I plan to give my students 5 minutes to work on today's Do Now problems. I've assigned these problems because my students have difficulty with subtracting mixed numbers when the second fraction is larger than the first fraction. I think it is important to regularly practice this skill.
After 5 minutes, I will have students exchange notebooks to check each other's work. (MP3) If their partner has solved it differently, this allows them to see and think about another strategy. If their partner has used the same strategy, it is an opportunity to compare their steps and validate their work.
This lesson is adapted from the CMP3 curriculum. For this lesson, I will give students colored pencils and the Multiplying Fractions - Brownie Pan Problem Worksheet. We will complete part A of the worksheet together as I guide students through the problem. I have several questions planned to help my students explore the problem and build their understanding of the mathematical operations involved in the work.
What shape is the brownie pan? Students should recognize that the problem stated that the pans are square. They should draw a square pan in the space provided on the worksheet.
How much of the pan is full? How can we represent this fraction? Students should use a colored pencil to show that two thirds of the pan is full.
How can we mark the brownie pan so that it is easy to see what part of the whole pan Mr. William buys? Students should suggest that you shade in half of the pan.
In which direction would it be helpful to shade half of the pan? On the board, I will demonstrate shading half the pan in the same direction as the two thirds.
Is this a good representation of 1/2 of 2/3? After students have discussed and agreed on how the half should be shaded, they should use a different colored pencil to represent the half the Mr. William buys.
How can we use this visual representation to find our answer? At this point, I plan to turn things over to my students. I will ask them to discuss, with their groups, how their area models gives them the solution.
After about 5 minutes, we will discuss their conclusions as a class to see if everyone is in agreement.
Assuming that Part A goes according to plan, I will have my students continue on to Part B with their groups. I will give them about 10 minutes to discuss and complete Part B. After about ten minutes, I will select a few students to share their answers.
After completing the worksheet, I will share with students a video that reinforces the concept of creating area models for multiplying fractions. This video uses the same idea as I used in the lesson. I focus on the second example in the video, where students are able to see the concept applied to a chocolate bar.
At this point, I want students to develop the algorithm based on the area models they've created. I will pose the following questions to students for discussion. I will use a "turn and talk" strategy where students will discuss their ideas with their group before we discuss them as a class.
How could we have found our answer through multiplication? Why does multiplying the numerators and multiplying the denominators work? What part of your drawing in Question A shows the denominator? What does the denominator of a fraction tell you?