October 9th Pre-Assessment
I decided to do a quick exit ticket to find out how my students would choose to represent a given number.  I wold them they could draw or write.  They each got a 5 x 7 index card and could use any writing utensils at their tables.  If they finished, they could show the number in a different way on the back.
All 18 students wrote the number 3 somewhere on the card.  They also drew 3 of something, generally all three objects next to each other.  All three focal students chose to draw 3 kids grouped together.  I found that the whole class can write the number 3 (albeit sometimes inverted) and all of the students have one to one when representing smaller numbers.  Only one student in the class just wrote the number without any pictures.

October 11th First Interview: "What is 5?"


On October 11th, I interviewed my four focal students about the number 5.  I wanted to get a base understanding of how my focal students think about numbers.  I chose 5 because it is big enough to start breaking apart if a student is thinking about numbers in that way and our hands have 5 fingers and most kindergarteners know that.
Kamaya
T: What do you know about the number 5?
S: I can do 5 cubes
S: I can count 5 leaves.
Shows me 5 on her fingers.
T: Do you know anything in the world that comes in 5's?
S: Five holes

Nora
T: What does the number 5 mean to you?
S: It's a number
T: Can you show me 5?
(shows me her fingers)
T: Do you know anything in the world that's 5 of something
S: 5 people in some families
5 fingers

Ivan: 
T: What do you know about the number 5
S: I don't know
T: Can you show me
(shows me five fingers)
T: How do you know?
S: Just 5

Anabel
What do you know about the number 5?
Well 5 is a number and 5 can be like  5 kittens or 5 anything or 5 houses
There's nothing like 5 hands but
5 plus 5 equals 10
and 5 is number that sometimes people can't write, it's a little tricky to write.


Reflection/Next Steps
After the interview and initial assessment, I started thinking more about what I actually wanted them to know about numbers.  How do I want them to think about and explain a number? 
 From teaching grades K-4 and knowing the continuum of the math curriculum accross th grades, I came to a few conclusions:
1.  I want my students to think about numerals  as not only the written number, but see that number of objects when they here the number.  When they see or hear the number three, they imagine three of something.
2.  I want my students to be able to show a number in as many ways as possible both through numbers and drawings.  For example, 6 can be 6 ones, 2 &4, 3 & 3, 5 & 1, 6 & 0.  The ability to break a number apart is a building block for math facts, division, multiplication, mental math, place value, problem solving, any many more math concepts they will learn.  
3. I need to come up with daily or weekly warm-ups before math or during calendar math to work on this concept.