Powerful PD--- Mathematical Discourse for the Small Group



I’ve been engaging in small group discourse with my Math students for 6 years.  I figured I “knew a thing or two because I’d seen a thing or two,” to quote Farmers Insurance commercials.  So when I recently attended a professional development course on Engaging in Discourse in Small Group Instruction, I figured I’d learn little but be able to share a lot. 


The PD I went to was taught at Region 17 Education Service Center by Carol Julian (she’s awesome and if I ever get the chance to attend anything else she teaches, I will be first in line).  One of the resources she based her instruction on is called, “Making Sense of Mathematics for Teaching the Small Group” by Juli K. Dixon, Lisa A. Brooks, and Melissa R. Carli.   Here is a picture of the cover:








I loved the book.  It will be a resource I will use again and again.


A feature I love! Is that there are video examples sprinkled throughout the text that show Juli Dixon with students demonstrating the ideas she discusses.  The video examples are accessible by QR code so are easy to access with any device with a QR code reader.   


One of the most PROFOUND things I noticed when accessing the video is the use of wait time. 


I know, I know.  You’re thinking the idea of wait time has been around for a long time. 


I give wait time when I ask a question.  BUT, I suddenly realized I was using it incorrectly. 


Let me explain. 


Ms. Dixon reads a word problem (or a student does).  Then she gives her students time to solve it without saying a word.  

WHAT!?  

If a student isn’t circling important numbers, underlining the question and solving immediately, I swoop in with my cape on and rescue them with scaffolding and guiding questions.  Then, at the end of the year, in frustration, I say, “These students wait for me to tell them what to do before they’ll even try.”  Why?  Because that’s what I’ve taught them.   

By giving students the opportunity to make sense of the problem themselves, I am giving them the opportunity to decode the problem, try their own solution that makes sense to them, and gain confidence in their problem solving strategies. 


A companion practice is to follow up answers with clarifying questions but not to say “Yes, that’s right,” or “No, that’s wrong.”  Those statements bring discussion to an abrupt stop!  If they are right, I can guide the discourse into enrichment.  If wrong, I can guide with questions like, “How do you know…” or “Tell me what you’re thinking…” to lead the student to make the discovery on their own (a discovery that will most likely stay with them much longer than if I tell the answer).


All told, I can’t say enough great things about this book.  I’ve only shown you the tip of the iceburg.  In this book, Dixon discusses:


  •            Purpose of small group learning
  •            The correct use of guiding questions
  •            All about TQE and how to use it to successfully plan and                           implement small-group tasks
  •            All about how to engage students in productive discourse


She also gives best practices for small group discourse and discusses the TQE process for delivering lessons.  It’s a small book, 74 pages and it’s published by Solution Tree.   But it’s SUPER Powerful.   


P.S.  I bought mine from Amazon.  


Texas Early Mathematics Intervention -- RTI for Kindergarten through 2nd Grade


FREE RtI Math Intervention Program 

is available online for all Texas Teachers.  The research and materials were funded by TEA.  Everything is aligned to the TEKS.

This program comes with a universal screener, units with daily lessons, unit checks, aims checks, and progress monitoring forms.  It's also available in Spanish.  

Here is the link to the site: 
http://3tiermathmodel.org/
sign in using the following login credentials:

Log In:  Texas Teacher
Password:  mathematics


SAIL Into Math -- Booklet and Games


There's also a wonderful resource for games and activities that are ideal for math rotations.  The resource is called Stategies and Activities for Indpendent Learning --  Mathematics (SAIL Into Math) Booklet and Games.    

I hope you find this resource useful and that you share with other Texas teachers!



Cool Online Fact Practice Games


Disclaimer:  This is not my work.  I found it on Donna Boucher's Math Coach's Corner blog.  You can access the pdf and the original post HERE.

Here is an amazing multiplication game reference sheet to send home to parents.  If you send it electronically, students or parents can access the hyperlinks to go straight to the games.  

Send this boredom buster out right before Spring Break!!!



Need one for Addition Practice?


Be sure and visit Math Coach's Corner for tons of awesome ideas and goodies!!!



Simplifying Fractions -- When Prime is Slime!


Simplifying fractions is challenging for students, requiring a process where errors are easy to make.  The process is also difficult conceptually causing students lots of questions.  Here are the questions I hear:


What is "simplifying a fraction"?

Simplifying a fraction is finding its smallest equivalent fraction.


Why do I have to do it?

It's easier to work with smallest equivalent fractions.  


How do I do it?

Divide the numerator and denominator by the Greatest Common Factor or "GCF".  


An Organized Approach




I created a Simplifying Fractions Mat.  The Mat gives students a place to complete T-charts on the numerator and denominator then identify the Greatest Common Factor "GCF".  Once identified, students divide by the GCF to find a simplified fraction.  


How do I know when I'm done?

Simplification is complete when the simplified fraction follows at least one of these 4 rules:

1.  Prime is Slime:  When the numerator and denominator are both prime numbers.

2.  Back to Back Jack:  When the numerator and denominator are back to back on a number line.

3.  One and Done:  The numerator of the simplified fraction is 1.

4.  The "No-Rule" Rule:  Sometimes the simplified fraction doesn't follow a rule (i.e. 2/15).  If this is the rule that the simplified fraction follows, make sure all factor pairs have been recorded in the T-charts and the numerator and denominator have been divided by the GCF.

Simplifying fractions, though very necessary, can be challenging.  I hope the FREE Simplifying Fractions Mat simplifies the process for you and your students.

What method(s) do your students use to simplify fraction?






Resources and Ideas for Teaching Prime and Composite Numbers



Sieve of Eratosthenes


Why Learn About Prime and Composite Numbers?

Dr. Math says: 

"Every time you send a credit card number over the Internet, it gets encrypted by your browser, and the encryption algorithm is based on the theory of prime numbers.  At some point, electronic money will become as common as paper money, and -that- will also be based on the theory of prime numbers.  And, what's used more in the real world than money?"

See the article in full here: Math Forum: Dr. Math


Conceptual Way to Introduce Prime and Composite Numbers

Donna Boucher, Math Coach at Math Coach's Corner, asks her students to identify all arrays of a specific number (i.e. 24).  They are then tasked with creating a poster showing the array, t-chart and organized factor list for each factor pair the class identified.  She hangs the posters around the room and students reflect.  What do you notice?  They may notice some numbers have more factors than others.  Cue vocabulary!  

My summary doesn't do the article justice.  You can access the original article at:


Prime and Composite by Math Coach, Donna Boucher


Video Lessons on Factoring Primes to Simplify Fractions

Math Antics videos are super -engaging and rich with conceptual ideas.  In the Math Antics video: 

Simplifying Fractions Part 1 and Part 2


learners see how to simplify fractions by factoring the numerator and denominator to primes then cancelling common factors.

One of my Favorite Resources


is a no-prep activity written by Shelley Rees, called, 

Prime and Composite Numbers Activities


It contains:
What is a Prime Number?  (Definitions and Explanations)
Cross It Out!  100 Number Grid Activity
Factor It and Label It!  List the factors and label numbers as prime or composite
Prime Puzzle:  Prime/Composite Number Coloring Puzzle
What Number Am I?  Use the process of elimination and number sense to solve number riddles
Prime Number Path  Identify prime and composite numbers and color a path.

All of this can be yours at a bargain price of $3.50


I've seen several ways to teach prime and composite numbers.  What are your favorites?


Free Holiday E-Book with 20 Teacher Tips, freebie links and resource links


Sometimes, as I surf the web, I come across something really awesome.  Like when I came across this free E-book by Shelly Rees.




A lot of the authors of these tips and resources, are authors whose blogs I follow so I was really excited to get all of these freebies!  If you are interested in this free ebook, click on the picture or link  below:



What did you enjoy about his free collection?  





Announcement: Eduphoria's 2019 Annual Bumper Sticker Contest



What's in it for you?
The winner will receive a $250 Amazon Gift Card, 100 Bumper Stickers with their winning slogan on it, and infinite bragging rights!

Previous Winning Slogans -
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  • 2017 - You Had Me at Jeans Pass!
  • 2016 -  Will Work for School Supplies!

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