Note: The mathematical content (the actual problems) for this lesson is found in the “Twizzler Math Problem”.
I quickly review with my students multiplying fractions, mixed numbers, & fractions & whole numbers. The students have been very successful with all of these this week, but I think when they see word problems, students will become less confident in their abilities. That being said, they're probably going to become frustrated.
To attempt to combat this I do a daily spiral review. Using a spiral review is crucial to keep kids great at math skills because it's only after continued practice that students master skills. Due to so much content, I'm constantly moving on to the next task, so the spiral review helps to identify who needs more practice, & it helps keep an assortment of content/skills fresh in students' minds. I pass out lyric sheets, incomplete ones that have a few blank spots to ensure attention, for the Dividing Fractions song. This song has a rap theme, and generally, my students very much enjoy this type of music. We listen to the song once, and attempt to fill in the missing words. We use a Flocabulary song, but you can only access it for free if you sign up for a free trial or have a subscription. The content that I’m looking for in this song is the catchy tune to remind students to: "Keep, Change, Flip" to solve division problems. In this, students can remember this instead of having to rely on a classroom poster or notes. We use a Flocabulary song, but you can only access it for free if you sign up for a free trial or have a subscription. The content that I’m looking for in this song is the animated action of the three steps. If you don't want to use Flocabulary, here is link to another resource: Dividing Fractions. It also provides an animation of the steps as well. This links to a 5 minute video which references dividing fractions as being as "easy as pie", and still uses a catchy tune to help students remember the process. It also uses pictures of pizza in real-life situations. Therefore, you wouldn't use the keep-change-flip procedure to teach students, but rather, the attached chant.
Then, as a class, we sing along with the song after I’ve reviewed the missing words. I then pass out one Twizzler to each student, and read aloud the Twizzler word problem on the board to the students. (Students have already been assigned table partners, of similar ability levels, and work together often. I switch table partners every nine weeks when S.T.A.R. Math tests are taken and scored.)
Rather than guiding students through the first problem, I encourage students to problem solve. As this was (deliberately - I'm growing confidence as well as skill here) an easier problem, my students are mostly successful. I facilitate learning while rotating throughout the classroom and monitoring on-task conversations.
I encourage students to draw models, and explain their reasoning/steps aloud. I take anecdotal note of strategies and misconceptions. Using the misconceptions that I noted, I then model my own Think-Aloud to students using the document camera, breaking the Twizzler into 3 parts, and then each of those 3 parts into 4 parts, ending up with 12 parts. (12 days that students could eat a piece as the final answer.) I also insert humor into a few groups by asking them if they would be tempted to eat more than their tiny allotted piece daily. This showcases my relationships with my students. We wrote a math journal entry/anchor chart about dividing fractions with visual models.
Using the misconceptions that I noted, I then model my own Think-Aloud to students using the document camera, breaking the Twizzler into 3 parts, and then continuing on to break each 3 pieces into 4 pieces when everyone is done). I’ll hold off until most students are done; problem solving getting bogged down, I’ll model now and redirect student thinking. I have used anecdotal notes as I've facilitated instruction to then address common misconceptions here.
Now we complete a step-by-step dividing fractions Anchor Chart. I include the directions for dividing fractions by fractions, dividing whole numbers by fractions, & dividing fractions by whole numbers. At the bottom I included the Keep-Change-Flip process.
My students learn best with small chunks of information, so today's handout (from Flocabulary) is shortened. I also trim handouts for my students prior to giving them out so that transitions are eased when they glue things into their Interactive Notebooks. Students glue the Dividing Fractions Guide into their notebook, & are instructed to get out 3 different colored crayons.
I model a sample problem for students, using color to code each action: “Keep” “Change” “Flip”. I also draw attention to how I write out the new equation directly underneath the old equation. (Select a word problem that your students can make a personal connection to - my model problem is about sushi. We discuss what sushi is, & if anyone has ever tried it.)
Students attempt to solve two more problems with partners, and we review the answers as well as the process to getting the answers. I'm guiding the students in the application of Mathematical Practice 7 - Look for and make use of structure. Students look to discover a pattern or structure. For instance, students use properties of operations as strategies to add, subtract, multiply & divide with whole numbers, fractions, & decimals.
I use inquiry-based methods so that I can guide students to ask questions that will lead them to answers.
Provide sentence stems, so that students can write out the steps, & do so using fill-in-the-blanks. Ex: To find the number of _______, divide ______ ( ) by _______ ( ). The number sentence for this is: _______________.
Following the quick review, students continue working on the remainder of the problems. I facilitate learning by questioning, listening to students' thinking, and if/when needed pulling a small group together to focus on a shared struggle. Throughout the lesson, I've focused on Mathematical Practice 1 - Make sense of problems and persevere in solving them. Students can check their thinking by asking themselves, “What is the most efficient way to solve the problem?”, “Does this make sense?”, and “Can I solve the problem in a different way?
To close out this lesson on dividing fractions, we review student work from independent practice by having each group write down their answers on individual white boards, modeling the "Keep, Change, Flip, process.
To incorporate literacy into Math, we also read aloud Hershey's Kisses: Multiplication and Division book. This book is relatively inexpensive, part of a whole series of books by author Jerry Pallotta, using real world context (candy) to visually represent mathematical concepts. The book illustrates multiplication and division, using different colors of Hershey's Kisses.