Here are links to all the posts I wrote this week:
I am without a doubt sick. Yet I was so excited about our fraction PD sessions today that I made myself get out bed and go to work this morning. I’m so glad I did! Both sessions went so well, and I had such a great time working with the grade 3 and 4 teachers today.
Being sick, I’m not going to write a lengthy post today because I really just want to curl up on the couch and watch TV. (I already came home and crashed in bed for a few hours.) I took pictures throughout the day so I’ll let those do the talking for me today.
The grade 3 session focused on several activities: measuring with Cuisenaire rods to develop understanding of equivalent fractions, making and using fraction kits to draw attention to the importance of the unit fraction when composing and decomposing fractions, and using pattern blocks as a model for changing units and renaming what fraction each pattern block represents. Unfortunately I only snapped pictures during the Cuisenaire activities:
The fourth grade section had a different focus. We focused on relating fraction and decimal notation to build strong connections between the notation systems and what they represent, using multiple representations to build a more robust understanding of fractions and a more versatile repertoire of modeling strategies, and encouraging multiple strategies for comparing fractions to build students’ fraction sense and support later work in fraction computation.
We built our PD sessions around the book Beyond Pizzas and Pies. I was really happy with most of the book, with the exception of the chapter on relating fractions and decimals. All of the activities shared in the chapter are focused on the symbolic representations of fractions and decimals, but the understanding of the symbolic forms and how they’re related comes from making connections to concrete and pictorial models. So I made sure to talk about that some before sharing the activities from the book:
I also modified one of the activities from the book. It had the students make a human number line of fraction and decimal values. I didn’t like this idea because if students are *in* the number line, that makes it extremely challenging to simultaneously observe the number line as a whole and to see how different values relate to one another. Instead, I did a clothesline number line that allowed teachers to position and reposition numbers as needed. From the session feedback, the teachers loved it!
Another favorite activity was Fraction and Decimal Flip. This is great for building some estimation and reasonableness skills. The teacher calls out a fraction or decimal. Students clip their clothespin on the blank number line where they think that number is located. On the count of 3, everyone flips their number line to check their accuracy. In a few minutes of practice over several days, students can become more and more accurate in identifying the correct locations of the numbers.
I just realized I never snapped any more pictures of the other major sections of the session. Oops! My partner Regina did snap one of me introducing the section on multiple representations. I even managed to have my eyes closed.
In the final portion of the 4th grade session, we talked about strategies for comparing fractions. I shared two resources that are not from Beyond Pizzas and Pies. I did share the activities from the book, but I wanted to share the extra stuff here since you can’t find it in the book. The first is an activity called Fix It that came from a recent blog post by Marilyn Burns. The other resource is three “books” I wrote and shared in a blog post last year. The thought was that teachers could project and use them to help students reason about three comparing fraction strategies: common denominators, common numerators, and comparing to 1/2. I’ve found the books work best when opened in Adobe Acrobat because then you can jump from page to page rather than scrolling from page to page.
And that’s a wrap! Copies of the book Beyond Pizzas and Pies should be on campuses in a few short weeks along with class sets of Cuisenaire rods. From the comments and questions we got during our sessions, teachers are excited and ready for them to arrive. I couldn’t ask for better than that!