I taught this lesson with a group of struggling 5th grade math learners during an after-school tutoring class. Each student stood at a whiteboard on the wall of my classroom. My goal was to help students conceptually understand why we must find a common denominator when adding fractions. To do this, I asked the students to construct their own number lines. All steps beyond #1 are directions I spoke to students as they wrote on their boards. These were the steps in my lesson:
- I modeled how to make a fraction number line: arrows on both ends showing numbers go infinitely in both directions; small dashes pinpoint exact locations of numbers; begin with zero; space each mark evenly; starting at zero, build your number line and work across the number line rather than starting with a 0 and 1 and subdividing the line into equal size lengths. I wasn’t modeling fraction concepts per se; just creating the number line. (Previous number line work showed students struggling with this.)
- Create a number line that shows thirds from 0 to 1.
- Draw a parallel number line below the thirds number line. Put 0 and 1 directly under the 0 and 1 in the top number line. Now subdivide the new number line into sixths.
- Draw arrows down to the second number line where fractions line up.
- Solve 1/3 + 1/6 using one of the number lines.
- Repeat the above steps with a number line showing fourths and then eighths. (See top photo.)
- Add a third parallel number line showing sixths. (See bottom photo.)
- Use the proper number line to solve 1/4 + 3/8.
Each time I asked the students to create something, I redirected with small hints and asked students to peer tutor until all students had a perfect model. We constantly discussed the models to help students make sense of their work. In step 7, we discussed how very few fractions aligned with the number line above (sixths and eighths.)
Students made excellent progress as shown in their work on the boards.
Inspiration for this lesson came from my esteemed colleague, Kristian Quiocho. Kristian is one of the most knowledgeable and passionate teachers I know.
A big thank you goes out to Big Ron Crowley, the genius musician behind the new bumper music for my podcast, the 5-Minute MishMash. Besides the new opener, episode 7 has a book recommendation, a gamification idea you can use tomorrow, a tech tip for adding photos to presentations, and a new mini-series called “The Power of Pair Share.”
It’s been a while since Scott and I have had time to record a new show, but it’s finally here. In this episode we interview the very enthusiastic, contagious, and knowledgeable Alex Kajitani. If you teach math, and even if you don’t, you will want to listen to this discussion about bringing the right approach to learning math…students, teachers, AND parents! You can learn more about The Rappin’ Mathematician, Alex Kajitani, by visiting his website.
If you like the show, please subscribe on iTunes and leave us a review. The only way we can impact teachers and thereby impact students is if educators listen to the show. Ratings and reviews will help bring The Bedley Bros podcast to more Internet searches. Perhaps you would be willing to Tweet about our podcast, share it on Facebook or other social media, or send out an email to your staff. Share the love.
Do you ever struggle with getting kids to get off to a strong start on an assignment? Do you have students who are masters of avoiding doing their work? Listen to a quick tip on episode 6 to address these issues. You’ll also learn about Kahoot and some practical, student-centered tips for teaching spelling.
The 5-Minute MishMash is a fast-paced blast of teaching ideas that you can use tomorrow in your classroom. If you enjoy listening and wish other teachers would listen, too, please subscribe to the podcast, write a quick review on iTunes, and share it with teacher friends on social media or email.
Are you going to the Palm Springs CUE conference this week? Be sure to say hi and ask for a free 5-Minute MishMash sticker. I’d love to meet you and talk some shop!
Does EdTech really suck? Of course not! The Bedley Bros use technology with our kids all the time…and we love the CUE Conference! This episode of the Bedley
Bros flashes back to our discussion with Andrew Campbell, a 5th grade teacher, who knows technology very well, but isn’t afraid to ask some hard questions about how we use it. The show provides a healthy look current practices. Enjoy this very edgy episode of The Bedley Bros…and we’ll see you at CUE!
Other posts you might enjoy:
Step-by-step Student Guide for Making Adobe Spark Video Projects (See! We don’t hate EdTech!)
“I’m finished!” That dead phrase all teachers don’t want to hear.
So what’s next?
First, I teach my kids that “finished” is the F-word. We don’t say that in our class when it comes to projects. There’s no such thing as finishing an open-ended project. You’re only satisfied, not finished. You ran out of time…or it’s good enough. But you’re not finished because there’s always something else you could do to improve your work. Like this blog post. I will reach a point where I’m satisfied with it…and I’ll slowly and reluctantly hit “Publish.” And then I will come back to it and edit some more. 😉
When we assign an open-ended project, it’s inevitable that some kids will become satisfied with their work before the deadline. Then what?
I give my students options, but I’m always aware of this: If the “finished” choice is more enticing than the project itself, then the quality of the project work goes down…drastically.
- Mentor. My favorite thing to do with these kids is have them mentor other students. I ask the mentees if they’d like Sarah to mentor them, walk them through the project. If both parties agree on the working relationship, I do a bit of coaching (don’t force your opinion on the mentees, listen to their needs, stay with them, your goal is mentee independence, don’t do their work for them, ask me if you’re confused, you don’t have to know all the answers, etc.) Here is some impromptu footage of Jake mentoring Alyssa and Karla in my 5th grade classroom.
- Create another mini-project. If enough time remains, students can zip through the creation process on any topic they’d like. This option reinforces the process and gives the students another iteration to improve quality. One example: How about you make another movie but do it on your favorite hobbies instead of the American Revolution.
- EduChoices. I ask the students what they’d like to learn about in the 20 minutes they have left. 99% of the time, I say, “Go for it! Have fun learning about ____.”
- Be a classroom helper. Some students enjoy contributing to the classroom environment by picking up, tidying, cleaning, etc.
- Share about our class. One other “finisher” activity is to ask the students to report something about what we are learning to the community. They can write a blog post, create a documentary-style video for YouTube, or write an email to the principal…anything that shares and reinforces their excitement for their education.
What do you have your students do when they’re fin… satisfied?
So I’ve uncovered another math misconception, and I’m fairly baffled.
I’m pretty sure most teachers write blog posts to share something they’ve mastered, something they’ve learned, something on which they consider themselves an expert. This isn’t one of those posts.
I’m admitting that I’ve got a lot to learn, even after 28 years of teaching math to kids. The more I learn about teaching math, the more I believe that I DON’T know about teaching math.
A 5th grader looked at these two fraction models today, and could not figure out where the yellow portion was shown in the red shaded model. I asked him to find the yellow part in the model on the top and outline it. He first drew a line around three sides of a 1/6 piece on the upper model. He didn’t even know what it meant to outline something, let alone find 1/3 in a model of sixths.
The students were trying to solve this problem: 1/3 + 1/6 =
My confused gentleman was looking at another student’s model of the problem, which looked like the red example above.
So how did I get him to see the 1/3 hidden in the model of sixths? I did some improv teaching and grabbed two pieces of half papers. I partitioned them like the models above. I shaded the yellow part on one paper with a dark sharpie, so that the shading would show through the other paper. Then I placed the sixths model over the top of the thirds so he could see the fraction lined up. He then said, “OH!” and was able to return to the model on the board and outline the correct portion.
Wow! It’s amazing what you learn about kids when you force them to explain things thoroughly.
Am I at a place where I can fully understand how kids think? No way! Do I know how to use progressive instruction to develop spatial sense in all my students, so they don’t lack the skills to identify equal portions? No way!
I’m going to need a few more lifetimes to master this job we call teaching.
Episode 5 includes:
- “Everyone?” Should teachers ask if everyone has a pencil? Listen to find out.
- Spelling instruction tips for upper elementary.
- Should teachers refrain from smiling until Christmas?
- Self-inking customizable stamp for only $10: What a time-saver!
Please share your reactions!
My fifth graders have been doing research in science and then presenting their findings in Adobe Spark Video. I noticed a real lack of understanding of the design process so I created a guide to use with them. It has really helped!
Today I met with each team to check in on their progress. It made things really concrete to say, “Show me your work. Where is step one? Where is step two? Etc.”
So I thought I’d share. Feel free to alter the guide and make it work for your kids. If you have suggestions to make the guide better, I’d LOVE to hear them! Let’s collaborate for the good of our students.
Here is the guide on Google Drive.
Here is an example of a student-created Adobe Spark Video.
Last year, it was my turn to be observed. After teaching for 27 years, I was ready to take a risk, try something new. So I went to my principal and asked, “Do I have to be in my classroom when you come do my observation?” As you can imagine, she didn’t exactly know how to respond. But since my boss was a good sport, and trusted me, she said, “Well, what do you have in mind?” After I explained, she decided to play along.
When the time came, my principal walked into my room and I walked out. It was a very good year, probably the best group of kids I’d ever had, a class of very mature fifth graders. One girl ran the class. She managed 32 students reviewing a language arts assignment. The students worked in groups, pairs, and held a whole class discussion. According to my principal, my observation went well. I had to take her word for it, since I wasn’t there.
So why would I do such a crazy thing?
About 12 years ago, I began my journey to make my students the most independent they possibly could be. I had read an archived newsletter at learningcentered.org that told the story of a sub who didn’t show up for school. The principal was walking the hallways, noticed the kids in one class working away diligently, but didn’t see any teacher. Upon inquiry of the students, the principal found out that the teacher hadn’t shown up, and neither had the substitute. So the kids just went about their business of learning. This struck me. Could my students do this? Would they?
So to me, the real assessment of my teaching is how my students work without me. And if that’s my goal, then why should I be in the room for my teacher observation?
Am I crazy? Did I get you thinking? Talk to me.