I ask the students to write down 10 creative ways to make 101. I think it is important to contextualize a request like this. I explain this is going to show me a little bit about how they think about math, and what they know.
I give a bit more guidance - I do not want to see 1 + 1 + 1... all the way to 100, nor am I particularly interested in 100 + 1 or 102 - 2. I explain that I want to see how creative they could get in combining their facts.
Could they, for example, come up with something such as: 28 + 2 + 37 + 3 + 27 + 3 + 1. I broke that down for them. I tell them using multiplication and division are fine, but not expected, that I am specifically looking for addition and subtraction thinking.
This simple pre-assessment gives me some information about their background skills, their perseverance, and areas in which I may need to do some additional review or at the very least keep an eye out for particular students. It also shows me who might also benefit from small "challenge problems" each day.
I take anecdotal notes on student work and sort them into fluid, temporary categories based on several factors: flexibility of thinking, mastery of 2nd grade addition and subtraction skills, ability to continue a pattern, and willingness to take a risk.
I save papers like these in their portfolios so that I have specific, individualized evidence of student progress over time. Here are some examples of the kind of observations I make about student work that I find helpful in planning instruction and getting to know the needs of individual units as well as areas for whole group remediation or enrichment.
I learn a lot on place value understanding from analyzing just a few pieces of student work.
It's important to know what they can already do so I don't drag them through something they've already mastered. For many students this is a sure way to become alienated from school, and this happens to gifted and hard-working students a lot, and it is a great disservice. What is so powerful about assessments though is what I can learn from their mistakes.
Skip Counting Mini Assessments are also very informative. I need to know about their gaps in basic skills as soon as possible and I feel like my experience in K and 1st is helpful because I know what fundamentals are taught in those early grades.
One more general assessment I like to use both at the start of the year and at certain times throughout is the "How many ways can you make this number" activity we all know, where you ask students to write ten equations equal to a certain number.
Here are a few more thoughts about these early assessments.