K-1 Number Sense Trajectory
Before I travelled to NCTM I was finishing up some district PL with K-1 teachers. As part of the workshop, teachers were asked to engage in a Number Sense Trajectory Cut-N-Sort match header and descriptor place in the order that students learn number Easy enough...
The Manipulative Whisperers: The model tells a story
If you listen carefully you will hear them. They sit motionless in every classroom, on top of desks, waiting to tell a story. Without the story they are nothing. What's most difficult is that you can't speak for them because the manipulatives speak through children....
A number line, number string, and Number Talk walk into a class…
As teachers and students ramp up for testing I was invited to visit a 5th grade class and asked to focus on fractions. Before the lesson, the teacher and I discussed the importance of a number line, which was an extension of a conversation we had a couple weeks back....
#WhyMTBoS? I need it to connect with “Z” kids
If you're reading this blog for the first time, you're now part of something big. Something special. Something empowering. You're now part of the MathTwitterBlogosphere. What you do next is completely up to you, but the members of the MTBoS want you to stay and...
Perplexity Drives Productivity
I think about the question mark every time I teach a lesson. I've been so carefully to get to this point. Yet sometimes my question mark comes from a path that looks like this. The opening part of the lesson is over and the work session is well underway. It's the...
Math is a Social Sport: Becoming a “Wise Consumer”
I'm continuously reminding myself that I need to be a "wise consumer" of math resources. Whenever I'm asked to review a resource, I reach for the Standards of Mathematical Practices. The SMPs are like Kryptonite and will break down even the most comprehensive...
Difficult Tasks Allow Misconceptions to Shine
Last week I was reminded why I love being a teacher. I’m currently throwing down a PL gauntlet in my district for all our elementary and middle school teachers. For each grade level I've focused on 1 or 2 of the big ideas outlined within CCSS. In 3rd grade, I really...
Undoing Concrete Models
Students can create models that represent their understanding, but can they undo models that explain the reasoning of others? It was time to find out. I showed this picture to a 5th grade class and asked them to write an equation or expression that matched the area...
Subitizing to Foster Multiplicative Thinking
UPDATE 3/17/19: The updated cards can be found in this post (Multiplication Subitizing Cards: An Upgrade to Building Fluency) ------------------------------ Learning basic facts through tricks or a mnemonic song lead students down a path of memorization, not...
Take a Math Trick and Make it Bleed
I hate math tricks and avoid them at all costs. Tina Cardone and many members of #MTBOS are huge advocates of conceptual learning which is how we became blessed with this gem. There's no denying that students love tricks, especially the ones that retrieve answers...