Multiplying Fractions: Puzzling Problems
Lesson 2 of 2
Objective: SWBAT solve real world problems involving multiplication of fractions & mixed numbers.
In the warm up, I'm using Cookies for Grampy, a game from Visual Fractions. The object of this game is to make whole cookies using fractional pieces. Students use the mouse to drag the pieces onto the circle to make a complete cookie. The Cookies Per Minute score is the average number of times a complete cookie is made in one minute. A score of 5 or more will make you a cookie builder expert. In this activity, students learn: The relative sizes of 1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/9, and 1/10, how to build a whole number with different fraction sizes, and students get more practice in addition, subtraction, and multiplying fractions. Ideally, I would want my students to work in pairs to make cookies, and share a laptop. We had to do this activity as a class. In order to maintain as much instruction as possible, before pressing START, students draw and create a solution with their partners on paper for about 5 minutes. Then, I solicit creation ideas, and we move forward together. Afterward, I challenge students to create yet another way to create a cookie. You can continue this for as long as time allows.
I model a step-by-step process to multiply fractions, which is shown in the top section of the student worksheet Multiplying Fractions. I walk the students through completing problem number 3, modeling how to set up the problem. (5 days multiplied by 1/4 of an hour.) I have an example of student work here.
The primary purpose of the modeling is to demonstrate thinking - I use a think aloud. After we complete our work together, I model the problem solving process needed in the next part of the lesson. This work involves increasing a cookie recipe to feed 3 people by writing an equation for each ingredient amount multiplied by 3.
Students benefit from multiple diverse opportunities to apply strategies to solve word problems involving the multiplication of a fraction by a mixed number. This standard includes multiplication of a fraction by a fraction, fraction by a mixed number, or mixed number by a mixed number.
Students work on the cookie recipe problem independently, for about 5 minutes. Students have to multiply each ingredient by the respective number of people in their group, so that there are enough ingredients to make cookies for the entire group.
I notice that some of my students wait to have one answer confirmed before moving onto subsequent problems. I see this as a lack of self confidence in their math abilities. To aid in increasing their self esteem, I group students into heterogeneous groups of mixed abilities. I also support and encourage students in modeling their thinking aloud for their group mates, and aloud to me as well. In doing so, as in reading, students often "hear" and self-correct their errors. Sticking with a problem, and working through your reasoning, are critical math skills and a real world problem encourages students to stay the course (MP1).
In the video, you'll notice that one of the student's (in the Angry Birds sweatshirt) misconceptions being addressed. He misses the last step of the problem; dividing the numerator and the denominator. He stops when he gets to a fraction, thinking that he was done. From previous problems, I know that he understands this process. If he didn't understand this process, I would ask him to diagram each step in his notebook using a different color for each step. I could also ask him to teach a partner the steps to solve a problem.
To incorporate literacy into math, we read aloud, Multiplying Menace. In this book, Rumpelstiltskin has returned and is threatening the kingdom if he is not repaid for the gold he spun 10 years ago. The baby that was promised to him in the fairy tale is now a ten-year-old boy, and he is the only one who can find Rumplestiltskin's secret multiplying wand (and save the kingdom).
Students learn about multiplying with whole numbers and fractions. The students who are having trouble multiplying fractions might have some trouble following the math solutions that Peter uses; students who are mastering the concept of multiplying fractions will enjoy solving the dilemma along with Peter. This being said, you would want to probably read this at a slower pace. You can then re-visit the book as well. You could also have the equations written out previously as well, and perhaps even assigned previously for a "do your best, but don't frustrate" task. Once in a while, I give my students a worksheet that has some challenging tasks which we may not have gone over lately. My intent is to see how they attack the problems. Knowing that some of my students frustrate easily, I take what I get on this worksheet. I tell students to attempt what they can, and if a problem takes longer than a few minutes, then to skip it. Since this is heavily laden with multiplying fractions, it's good to use at the end of the unit.