dividing by 1000.
We then discussed the partial liters. One group of girls so proudly explained how they knew 1:4 L = 250 mL. This was one of my favorite moments of the whole lesson. I loved hearing them relate fractions to money (1/4 = 25 cents).
During independent work, I found one student had incorrectly responded to the number of liters equivalent to 100 mL, 200 mL, and 300 mL. Instead of correcting him, I gave him a 100 mL graduated cylinder and a 1000 mL graduated cylinder and asked him what he could do to find what part of a liter is equal to 100 mL. He realized that he needed to count the number of 100 mL cylinders that would fit into a liter. Here, he explains his realization: How many groups of 100 mL are in 1 Liter?. This again, was another amazing moment!
To bring closure to the lesson today, I asked students to Turn & Talk: What did you learn about milliliters and liters today? After giving students a few minutes to discuss, I asked some students to share responses:
"That 1.5 liters is the same as 1 1/2 liters. They are both 1,500 milliliters."
"There are 10 one-hundred milliliter cylinders in a 1 liter."
"It takes four 250 milliliter cylinders to fill a liter."