# Category Archives: 6-8

## 3-Act Task: A 5th-grade lesson captured

A while back I shared a kindergarten lesson and I was really happy with the way it turned out. The 5th-grade lesson below, not so much. The students did great but there are definitely some things I need to improve. We recently finished up … Continue reading

## I’ll Rip Your Face Off: The Art of Defacing Manipulatives

It’s our fault. We have no one to blame but ourselves. We unknowing pigeonhole student thinking with the manipulatives we use. Take fraction tiles for example. Much to my disappointment, they come with labels and it kills me. Manipulatives that … Continue reading

## Making Sense of Invert and Multiply

As elementary teachers, we rarely have the opportunity to explore division of a fraction by a fraction. When we do, it’s normally accompanied with Keep-Change-Flip or the saying “Yours is not the reason why, just invert and multiply.” Both are conceptual … Continue reading

## I’m Placing a Hit on the Pseudo-Context

This robs students of everything mathematics should be… The “real world” connection The step-by-step procedure Circle the numbers you need to solve the problem The pseudo-context word problem. Lesson 19.2 infers that this unit is front-end load with procedures and formulas … Continue reading

## The Progression of Division

Last month I posted The Progression of Multiplication hoping that a couple of friends and parents would find it helpful. Well, here’s my stab at the progression of division. I understand that there’s lots of ways to model division and this is only … Continue reading

## Get Your Model On: Modeling in the Elementary Grades

Dan Meyer’s work on mathematical modeling has been instrumental in shaping my own understanding. I’m super thankful for Dan’s commitment to SMP #4 over the years. So when he recently posted that he was shifting gears, I was bummed. It was like … Continue reading

## 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 … Continue reading

## Subitizing to Foster Multiplicative Thinking

Learning basic facts through tricks or a mnemonic song lead students down a path of memorization, not understanding. I previously discussed the idea of conceptual development here. When students practice their multiplication facts, they’re expected to move from concrete to abstract … Continue reading

## 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 … Continue reading