Question about Tiered Math Tubs and Differentiation

Hi  friends!  I've had lots of interest in my tiered math tubs and questions about how I differentiate for math levels in my classroom.  It is exciting to know that other students (besides my 22 sweeties) are benefiting from these leveled activities!  Click..HERE to read a previous post about the difference between a math tub and a math center in my classroom.  Below is a question I received this week on TPT and I wanted to share my response with you all as well...

Hi-
I love all of your stuff. I was wondering though, how do you decide how the kids get separated for each tier. Do you give them a pre test for the unit that you are about to teach? I'd really be interested in doing this for my 4thies as well. They could really use the different levels. 
Is there a book that you read that helped you start? 

I wrote back...
Thank you for your interest in my Tiered Math Tubs.  You were asking how I select the tiers students should be placed on.  My tiers are leveled according to Common Core standards or levels of difficulty.  I decided to create these tiered tubs last school year due to so many different math levels in my classroom.  I was already differentiating reading and writing activities in reading groups, HOTS center activities, etc... so I set a goal to do the same in Math through tiered tubs.   I knew I wanted to start with a pretest to determine prior knowledge and build from there.  Each tiered tub includes a pretest to determine the tier or level each student should work on.  These tests all include 12 items (4 for each tier). I look at the Common Core standards and decide which grade levels I want each tub to stretch across. I have K-2, 1-3, and 2-4 tiered tubs.  The activity cards/game ideas/skill are all the same for each level.  The level of the skill is what increases with each tier.  Here are some pictures from my Flower Power Place Value Tiered Tub to help you see what all is included.  Basically, each child is doing the same activity but the skill level becomes more difficult with each tier. You asked could you make these for your 4th grade students??? Sure you could.  My recommendation would be to keep your leveled activities tiered to 3rd through 5th grade standards.  Just look across the standards and see how each skill increases each year. Good luck with this and let me know if I can help you.  Thanks so much!!!-Yvonne Dixon (Sassy in Second)