Wednesday, September 28, 2016

Floating Down the River

In an effort to support teachers across the state with the implementation of the revised NC Math 1, 2, and 3 standards, the K-12 Mathematics team are hosting weekly webinars. Each Thursday focuses on a different course: Math 1, Math 2, Math 3, and Math Leaders. Find out more here.

The sessions present a math task (if you register early you will get it in advance) and frames the discussion on standards, implementation, anticipating student misconceptions, and connections.

This past month I was able to participate in the Math 1 and Math 2 sessions. The Math 1 session was on Functions and we were given the Floating Down the River task. (Which I tweaked a little. You can find the original version here.) I really like this problem especially to discuss the key features of the functions and interpreting them in context.

This is one of my SOAP BOX concerns: the difference between F-IF.4 and F-IF.7. When we discuss functions it quickly becomes about the "families of functions." You know the ones I am talking about - linear, quadratic, exponential, etc.). With these functions we are able to use the symbolic representation and determine key features. For example, rewrite a quadratic into vertex form and identify the vertex. This is F-IF.7.

So what is F.IF.4? It doesn't seem like it should be the same thing. IMHO - it is not. While F-IF.7 focuses on those classical function families, F-IF.4 is broader. It includes all functions. This includes functions I refer to as functions that tell a story. These functions may be represented symbolically, often by a piecewise function, which is well beyond the focus of Math 1. However, it is not unreasonable for students to reason with and interpret the key features using a table or a graph.

That's why I like the Floating Down the River task. Students are given multiple tables of values and a simple question is posed. I would expect students to do what we did during the session and graph the values. (Further commentary could be given on whether depth is positive or negative but I'll leave that up to you to decide.) Now, there are opportunities for students to discuss intervals of increase/decrease, maximum/minimums, average rate of change, and intercepts. They also have to compare and connect the events. Such as, when the water is shallow the speed increases. Can students also recognize that the distance function becomes steeper? Will they recognize why that would be occur?

There is great potential in the task which is why I am encouraging my teachers and sharing with you. Try it and see what students do with it. I guarantee learning will take place. Also, consider joining me and others at the next Math 1 webinar.

Friday, August 26, 2016

Starting a New School Year!!!

The 2016-2017 school year begins next week and we are busy getting ready. North Carolina revised the standards for Math 1, 2 and 3 so the past few weeks have been focused on getting the curriculum materials aligned. Math 1 has some changes but Math 2 and 3 had a lot.

I've been getting requests for our pacing guides and outcomes. They have been updated on the respective pages (Math 1 and Math 2).

For Math 3, a major concern is to make sure students do not experience gaps in concepts due to the movement of some standards out of Math 3 and into Math 2. For example, complex solutions to quadratic equations is now in Math 2. This year is a transition year in Math 3 and won't look the same as last year or next year. Therefore, we are not revising anything as much as we are "tweaking" some things. If you have questions about Math 3 please contact me and I'll share what we are doing. If there is enough interest I may post it here.

Okay, time to get started with the new year!!! Thanks for checking in.

Thursday, May 19, 2016

NCFE Review Solutions

There have been multiple requests for answer keys for the NCFE review sets. Well, I have finally had some time to sit and work on them. I have posted the solution sets for Math 2 and Math 3 right now. My goal is to work on Math 1 in the next few days and also get it posted. Yeah!! Math 1 is also done!

There may be mistakes. Actually, I would be surprised if there weren't any mistakes. So, if you find one (or two or three or....), please let me know.

Mistake #1
Math 1: Review 4: Problem 2 -- the area of the triangle should be 13 unit squares not 26.

Saturday, May 14, 2016

Math 1 EOC Review Materials

Your students have spent all semester or possibly all year studying the Math 1 standards. Now they must take the Math 1 EOC. In an effort to provide review material for teachers, my colleague and I put together some resources.

We designed the resources around the conceptual categories: Number & Quantity, Algebra, Functions, Geometry, and Statistics. We also did a Linear & Exponential folder. In each folder you will find Resource Description. In this document we have listed the resources along with the alignment to the standards, type of resource, recommendation about calculator use, and some instructional suggestions. Our intent was to provide some variety for review along with opportunities for class discussion and strategies for solving problems.

There are two other folders. One is General Resources which provides information about the specifics of the Math 1 EOC. The other is Comprehensive Resources. This folder has some calculator inactive tasks, midterms we have used in our district, the released EOC and the mini quiz review sheets.

I hope you find some of this beneficial and I wish your students the very best on the exam.

Here is the link to the entire Math 1 EOC Review Resources. I will also post on the Math 1 page.

Tuesday, March 1, 2016


Contact Information
Wow!!! The traffic to this website has exploded overnight. More and more people are visiting every day. To help in communication, I have placed a contact form on the left hand side. This will allow you to email me directly with comments or requests.

EOC and NCFE Reviews
Several of you have requested answer keys to the review resources. I'm not ignoring your request. I just don't have them. However, I am working on them. I hope to have them posted and revised before the testing in May/June.

Curriculum Maps
These are coming. I added two more in Math 1 today and should add more to Math 2 soon. As the maps are added so are the resources noted in the maps.

Thursday, February 18, 2016

PtA Series #2: Implement Tasks the Promote Reasoning and Problem Solving

Let's begin this discussion with a question. What is a task? I once asked a teacher what task students were going to do in class that day. The response was "No task. They are just going to complete a worksheet and then start on an investigation." Hmmmm..... aren't those tasks? My guess is that for some teachers a task is a rich math problem that stretches your mind. Like the one below:

For me a task is any activity given to students to do. That includes worksheets, quizzes, writings, discussions, etc. Suffice it to say -- tasks come in all shapes and sizes. That may be a little cliche but the emphasis is important. Teachers chose every day what tasks to give students.  This choice is extremely important and one that bears deeper discussion.

"Effective mathematics teaching uses tasks as one way to motivate student learning and help build new mathematical knowledge through problem solving." (p.17)

What should a teacher consider when choosing a task? The decision is about the opportunities afforded students to make sense of problems and explore solution methods connected to the established goal of the lesson. (see practice 1) So what do I think about the task we used in the Leaping Lizard Lesson?

Using the taxonomy designed by Stein and Smith, I think that the Leaping Lizard task falls within the category of a higher-level demand. Students are encouraged "to engage in active inquiry and exploration" (PtA p. 19) I lean more towards procedures with connections as suggestions are provided to students for ways to look at the transformations (i.e. connect image and pre-image points). However, students are required to expend some cognitive effort to develop a deeper understanding of the definitions of the transformations.

While selection of the task is important so is its implementation. In an effort to help students that are struggling, a teacher can inadvertently GPS the task by "taking over the thinking" for students. This lowers the demand and effectiveness of the task. I've witnessed this happening with the Leaping Lizards task. The teacher told students upfront what they would discover and consequently students were no longer invested in doing the task. A teacher has to mindful to "support students without taking over their thinking" (p.24).

Knowing not to GPS and not doing it are two different things. It takes practice and intentional planning to change and prevent oneself from falling into that habit. I recommend the book 5 Practices for Orchestrating Productive Mathematics Discussions by Margaret Smith and Mary Kay Stein. A number of years ago I was introduced to this book during a lesson study. It has been my guide ever since in implementing tasks in the classroom. We will revisit this again in part 4 of this series when we talk about student discourse.
Next time, the practice is use and connect mathematical representations and I will share one of my favorite tools when studying functions.