Juice Bar Problem Solving

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Objective

SWBAT solve word problems involving customary capacity units.

Big Idea

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

Opening Activity

15 minutes

Prior to this lesson, I projected the following image on the board to trace the Juice Bar and attendant: Juice Bar Drawing. The goal was to stimulate student interest and to provide a context for solving problems involving measurements of capacity. This also supports Math Practice 4: Model with Mathematics.

 

Immediately upon walking into the classroom, students were interested in the image on the board! “What’s that Mrs. Nelson?” “What do we get to do?”

I began by explaining: Fourth graders, I want you to meet Cindy! Cindy owns a Juice Bar! Each morning, Cindy gets to work early and makes each of her juice combinations.  Look at all of the drinks she has on her menu! Turn & Talk: Which drink would you order at Cindy’s Juice Bar?

I then introduced today’s goal: GOAL and continued: Before we begin, I’m going to give you a list of Capacity Word Problems. I’d like you to cut out each problem and paste them down in your math journals, one problem per half page. Make sure you leave room for two strategies and include a place to record your answer by writing “Answer:_____________.” Having followed this procedure before, students quickly went to work cutting out and pasting down. After all the cutting and pasting was complete, I directed students’ attention to the first problem.  

Teacher Demonstration

20 minutes

Today, we are going to see what it’s like to be Cindy! She’s going to have all sorts of problems that she’ll need your help with! To begin with, as a Juice Bar owner, Cindy will have to decide the size of drinks that she would like to sell. If Cindy has one gallon of Strawberry Paradise, what ways could Cindy sell one gallon of Strawberry Paradise using ounces, cups, pints, or quarts? Students were a bit challenged at first, but then quickly realized how they could use Gallon Guy to help solve this problem. Soon, a few students’ hands were raised. As students began sharing, more and more students were eager to participate! I recorded student thinking on the board: Ways to Make a Gallon on the White Board. At first students offered: 1 gallon = 4 quarts, 1 gallon = 16 cups, and 1 gallon = 8 pints. Then student responses gradually became more complex, such as 1 gallon = 8 c. + 4 pt. 

I then asked students to continue finding ways to make one gallon on their own. I loved watching this student “decompose” a gallon in the same way he would decompose a number: Student Figuring 10 Ways to Split a Gallon. Some students drew models, Making One Gallon in Student Journal, while other students wrote Gallon Equations. Many students wanted to share their thinking on the board. Here, a student proved that Half gal. + 4 c. = 1 gal while other students showed how 2 qt + 2 pt + 4 c = 1 gal and 8 c + 1 qt + 2 pt = 1 gal copy are evidence-based conclusions (supporting Math Practice 3: Constructing viable arguments).

A couple other students explained their thinking on the board. Here, a student explains that 64 oz + 4 pints = 1 Gallon.  I guide and encourage him to accurately use math vocabulary. This student was convinced that 1 qt + 2 pt + 3 c + 8 oz. I used the Gallon Guy Poster to help the student identify his mistake. 

Student Practice

60 minutes

After students successfully documented ten ways to make a gallon for the example problem, I assigned math partners based on math skills, leadership abilities, communication skills, and behaviors and asked students to move on to Cindy’s next problem.  I reminded students to show two strategies for each problem and to make their answer clear by creating an answer line.

During this time, I conferenced with each group and provided support through questioning, modeling, and providing explicit instruction.

When Solving Problem #1, one student “crossed off” the quarts that Cindy sold to find the remaining pints. She had to figure out the number of quarts of Just Peachy that Cindy had left and then convert this measurement to pints. The Gallon Guy model proved to be a helpful tool for all students! I purposefully included two-step problems such as this to provide students with rigorous task and to also encourage students to expect multiple steps within problems.

For problem #2, some students struggled with finding the number of ounces in five pints. Here’s a series of video clips showing the steps taken to help guide and direct two students as they solve this problem.

1.Supporting Students Step 1: This is when I realized that these two students were still developing the understanding of ounces, cups, and pints.

2.Supporting Students Step 2: Here, I decided to grab a math manipulative to help students grasp the concept that 8 ounces = one cup.

3.Supporting Students Step 3: Next, we built upon this understanding by connecting cups to pints.

4.Supporting Students Step 4: In this video, the students realize that two cups are equal to one pint and one pint is equal to 16 ounces.

5.Supporting Students Step 4: I knew we could then move on to solving the word problem. I continued to refer to the manipulatives to help support student understanding.

6.Supporting Students Step 5: Once the students figured out that 5 pints = 80 ounces, I drew another picture on the board to help these students see the problem in another way.  With time and support, the students realized that Cindy would not have enough Mango Madness for the customer because the requested 5 pints is more than the 64 ounces that Cindy had left to sell. After successfully solving this problem, I split up this partnership by placing each student with a partner who would take the time to question and support their thinking. When two struggling students are working together, they'll often become confused and frustrated and consequently, little learning will take place. I wanted to make sure this wasn't the case!  

Here, students work at Solving Problem #3 using two different methods (paper & pencil) and manipulatives: Proving 96 oz + 4 c = 1 gal. These students had actually arrived at two different answers. One student thought that 96 oz + 5 cups equaled a gallon while the other thought it was 4 cups. The student pouring so thoughtfully and respectfully said, "I guess that's 4 cups" and the other student admitted, "Yeah, I guess you're right." This is a perfect example of the importance of student discourse (Math Practice 3). 

I loved seeing the multiple ways students solved problems, depending on their math skills and level of understanding. Here are two ways students tried Solving Problem #5 and Solving Problem #5 Another Way

 

Closing

5 minutes

To bring closure to the lesson, I celebrated students who worked well together and persevered when solving these problems! By taking the time to recognize the expected behavior, students will be more likely to continue making positive choices during our next math lesson.