Got to Teach!: September 2015

Non-Routine Problem Solving

What is a non-routine problem?
A non-routine problem is any complex problem that requires some degree of creativity or originality to solve.  Non-routine problems typically do not have an immediately apparent strategy for solving them.  Often times, these problems can be solved in multiple ways.

Incorporating non-routine problem solving into your math program is one of the most impactful steps you can take as an educator. By consistently allowing your students to grapple with these challenging problems, you are helping them acquire essential problem solving skills and the confidence needed to successfully execute them.

One of the best ways to prepare students for solving non-routine problems is by familiarizing them with the four steps of problem solving. I have a set of questions and/or guides for each step, that students can use to engage in an inner-dialogue as they progress through the steps.  You can download this free Steps to Non-Routine Problem Solving Flip-Book {HERE}.

1. Understand: This is a time to just think! Allow yourself some time to get to know the problem.  Read and reread. No pencil or paper necessary for this step.  Remember, you cannot solve a problem until you know what the problem is!
  • Does the problem give me enough information (or too much information)?
  • What question is being asked of me?
  • What do I know and what do I need to find out?
  • What should my solution look like?
  • What type of mathematics might be required?
  • Can I restate the problem in my own words?
  • Are there any terms or words that I am unfamiliar with?

2. Plan: Now it’s time to decide on a plan of action! Choose a reasonable problem-solving strategy.  Several are listed below.  You may only need to use one strategy or a combination of strategies.
  • draw a picture or diagram
  • make an organized list
  • make a table
  • solve a simpler related problem
  • find a pattern
  • guess and check
  • act out a problem
  • work backwards
  • write an equation
  • use manipulatives
  • break it into parts
  • use logical reasoning

3. Execute: Alright! You understand the problem.  You have a plan to solve the problem.  Now it’s time to dig in and get to work! As you work, you may need to revise your plan. That’s okay! Your plan is not set in stone and can change anytime you see fit.
  • Am I checking each step of my plan as I work?
  • Am I keeping an accurate record of my work?
  • Am I keeping my work organized so that I could explain my thinking to others?
  • Am I going in the right direction? Is my plan working?
  • Do I need to go back to Step 2 and find a new plan?
  • Do I think I have the correct solution? If so, it’s time to move on to the next step!

4. Review: You’ve come so far, but you’re not finished just yet!  A mathematician must always go back and check his/her work. Reviewing your work is just as important as the first 3 steps! Before asking yourself the questions below, reread the problem and review all your work.

  • Is my answer reasonable?
  • Can I use estimation to check if my answer is reasonable?
  • Is there another way to solve this problem?
  • Can this problem be extended? Can I make a change to this problem to create a new one?
  • I didn’t get the correct answer.  What went wrong? Where did I make a mistake?
My Brain Power Math resources are the perfect compliment to this free flip-book.  Each book has a collection of non-routine math problems in a variety of formats.  

Halloween Latin Root Word Activity

Instructional time is so limited.  It's difficult for teachers to justify spending any time on fun holiday activities in the classroom, especially if you teach in upper elementary or middle school.  If you want to do something engaging with your students this Halloween, but don't have time for "fluff," then check out this Interactive Notebook page based on the Latin root "mort."  I promise, your students will LOVE it, and they won't even realize that they are doing some serious "word work."  Fun + Academic = A Teaching Gem!!!

All of the components of this INB page fit on two sheets of paper.  Have the students color and cut out the pieces. They will then provide definitions and/or sentences for the five vocabulary words (morbid, mortuary, moribund, mortgage, etc.) that are related to the Latin root "mort" (which means death).

The largest piece is glued down first.

The remaining pieces have tabs on them that will be folded up and glued down, one on top of the other (from the largest to the smallest).

The final page will look like this.  A label is included to glue on to the top of the page.  There are 3 flaps that can be lifted to reveal the students' work for each word.

You can grab this and several other Halloween "tricks and treats" by downloading Upper Elementary Snapshots' free "Tricks and Treats for Upper Elementary Teachers eBook."  Click on the image below!

Teaching Plot with Picture Books

I am a huge fan of using picture books with upper grade and middle school students.  These books can cover complex issues and can lead to some pretty thought-provoking discussions.  I also love that they are are short, which makes them the perfect medium for teaching some difficult concepts when time is limited (which it always is).  With my students, I always explicitly taught the elements of plot or story structure using picture books.

My favorite plot lesson used the book Henry's Freedom Box (written by Ellen Levine, illustrated by Kadir Nelson).  My ultimate goal for the for these types of lessons was to have students complete a story map on their own for any story they have read  (you can grab the story map for free HERE).  But before this was possible, I modeled the process with a few shared reading lessons similar to what I am about to describe.

Before any writing takes place, a lot of time is just spent on identify the various components of plot (inciting force, rising action events, climax, etc.).  I have found the best way to do this is with post-its or flags.  Students can reposition the post-its as they decided just where in the story these elements of plot take place.  Not every event can be placed on the story map, so students need to be decisive and evaluate which ones are the most important to include and which ones can be left out.  During my shared reading lessons, the students and I would discuss the positioning and reposition of these post-its as we evaluated which events were the most critical to the story's plot.

After a few of these whole-group lessons, my students could then start completing the story maps on their own or with a partner for a short story or novel they had just read.  The process really helped my students understand the "big picture" of what they were reading as well as visualize plot. 

A few other titles I like to use for these lessons are:
Tight Times by Barbara Shook Hazen
Faithful Elephants by YukioTsuchiya (warning: tear jerker)
The Butterfly by Patricia Polacco


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