5 Practices: applying lessons learned from chapter 2

5 Practices for Orchestrating Productive Mathematics Discussions

Chapter 2: Setting goals and selecting tasks

If I want my seventh graders to have a meaningful mathematical discussion I have to raise the level of thinking in the learning target. But it’s not over yet. I also need to select an appropriate task to support the learning goal.

As I wrote last week, I’m really enamored with this number puzzle.

Choose any number. Add the number that is 1 more than your original number. Add 11. Divide by 2. Subtract your original number. What is your answer?  Do the puzzle again for other numbers. Why do you get the answers that you get? Will this always work?

This puzzle fits nicely with our 7th grade expressions and equations unit and has the potential to be an anchor problem. Let’s look at how I can modify the learning target to raise the level of thinking and mathematical discussion.

Original target: Students will translate verbal phrases into an expression or equation.

I know my students can handle a more robust learning target. The number puzzle can certainly support it. This is still a work in progress, but here’s my revised target:

Revised target: After translating a verbal phrase into an equation, students will discover how grouping symbols and order of operations provide clarity.

When I gave the puzzle to the students, their first inclination was to simply follow the directions. Based on their work, their equation would look something like this:


This lesson now has a much better chance for meaningful mathematical discussion by focusing on grouping symbols, order of operations and how their use provides clarity. I could begin by saying, “Take out the equals sign and question mark. Make equivalent expressions using parentheses, brackets, fraction bars, etc.” We could then have a discussion as to which equations best represent the puzzle.


As I mentioned this is still a work in progress. If you have insights, please share.

Other bloggers discussing Chapter 2 can be found at the link below.


5 Practices–establishing a purpose for reading

Middle School Math Rules blogger Sherrie Nackel is facilitating an online book study on 5 Practices for Orchestrating Productive Mathematics Discussions. I read the book last summer, but I honestly didn’t get much from it. It wasn’t the book’s fault. It was mine.

Enter the reading fix-up strategies…

Re-read.  I’m going to re-read this book, but as I do I will take a different approach. If I re-read it the same way I first read it, I’ll get the same results. I need to do something different.

Establish a purpose for reading. Over the summer I read the 5 Practices in a survey mode. This time my purpose is to directly apply what I’m reading to improve specific mathematical discussions taking place in the classroom.

Make connections. When I re-read Chapter One I immediately thought about a discussion my students recently had on a Number Puzzle. I want to improve that conversation.

number puzzle

There are a gazillion more discussions I want to improve, but let’s take one thing at a time.

I know I’m a bit ahead of myself; chapter two is about selecting goals and tasks. But given all of this, I want to put that Number Puzzle task under the 5 practices microscope.  It has the potential to be an outstanding anchor problem that can be revisited and discussed throughout our expressions and equations unit.

Chapter One of the 5 Practices introduces anticipating, monitoring, selecting, sequencing, and connecting. I’ll be looking at how to improve the math talk by doing a better job of anticipating responses, monitoring student responses in real time, selecting specific students’ work to advance the discussion, sequencing those selections, and connecting mathematical ideas.

I appreciate Sherrie spearheading this book study.  Be sure to click the link below to read other bloggers who are writing about the 5 Practices.

Exploring a WTF problem

We’re starting a new unit on expressions and equations and I was looking for an appropriate warm-up. I wanted something intriguing but could also double as an intro to translating verbal phrases into expressions and equations. After thumbing through this Walch resource I picked the following. Only later did I connect it to Dan Meyer’s post on WTF problems. His Problem #4 is similar to this:

Choose any number. Add the number that is 1 more than your original number. Add 11. Divide by 2. Subtract your original number. What is your answer?  Do the puzzle again for other numbers. Why do you get the answers that you get? Will this always work?




As I visited each group I asked, “Why are you always getting 6?” I heard vague responses such as, “It has to do with a pattern.” Time was running out so I set the exploration aside to return to my original objective–translating verbal phrases.

We translated the problem as:


It’s at this point where I think the exploration will become more fruitful. Right now the students are not making any generalizations with the work they’re producing. But if I have them take one of their problems and represent it similar to this, perhaps they’ll see:


I’ll be anxious to explore this warm-up more when the weather warms up. Hopefully we’ll be back in school tomorrow.