Goal & Lesson Introduction
To begin today's lesson, I invited students to the front carpet with their white boards. Next, I reviewed the students' current learning goal: I can multiply a fraction by a whole number. To make fraction x whole number multiplication more relevant, I decided to bring in a cookbook from home:
I explained: Today we are going to be talking about recipes! If you have ever followed a recipe, you might remember that many measurements of food ingredients are fractional amounts. Often times, you'll make multiple batches of a recipe. For example, if I was having many people over for a barbecue, I might double or triple a recipe to make sure I have enough food for everyone!
Two Batches of Iced Green Tea
Today, we are going to start off by looking at two drink recipes. First, we'll look at iced green tea! I drew a 3 x 4 chart on the board to organize the ingredient measurements needed for 1 batch, 2 batches, and 5 batches. Here's what the chart will look like at the end of this activity: Number of Batches Chart.
Then, I showed students the Iced Green Tea Recipe. Let's take a look at the measurement of sugar needed for one batch. Students responded, "1/4 cup!" I wrote "1/4 c. sugar" under 1 batch.
I continued: Let's say that I have a large group of people coming over for a barbecue and I need to make 2 batches of iced green tea. I wonder how much sugar would be needed for 2 batches. What operation could you use to double a recipe? One student said, "Add 1/4 + 1/4!" Another student said, "Or you could just multiply 2 x 1/4." Great thinking! Let's show our thinking on our white boards using an equation and a visual model, such as a number line or an area model. (Most students choose to do use both models!) Turn and talk about how you would calculate this! Here's an example of student calculations during this time: 1:4 x 2.
After giving students some time, a student shared, "2 x 1/4 = 2/4 because 1/4 + 1/4 = 2/4, which also equals 1/2." I responded: So what you are saying is that I could simply use a 1/2 cup as a measuring tool instead of having to use a 1/4 cup to get 2/4 cup of sugar? I tried to relate this process to the real world as much as possible to engage students in Math Practice 4: Model with Mathematics. I want math to become more than just numbers you calculate at school!
Five Batches of Iced Green Tea
Next, I asked students: What if I wanted to invite an even bigger group of people to my house for a barbecue? Let's say that I need to make 5 batches of iced green tea. Can you show me how much sugar I would need using an equation and visual model? Again, many students used both models and an equation to represent their thinking: 1:4 x 5. I asked student to turn and share their thinking throughout this calculation process. Finally, we discussed the solution as a class and completed the chart.
Dessert Coffee Recipe
To ensure student understanding, I showed students one more drink recipe, Dessert Coffee. Following the same process as above, students documented the amount of coffee needed for 1 batch, 2 batches, and 5 batches of dessert coffee. Here are a couple examples of student work during this time: 2:3 x 2 and 2:3 x 5.
Picking math partners is always easy as I already have students placed in desk groups based upon behavior, abilities, and communication skills. Before students began working, I asked them to discuss how they would like to support each other today. I gave them many examples: Do you want to take turns talking out loud? Do you want to solve quietly and then check with each other? Or do you want to turn and talk anytime you get stuck? Students always love being able to develop a "game plan" with their partners!
I explained: For practice today, I'd like for you to continue by calculating the ingredients needed when making multiple batches of brownies. Students immediately connected with the activity. Several said, "I love brownies!" Many students even asked if they could take the recipe home!
Let's say that Emily (a student in our class) wants to make 2 batches of brownies for one event and 6 batches of brownies for another event! I wonder how much she will need of each ingredient for both events! I passed out copies of the Brownies Recipe to each student.
I modeled how to complete the first few problems by writing out an equation on each line: If one batch of brownies requires a 1/2 c., then what equation will represent the amount of butter needed to make 2 batches? Students respond, "1/2 x 2." I showed students how to write 1/2 x 2 = 2/2 = 1 c. I also stressed the importance of including the measuring tool (cups, tsp, tbsp).
Monitoring Student Understanding
Once students began working, I conferenced with every group. My goal was to support students by providing them with the opportunity to explain their thinking and by asking guiding questions. I also wanted to encourage students to construct viable arguments by using evidence to support their thinking (Math Practice 3).
During this conference, Students Making 2 Batches of Brownies, the students did a great job explaining their steps and writing equations.
Here, Six Batches of Brownies, a student drew a visual model to explain her thinking. I always love asking the questions, "Are you sure?" or "How do you know?" These questions almost always challenge students to check their thinking again using another method.
School Bake Sale Task
As a final task today, I asked students to complete the following task independently: School Bake Sale Task. I was truly impressed with the number of students who successfully used a number line and equation to show their thinking when problem solving.