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Hands-on Activities for Developing Conceptual Understanding of Fractions

So how important are fractions in math instruction? Well, a recent study out of Carnegie Mellon University shows that students' understanding of fractions and division directly predicts how well students will perform in algebra and more advanced math classes. Of course, fractions tend to be one of the most challenging math concepts for students to master, and so I've spent that last 6 years learning more about fractions and best practices in developing conceptual knowledge in students. First, an short overview of the progression of fractions instruction in Common Core math: Students are first explicitly exposed to fractions in 3rd grade (indirectly, students are exposed to factional concepts as early as 1st grade in geometry units), where they are introduced to the concept of fractions as numbers and develop an understanding of fractions using part/whole models (including number bonds, bar models, etc.) and number lines. Students also explore the idea of equivalent fracti...

Humpty Dumpty: Using inquiry-based math tasks in grade 1 to teach addition/problem solving

This week I had the pleasure of demoing/co-teaching a 3-Act math task, created by Graham Fletcher , in a 1st grade classroom in my district. I have always been a big fan of making math relevant to my students, and incorporating open-ended tasks that they can relate to, so when I first learned of Graham Fletcher's 3-Acts for primary age students (inquiry-based math tasks), I was hooked. I am sharing these like crazy at my math trainings, to encourage more inquiry-based math and student-driven problem solving in classrooms, and teachers' interests are piqued! A reflection on our "Humpty Dumpty" 3-Act lesson in grade 1-- Prepping the Lesson A common request from the teachers I support is for ideas on how to customize and differentiate our current math curriculum, Eureka Math/EngageNY. With that in mind, the first part of prepping this lesson involved finding the specific grade 1 lessons and math standards that the lesson aligned with. I also identified alignment w...

Sense Hat pinout for Raspberry Pi

Recently I wanted to attached a Sense Hat to my Raspberry Pi without using all 40 GPIO pins. My plan was to attach an additional output device to the pins to use at the same time as the Sense Hat. I'd also read that if I was going to use the temperature sensor on the Sense Hat, the temperature of the computer itself tends to interfere with the temperature readings of the atmosphere when the Hat is plugged directly onto the GPIO pins. One option-- buy a pin header with extra long pins . Easy access to GPIOs! As I mentioned above, though, if you want to use the Sense Hat for reading the temperature, the Pi itself can interfere when your Hat is too close to the Pi board. If you don't need any of the other GPIO pins, it is also easy enough to use a GPIO cable extender to connect your Sense Hat without attaching it directly onto the Pi itself. But, if you want to attach additional outputs to your Raspberry Pi, using all 40 pins for the Sense Hat can be a bit of an inconvenience....

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