Water Balloon Problem Solving Part II

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Objective

SWBAT solve word problems involving liters and milliliters.

Big Idea

Mathematically proficient students can apply their understanding of measurement concepts to solve problems arising in everyday life.

Opening Activity

20 minutes

Today's lesson is an extension of yesterday's lesson, Day 4: Water Balloon Problem Solving. Students will continue finding the number of 30-milliliter balloons they are able to fill using a set number of liters. Yesterday, I asked students to solve for the following number of liters: 1 L, 2 L, 3 L, and 10 L. Today, I wanted to build a more gradual staircase of complexity and decided to use the following number of liters: 1 L, 2 L, 3 L, 4 L, and 5 L. Yesterday, many students struggled with finding the number of balloons that could be filled with 3 L. After reviewing yesterday's lesson, I realized that students needed an visual and hands-on model (such as paper balloons) to help them visualize the number of balloons that could be created per liter. 

To prepare for today's lesson, I handed out construction paper to each student and asked them to cut out 60 little balloons about an inch in size: Balloons. Even a simple activity such as this requires some problem solving. Students discovered more and more efficient ways to cut out multiple balloons at a time (such as cutting through multiple layers of paper). They loved being able to choose their favorite colors and cut out balloons!  

Next, I passed out stapled packets of three lined sheets of paper to each student. This way, students would have at least 5 pages, one for each of the upcoming problems. I also passed out copies of the Balloon Problem Solving (half sheet per student). I modeled how to Paste a Problem at the Top of Each Page.

I provided students with enough time to cut out all the balloons and paste down all problems before beginning our lesson as I wanted students to be able to solely focus on problem solving, instead of cutting and pasting! 

Teacher Demonstration

20 minutes

To begin, I reviewed the goal of the lesson: I can solve word problems involving units of measurement (milliliters and liters). I also reminded students to take risks by trying new ways of solving problems. I pointed to the Problem Solving Anchor Chart and asked students to Turn & Talk: Name two new strategies that you would like to try using today! I wanted to make sure students were learning how to use more strategies than just one as some strategies are not applicable to every problem solving situation!

Next, I explained: Fourth-graders, we are going to build upon yesterday's lesson, only today, we are going to be pasting down balloons to help us visualize each problem! Let me show you what I'm looking for! I projected a notebook paper, pasted down the first problem, and asked students to follow along with me on the first pages of their paper packets as I Modeled Problem Solving Expectations

I continued: First, let's read the question together. What is the question asking for? "How many balloons?" This was important for me to review as some students mistakingly responded 900 mL yesterday instead of 3 balloons. Next I explained: This is a two-step problem. I know this because the problem provides the number of liters, but I will have to first determine the number of milliliters there are in one liter before going on. I wrote, "Step 1. 1 L = 1000 mL." Then I said, Okay, let's move on to the second step, where we'll have to find the number of balloons in one liter. I wrote, "Step 2" and glued down one balloon. How many milliliters are in one balloon? What should we do to make our work more precise? Students responded, "Label each balloon with 300 mL."

After pasting three balloons in a row, labeling the balloons, and showing the total milliliters needed, I explained to students how they could show the "left over" amount of water by subtracting 900 mL from 1000 mL. This, again, was an important expectation to go over as some students had 400 mL left over yesterday and forgot to take into account that this amount could fill one more 300 mL balloon! 

Next, we moved on to our next problem solving strategy. Together, we decided to make a T-Chart (or In & Out box). I took this opportunity to show students how to show too many balloons. I added in one more balloon (4 balloons = 1,200 mL) and show students how to label this as "too much!" We also wrote the rule of the table off to the side of the paper. 

Finally, I asked students to create an "Answer: _________" line at the bottom of the page. I took one more opportunity to ask the students to always reread the problem when they have a potential answer. I asked: What is the problem asking for again? "The number of balloons!"

Here's an example of a student's work as she completed this problem with me: 1 Liter.

 

Student Practice

60 minutes

Students were ready to move on to the next problem: How many 300 mL water balloons can you make using 2 liters of water? To encourage independent learning an perseverance (Math Practice 1), I asked students to work on their own, but to check in with each other frequently to make sure others in their groups were on the right track. 

During this time, I circulated the room, asking students questions to encourage a deeper understanding of concepts, holding high expectations, and providing support. I noticed immediately how engaged students were in problem solving. Students who are sometimes off task seemed to be more engaged than ever! Students who struggled yesterday, were now able to successfully visualize the problem and were much more successful! In addition, more students were trying new strategies! I was so impressed!

Here, a student solved for 2 Liters by pasting down six balloons in groups of three for easy calculating. She used a number line as a second strategy, but mislabeled the 900 mL. She also uses two more strategies (Showing Calculations: 900+900=1800 and Look for a Pattern: 3...6...9...12...15...18, 18 = 3 x 6 so 1800 = 300 x 6).

This student solved for 3 Liters. I loved seeing how she grouped three balloons and accounted for the 100 mL left over out of a liter. Then she added up the amount left over from each of the 3 liters and multiplied: 3 x 100 mL = 300 mL which equals one more balloon! This is the EXACT spot that students were getting confused at yesterday. However, today, they were successful because they were taking into account the leftovers! 

Here's an example of a student's solution for 4 Liters. While it may seem a bit messy, this is the neatest and most accurate work that this student has ever produced in math! Normally, I can hardly read it! Again, this visual model of paper balloons truly provided the student with the needed support. In addition, he didn't just stop at one strategy, he showed how 4 x 900 + 1 x 300 = 3900 using a number line!

Finally, here's an example of how a student solved for 5 Liters. First, she began by pasting one balloon down per liter. Then she showed how 300 x 3 = 900 for each balloon. She accounted for the extra 100 mL per liter and added 100 five times (once for each liter). This is where she discovered that 5 L = 3 balloons x 5 liters + 1 more ballon out of the extra milliliters. Finally, as a second strategy, she added 300 until she arrived at 4,800 milliliters and then counted the number of 300s in her calculations.  

As students finished, I asked them to choose their own number of liters to "solve for." Working together with others, many students found the number of balloons that could be filled using 10 liters, 50 liters, 100 liters, and 1000 liters. They were self-motivated and nearly unstoppable!   

 

Closing

5 minutes

Since we worked on problem solving to the very end of the math period, as a closing, I took the time to celebrate students for using multiple strategies, checking their work, accounting for the left over milliliters, persevering when confused, and pushing themselves to solve a harder problem! I truly believe: what you focus on and celebrate as a teacher, you'll get more of!